I do agree with the claim that typical engineers do not do too much math in industry. To some that will be great, but to others that might be disappointing. For those who might feel disappointed hearing that, there do exist jobs that flex more on the math side of things. In my case as an aerospace engineer, I worked in defense doing guidance, navigation, and control algorithms and I did advanced math daily. Lots of differential equations, optimal control, calculus of variations, numerical algorithms, machine learning, etc. So there does exist some options that use math a lot if you want that, you just need to try and find them!
@@WissamSeif I think your message was fine and definitely is a good representation to how the typical engineering job will go, eg. complex math is done with software (like FEM packages) but the engineers should (hopefully) understand how those things work so they can use them properly. I personally worked mostly on missile guidance and estimators, with a little time spent building simulation related code, and so lots of the more advanced math I did was related to that. Sometimes we used variational game theory approaches to formulate optimal missile policies under the assumption of an optimally maneuvering target, so these sorts of tasks required working things out by hand based on (simplified) models of our system. Sometimes we would need to formulate numerical algorithms for more complicated versions of these problems which would lead to lots of numerical optimization work by hand before implementing things in software. For example, I used numerical techniques once to work out an optimal control algorithm that could get two missiles launched separately to impact at the same location and at the same time (a tough problem!). Those are just two examples but my team and I used pretty advanced math all the time and I really liked that about the job.
If the base pay of an engineer is a little over 6 figures I'm willing to bet that u make double that or more sheesh thats a lot of math and IQ points needed to do that stuff
hi!!! ive always wanted to go into a maths heavy career, so what other (engineering) options r there? u've already mentioned aerospace engineering, but what else is there? another question, on a typical day, what does an aerospace engineer do?
@@zee6726 I would argue every field of engineering has the potential for having a math heavy job, though finding them and obtaining them may be tough. Research oriented jobs tend to be more math heavy but getting them usually requires a graduate education, potentially up through a PhD. To your last question, this ultimately depends on the job of the person. For me, my typical day was along the lines of: - Get to work and pass through the various levels of security until I got to my desk in a classified lab - Check emails and refresh myself on what tasks I should be prioritizing - Start working on the list of tasks I have. Some of these tasks required working out a bit of math on paper for a bit and then writing algorithms based on the math in software. Some tasks required processing a culmination of data to understand the performance of a missile that was fire. Some tasks required doing some distributed computing to generate data or optimize some aspect of our missile. This is only a sample of what the tasks could look like as there was a bit of variety. - After doing a bit of work, I sometimes take a break to work on some software tool that I felt would help my team. An example of this was I built a distributed optimization framework that could take any objective function and use a variety of heuristic methods like particle swarm optimization (PSO) to optimize the function in a parallel manner. I used this to optimize our bayesian estimator for our missile and achieve much better than human-tuned performance. - Lunch and take a walk - I get back to working on the list of tasks, maybe having meetings at some points or needing to present something to the military - Finish work, head out of my lab, and enjoy the rest of my day doing non-work related things As you can see, my day is structured in a similar way to probably most people but it was just the types of things I worked on tended to be different!
I love math but I think Math Classes spend too much time on testing your ability to remember equations, and not nearly enough time discussing what the answers you get actually mean and why you should care about them. Being able to analyze and understand the answers is way more important than remembering 100+ equations you'll forget within a year of finishing the class.
thank you, yes. i am currently in engineering school, and i feel this is too important to be overlooked. im good at math, because i can memorize equations. what im not good at, is know what the equations mean or what they help you solve for. it feels really icky that i have to turn to youtube just to know WHY im learning what i am in my college courses.
I get what you're saying and I dont disagree to an extent, but technically what you're asking of math what is meant to come from physics. Your answers in math are abstract and arbitrary and essentially have no deeper purpose than merely existing as a solution to a process that's built on rigor and a sense of clinical, detached exactness. The 100+ equations you memorize, or rather the definition and defense of the processes behind them, are the purpose of math itself, not applicability.
The problem with the "math classes" engineers take is that they're very low level stuff like calculus. You can't truly explain calculus rigorously (real analysis) without a strong basis in group theory, fields, set theory, some topology, and just general proofwriting. Even the most advanced concept in calculus III is handwaving "trust me that this works, just remember this formula" stuff compared to the first week of an undergraduate intro to real analysis course. Real analysis is the process of building a rigorous understanding of how the reals behave from the most fundamental axioms upwards, and even those fundamental axioms would probably fly right over 99.999% of people's heads -- enough people get weeded out by baby calculus already, no need to make it any more difficult if all you're going to use it for is application fields.
Man, you’ve taken me down memory lane with all the math and physics analysis. In my journey, I haven’t used that much math, and by that I mean doing hardcore calculations. Usually use software for all of that, but it’s def useful to know the background and understand what’s happening. The hardest math I dealt with was in school.
@@CuteAnimals-zi2cc yea it’s one of those classes but welp, my cumulative GPA is not that high either way😂😂😂 Right now I’m at 3.02 but pretty sure it’ll be
Great discussion. I graduated BSME back in '82 and have used calculus twice and PDE once and a whole boatload of plain and matrix algebra. Your casing hanger problem was one of the first things I started working on around 1985. We used Belleville washers to overcome the near constant load problem (this is useful for varying temperatures and packer hardness). We used paper and pen and had to be real careful not to make little errors. The current equation solvers and FEA programs make this all very easy and productive. The current programs make engineering much more fun and accurate. Try getting the mass and CG of a 2000 piece assembly back in 1982. You would be doing that for a week, now it takes 5 seconds. My favorites are aero and hydrodynamic flow FEA programs.
This is the sum of people asking how much math I know as a finance and accounting major and my mind goes blank and I don’t know how to tell them I just use excel for everything, EVERYTHING.
I haven't watched the video but I feel the need to chime in with opinions, answering simply to the video title, "How Much Math Do Engineers REALLY Use??" Engineers will use their math experience CONSTANTLY, it just won't be in the obvious formalised format found in the exams they studied hard for. Simply having completed the work behind studying for and ultimately doing exams will have burned itself into an engineer's brain. The concept of an integral or derivative doesn't get forgotten in the same way as the specific steps required to solve textbook problems; That concept lives on in their heads whether they are conscious of it or not. Rates of change exist and problems are rarely static, simply knowing this is enough to change the way you approach problems. While they likely won't take a week to do a bunch of maths by themselves, they will recognise when a problem requires a certain level of deeper thinking and they would be wiser to pass the problem onto someone else. I think this is a good thing.
This guy is doing math he learned years ago but I struggle to remember calculus 2 from this semester :( I guess that’s why my professor told me to study to understand rather than study to remember. Anyways you motivated me to hit the books again before I take Calculus 3 thanks
I teach calculus at the University of Buenos Aires, Argentina. Here, we have virtual lessons since the beginning of the covid pandemia. And other colleges and I are making an experiment: instead of forbidding the help of technology, we encourage their use. We think the replacement of hand-made calculations with online calculators could be very positive, in terms to achieve a more profound understanding of the core of the concepts, without wasting time in calculation techniques.
@@WissamSeif That depends. For example, you won't learn integration better if you solve integrals by simple fractions decomposition with 4 or 5 terms instead of two terms. Or if you calculate a very long derivate. Or making 3 or 4 steps of Runge-Kutta by hand instead of doing it with excel or python. Obviously, the evaluation process needs to change. It has to be focused more on the concept than calculation. And that´s hard for many lazy professors. I also teach precalculus for admission at Universidad Tecnológica Nacional (Our top university in engineering) and we are aware that students can use technology in virtual exams. So we decided to guide them and help them with that.
I would say this is true for most jobs, but if you do more research and development related work you use a lot of math. Everyone I work with closely at NASA JPL use a lot of different math since the work is very innovative. That being said, great video :)
@@WissamSeif yep thank you! And for example in wireless communications, we would like to be able to send information faster and this requires more clever encoding and decoding algorithms of information , and in order to come up with new ones (if you have an R&D job in a place like apple or Samsung for example) you have to derive math equations that represent or sometimes even invent new algorithms to achieve such a goal. You would then use something like Matlab to test the math you just derived.
CFD can have a lot of math. And if you want to be a good CFD engineer, you MUST understand the math behind: calculus 1 2 3, dif equations, linear algebra and numerical methods + the physics behind (heat transfer thermo and fluids) FEA too. Though you probably need a MS/PhD for most positions.
You couldn't be more accurate. Actually my Thesis is in ANSYS about CFD and is exactly as you said all the equation's are ready and you just give instruction to the software how to solve it you don't solve nothing on your own like in math. Really nice video and hope People don't drop out because they are afraid of Math.
From my own experience so far, I've used iterative root-finding algorithms, fair bit of curve fitting to create surrogate models (tends to get a bit creative for funky multi-dimensional data), transforms for converting between different coordinate frames of reference, vector-matrix operations, some basic statistical analysis, and had to brush up on comprehending quaternions. Bit of a variety of different tasks/projects, but very satisfying to be able to apply so much of what I learned (& taught) and to learn and apply concepts beyond what I ever studied. Really depends on the field and the type/stage of business though. If I worked at a massive well-established engineering giant, I suppose I'd rarely do much outside of using common engineering software packages and picking through spreadsheets.
If you are truly employed as an engineer, and by that i dont mean truly in a gatekeeping way but more so in a not manager type way, you should know your math. Yes you wont use those mathematical skills literally but you build all your understanding on it. And i also believe that your degree to which you use math depends on how well you where able to master it in the first place
there are valid points. obviously, modern day engineers rely (too much) on software to compute unbelievably hard problems quickly and accurately. this is undertaken to such an extreme, in some cases, that many engineers are reduced to specific program operators, such as simulators and design/manufacturing tools.
@@WissamSeif Maybe not purely hand-calculations, but definitely a quite a bit of math as you need to calculate all sorts of things like power, resistance, capacitance, frequency response, filters, etc to properly design your circuit.
I've learned this also really depends on what and where your job is. My title is Electrical Engineer but I'm more of an industrial automation engineer using off-the-shelf parts like relays, power supplies, and servo drives. Also do a lot of programming for the controls of what ever the machine is. I do very little math in my job but I wish I had opportunity to need to do more.
@@vex123 this is true of any discipline if anything mechanical and civil *more*. Your entire job is calculating in order to design. The point of the video is you don’t actually plug these numbers into a calculator anymore, and use software for most of the hard stuff like multi variable calculus that we learned in school
This will probably be lost in the comments, but I think that it is much more important to understand the underlying principle and the way the numerical solution works than to find a rigorous analytical solution to very simple problems. This due to the fact that once the problem gets hard enough you won't get an analytical solution anymore or it's not worth it to spend the time to obtain it. don't get me wrong, the analytical solution to a simplified is indeed useful, but only as a very rough estimate for comparison purposes.
He is so right. i have been in aeronautical engineering for years, G650, G600, SLS, 787,767,more. the only math crunching is by stress engineers for the most part. most companies have standards to follow. there are some math needed to deviate for custom elements but usually the creates of the documents are super smart and leave formulas in in the documents. So basically the company standard documents are a great guide. however software does most of the work these days. and wait till AI is full incorporated into everything. but like he states math is important to understand whats going on.
As an aerospace systems engineer, I use ZERO math at work. My job consists in looking at documents and organizing meetings. And I am not even a manager. Truth is, the modern workplace has a LOT of paper pushing (certain industries even more than others). Be aware of that, if you are just starting. It may be your future career (but it's not guaranteed).
@@WissamSeif yeah I think a lot of the misconception comes from the fact that universities mostly teach the design and analysis stuff, so people might expect the job to be like that. But in reality there is a lot that is glossed over: documentation management, procurement, sales, project management... And these jobs can be done, and are often done, by engineers.
I use a huge amount of math in my day-to-day work as an electronic engineer. Plenty of math graduates excel in electronic engineering and (in my specific line of work) I would rather hire a strong math graduate with no engineering background than any engineering graduate who struggles with math. It's virtually impossible to say anything general about "engineers" because engineering is such a vast and diverse field, encompassing countless industries, each requiring their own skillsets.
Its not about to use it, but have the basic understandment of the possibilitys. You know its possible to calculate a optimal design by variation and a FEM simulation. A mechanic wouldnt go for that approach since he doesnt know what the FEM simulation even does.
In 15 years: High school algebra: I do a lot of back of the hand calculations for heat transfer, material stress, electrical calculations, etc. I do a lot of design work so this happens frequently. Maybe every other day. Differential calculus: Rarely. It happens once in a while that I need to differentiate something. Maybe every 6 months? Integral calculus: Rarely. Annually? Less? Differential Equations / Partial Differential Equations: Never. Not once. I have literally never used this. I visualize gradients almost non-stop in my head. Lets call that daily, if not more frequently. Put math behind the ideas? Never. I doubt I could even remember how to do it at this point.
@@WissamSeif All over the place. Manufacturing, then oil and gas, then mining, then forestry. I was project manager on a few medium-big construction projects. Now I have a small tech company building very oddball industrial robots.
having just had a homework on deriviving equations using Navier-Stokes equations in Aerodynamics, i happy to hear that the computer takes care of that for me from now on,, but i wasted my time
Hey wissam! I love your videos, i would really appreciate a video showing us how to get better grades in university for the more intense physics courses.
I’ve contemplated this fact, and I’ve talked to my good buddy who takes the same classes as me, we find the material and info the teachers give us is normally not so helpful, (30% of teachers are good and help). But honestly we were quite upset that teachers act like they know everything but expect us to learn so much on our own. You could argue you should read your textbook more, but after having internships and real jobs, there is a lot of learning on your own, so yes the struggle sucks but I think it makes for a stronger individual in the future
Not only do computers handle a lot of the math used in industry, but you have to also remember that most of that math concepts being used in even the most technical applications are hundreds of years old now and very well understood, so it's not going to be a source of stress.
If you don't want to spend years looking for a job when you graduate, they are essential, in my opinion. We hire the best interns as full engineers the day they graduate. The average is 3.2 years before they seek another job, but they are off and running to be able to have a successful career. I know someone right now who focused on grades and working at Walmart. He is on his 2nd year of looking for an engineering job. Even with a reference letter from me, HR threw his resume in the trash upon receiving it. I told him, man you screwed yourself by not interning. No way to turn back time now. Every year you delay, the worse it gets.
Are there finite element analysis packages that take corrosion into account? Like ... if you had a beam under mechanical stress in a saline environment like a river or ocean
I dont thing you can solve corrosion via final element analysis, but i would guess you could do it with final volumen methode and couple it to the final element method to simulate the stress :)
Not sure if you made a video on this yet, but what are good books or literally anything for a future mechanical engineering student. I want to prepare myself before I even start my engineering program. I am barely doing my calculus courses.
Mathematical justification is the main reason why engineers would dare design a 150 plus storey building or a plane that can carry more than 500 people although nobody had ever done them before the Burj Khalifa or the A380, and on the frontiers of the field mathematics is usually all there is, so engineers can never know an excess of mathematics.
I have used math constantly over my 39 year engineering career. My focus has mostly been on electronics and software for autonomous mobility (incorporating AI), and many years of military vehicles and robot sw in the defense industry, so maybe I'm an odd case. As an example, the other day I was working out the partial derivatives (Jacobians) for a Kalman filter. I use trig constantly for translating between multiple coordinate systems used in physical systems. It is quite apparent that many of my engineering coworkers often don't have a clue about the math I'm doing. I see their eyes glaze over in my presentations, but perhaps that's why I'm a top engineer most places I go. I constantly had to work out battle damage calculations and equations of motion for projectiles, quite frequently, while working on defense systems.
@@WissamSeif First I had to study the physical tests/experiments that had been performed with real military projectiles and vehicles, with detailed damage metrics taken, with regard to damage caused by various projectiles that hit at various points and angles on the vehicle. I could classify different bounding boxes on and around the vehicle, that if hit with a projectile of a certain type, different damage would occur at each rough location, and at different angles. This is usually some floating point number that represents a damage percentage. I can't say a lot about that without exposing IP, but I can say that 'spall' and the placement of critical systems is a major consideration. This was all done in a 3D simulation environment with 6DOF motion simulators. Man that was a very fun time as an engineer. We developed all of that from scratch over years. So I knew I needed a data structure that would allow me to break up the vehicle into an multi-dimensional array of battle damage percentages based on where and at what angle, and of what type, would cause a certain amount of damage. Then, using trig, you build an overall bounding box, so anything outside of it get's ignored. Anyway, anything about where is best to hit a vehicle or anything like that is strictly classified and I would never consider getting into that kind of thing. Most modern video game engines do all the work for you now, so much so that they are used across the industry. No sense in creating a framework for it from scratch, like we did back then! Sorry, I'm off topic. As for math, well a lot of knowledge trig is very good to do cheap and efficient checks. Always start with broad checks, and narrow down and down until you do that final calcs of actual damage on only relevant interactions. The projectile might hit the ground near to the vehicle, and still do damage. So a lot of trig is very important to work out of the physics of it all. I like, and regularly use, law of sins, law of cosines, heron's formula, cross products, dot products, linear algebra. Also a formula as simple as Pythagoras theorem, can be applied in many interesting ways. One is: Everyone knows that A^2 + B^2 = C^2, but if you express a line in standard form (Ax + By + C = 0), not slope/intercept, and plug in a point for x and y, that A^2 + B^2 > C^2 vs less than C^2, then one can determine if the point is left or right of the line. In standard form, the line is more of a vector because it has a direction vs in slope/intercept it has no direction. There is a ton of tricks like that to check bounds very quickly. Edit to add: As far as hand-calcs, only drawing diagrams to get the math right and a couple spot checks, as when the computer does millions of calcs to make decisions, it's obvious pretty quickly that the calcs are wrong. Most multi-dimensional lookup tables are used as confidences based on empirical data.
So how does one make a model of the system without understanding the fundamentals of diff eq??? Please enlighten me. When I open Simulink, to make the model, I have to understand the physics that goes into the equations and the relationship between the real world and the math, how can I even lay out the integrator and differentiator blocks on the screen? You can't just plop down a bunch of random 1/S blocks and connect them up randomly to make a real time control system. Right?
I hope you don't like sleep. I worked part time in my first 2 years, and almost full time my 2nd two years. I also maintained a social life. I got about 2 hours a night and slept until at least noon on Saturdays. It is sometimes that way when you are working too. I worked from 7am until 8pm today working on something hot to meet a deadline. It's good practice for working 12 hour days for 8 hours of pay. What? Did you think they pay you more than 100k for 40 hours of work?! Ummm no. Not the best jobs anyway.
What type of engineer are you? I am thinking of becoming an engineer one day, and right now am taking engineering classes I'm not sure if I want to do it, so I'm taking a computer science class as well as advanced math (algebra 2 honors). If possible, I might take accounting or other math related course. But right now I'm hoping engineering is for me
Got to tell the truth to viewers. How much math do engineers really use? My answer is ALL THE MATH. Starting from Algebra up to how good engineer you want to be. How you are supposed to use CAD (p.s) if you don't understand Trig. How you are supposed to give any kind of input to computer if you don't understand how to look and understand geometric shapes and master calculus. Long story short. Math is not about solving equations but to develop the analytical thinking and problem solving. If you don't understand math, you are not a problem solver. Not a problem solver = not an engineer. So, you better go and learn that math. All of it!
Yes, but engineers are being hired in the belief that the work is too easy for them to make stupid mistakes, and can get quickly up to speed in a week. Whereas hiring someone bright but without the engineering background might take months in comparison and then having to deal with their mistakes.
Some of the worst math I encountered was in my chemistry minor, while doing Chem E, PCHEM is a weed out course of the highest order for Chem students, and I can honestly say it’ll give an engineer a run for their money, it was a god awful class.
So all the tiring math they force us to learn from high school and beyond comes down to the push of a button? 🤦♂️ So why bother everyone like that? I just do not understand. Something here does not make sense
Well first you may have to model a complex physical system into a computer using the equations you have learned. Then you push a button and it does all the math in real time. It's not like you're getting out a blue book and working the equations down to the final answer. But you have to understand how and why the equations actually work, to model a system using them, before that 'button' can be pushed. Does that make sense? That's why you have to work through them painfully, at least once in your life, or you wouldn't even know what equations to start using to solve a problem.
Disagree, DSP engineers use a ton of math on the job. Maybe not hand calculations but if you don’t understand the math you are implementing into the computer, you might as well be throwing shit at a wall. Don’t speak for all disciplines, Electrical ain’t Mechanical.
Read the comments and you'll see that many of us do, but a lot of people are also just mindless drones that push paper, manage bills of materials or people. If that's what you want to do, then no, you won't use much more than arithmetic done by a spreadsheet. On the other hand, if you want to work in R&D and design a state of the art real-time control system, you may use a ton of higher math. I prefer the positions of the later variety. I know a lot of people who went to school for engineering, and graduated, but knew deep down they were no good at it. There are many positions for trainers, sales people, project managers, and other that will never work an equation a single day in their careers and are paid very well.
I do agree with the claim that typical engineers do not do too much math in industry. To some that will be great, but to others that might be disappointing. For those who might feel disappointed hearing that, there do exist jobs that flex more on the math side of things. In my case as an aerospace engineer, I worked in defense doing guidance, navigation, and control algorithms and I did advanced math daily. Lots of differential equations, optimal control, calculus of variations, numerical algorithms, machine learning, etc. So there does exist some options that use math a lot if you want that, you just need to try and find them!
@@WissamSeif I think your message was fine and definitely is a good representation to how the typical engineering job will go, eg. complex math is done with software (like FEM packages) but the engineers should (hopefully) understand how those things work so they can use them properly. I personally worked mostly on missile guidance and estimators, with a little time spent building simulation related code, and so lots of the more advanced math I did was related to that. Sometimes we used variational game theory approaches to formulate optimal missile policies under the assumption of an optimally maneuvering target, so these sorts of tasks required working things out by hand based on (simplified) models of our system. Sometimes we would need to formulate numerical algorithms for more complicated versions of these problems which would lead to lots of numerical optimization work by hand before implementing things in software. For example, I used numerical techniques once to work out an optimal control algorithm that could get two missiles launched separately to impact at the same location and at the same time (a tough problem!). Those are just two examples but my team and I used pretty advanced math all the time and I really liked that about the job.
If the base pay of an engineer is a little over 6 figures I'm willing to bet that u make double that or more sheesh thats a lot of math and IQ points needed to do that stuff
@@c.howard9413 Hey can I contact you in some social media or maybe email?
hi!!! ive always wanted to go into a maths heavy career, so what other (engineering) options r there? u've already mentioned aerospace engineering, but what else is there?
another question, on a typical day, what does an aerospace engineer do?
@@zee6726 I would argue every field of engineering has the potential for having a math heavy job, though finding them and obtaining them may be tough. Research oriented jobs tend to be more math heavy but getting them usually requires a graduate education, potentially up through a PhD.
To your last question, this ultimately depends on the job of the person. For me, my typical day was along the lines of:
- Get to work and pass through the various levels of security until I got to my desk in a classified lab
- Check emails and refresh myself on what tasks I should be prioritizing
- Start working on the list of tasks I have. Some of these tasks required working out a bit of math on paper for a bit and then writing algorithms based on the math in software. Some tasks required processing a culmination of data to understand the performance of a missile that was fire. Some tasks required doing some distributed computing to generate data or optimize some aspect of our missile. This is only a sample of what the tasks could look like as there was a bit of variety.
- After doing a bit of work, I sometimes take a break to work on some software tool that I felt would help my team. An example of this was I built a distributed optimization framework that could take any objective function and use a variety of heuristic methods like particle swarm optimization (PSO) to optimize the function in a parallel manner. I used this to optimize our bayesian estimator for our missile and achieve much better than human-tuned performance.
- Lunch and take a walk
- I get back to working on the list of tasks, maybe having meetings at some points or needing to present something to the military
- Finish work, head out of my lab, and enjoy the rest of my day doing non-work related things
As you can see, my day is structured in a similar way to probably most people but it was just the types of things I worked on tended to be different!
I love math but I think Math Classes spend too much time on testing your ability to remember equations, and not nearly enough time discussing what the answers you get actually mean and why you should care about them. Being able to analyze and understand the answers is way more important than remembering 100+ equations you'll forget within a year of finishing the class.
thank you, yes. i am currently in engineering school, and i feel this is too important to be overlooked. im good at math, because i can memorize equations. what im not good at, is know what the equations mean or what they help you solve for. it feels really icky that i have to turn to youtube just to know WHY im learning what i am in my college courses.
I get what you're saying and I dont disagree to an extent, but technically what you're asking of math what is meant to come from physics. Your answers in math are abstract and arbitrary and essentially have no deeper purpose than merely existing as a solution to a process that's built on rigor and a sense of clinical, detached exactness. The 100+ equations you memorize, or rather the definition and defense of the processes behind them, are the purpose of math itself, not applicability.
So, in simple words: pay attention
The problem with the "math classes" engineers take is that they're very low level stuff like calculus. You can't truly explain calculus rigorously (real analysis) without a strong basis in group theory, fields, set theory, some topology, and just general proofwriting. Even the most advanced concept in calculus III is handwaving "trust me that this works, just remember this formula" stuff compared to the first week of an undergraduate intro to real analysis course. Real analysis is the process of building a rigorous understanding of how the reals behave from the most fundamental axioms upwards, and even those fundamental axioms would probably fly right over 99.999% of people's heads -- enough people get weeded out by baby calculus already, no need to make it any more difficult if all you're going to use it for is application fields.
You don't study maths, do you?
Man, you’ve taken me down memory lane with all the math and physics analysis. In my journey, I haven’t used that much math, and by that I mean doing hardcore calculations. Usually use software for all of that, but it’s def useful to know the background and understand what’s happening. The hardest math I dealt with was in school.
I have a final exam in Mechanics of Materials this Monday, thanks for another dose of motivation to go study right now!
And i am also preparing for MOM but this god damn subject is going to get me C
@@CuteAnimals-zi2cc yea it’s one of those classes but welp, my cumulative GPA is not that high either way😂😂😂
Right now I’m at 3.02 but pretty sure it’ll be
Yeah exactly i tried my best and CGPA from 3 to 3.35 but its gonna go down i think. Best of luck. Do let me know your result 🙂
@Ihsan Ogulcan Yardimci nope, Mech
@@CuteAnimals-zi2cc so how was your exam? Mine sucked, hope I at least passed the class :(
Great discussion. I graduated BSME back in '82 and have used calculus twice and PDE once and a whole boatload of plain and matrix algebra. Your casing hanger problem was one of the first things I started working on around 1985. We used Belleville washers to overcome the near constant load problem (this is useful for varying temperatures and packer hardness). We used paper and pen and had to be real careful not to make little errors. The current equation solvers and FEA programs make this all very easy and productive. The current programs make engineering much more fun and accurate. Try getting the mass and CG of a 2000 piece assembly back in 1982. You would be doing that for a week, now it takes 5 seconds. My favorites are aero and hydrodynamic flow FEA programs.
This is the sum of people asking how much math I know as a finance and accounting major and my mind goes blank and I don’t know how to tell them I just use excel for everything, EVERYTHING.
Currently at my 8 month co-op watching your vids! Thanks for all the info you give us
I haven't watched the video but I feel the need to chime in with opinions, answering simply to the video title, "How Much Math Do Engineers REALLY Use??"
Engineers will use their math experience CONSTANTLY, it just won't be in the obvious formalised format found in the exams they studied hard for. Simply having completed the work behind studying for and ultimately doing exams will have burned itself into an engineer's brain. The concept of an integral or derivative doesn't get forgotten in the same way as the specific steps required to solve textbook problems; That concept lives on in their heads whether they are conscious of it or not. Rates of change exist and problems are rarely static, simply knowing this is enough to change the way you approach problems. While they likely won't take a week to do a bunch of maths by themselves, they will recognise when a problem requires a certain level of deeper thinking and they would be wiser to pass the problem onto someone else. I think this is a good thing.
This guy is doing math he learned years ago but I struggle to remember calculus 2 from this semester :( I guess that’s why my professor told me to study to understand rather than study to remember. Anyways you motivated me to hit the books again before I take Calculus 3 thanks
i thought that too, but once u start calc 3, DE, or other math you'll be surprised how much you remembered
I teach calculus at the University of Buenos Aires, Argentina. Here, we have virtual lessons since the beginning of the covid pandemia. And other colleges and I are making an experiment: instead of forbidding the help of technology, we encourage their use. We think the replacement of hand-made calculations with online calculators could be very positive, in terms to achieve a more profound understanding of the core of the concepts, without wasting time in calculation techniques.
@@WissamSeif That depends. For example, you won't learn integration better if you solve integrals by simple fractions decomposition with 4 or 5 terms instead of two terms. Or if you calculate a very long derivate. Or making 3 or 4 steps of Runge-Kutta by hand instead of doing it with excel or python.
Obviously, the evaluation process needs to change. It has to be focused more on the concept than calculation. And that´s hard for many lazy professors. I also teach precalculus for admission at Universidad Tecnológica Nacional (Our top university in engineering) and we are aware that students can use technology in virtual exams. So we decided to guide them and help them with that.
Welcome back. Missed that smart and useful flow of information from your videos 😄
This makes me think of my mechanics of materials course, specifically loading and unloading stress strain relations. Cool video :)
I would say this is true for most jobs, but if you do more research and development related work you use a lot of math. Everyone I work with closely at NASA JPL use a lot of different math since the work is very innovative. That being said, great video :)
@@WissamSeif yep thank you! And for example in wireless communications, we would like to be able to send information faster and this requires more clever encoding and decoding algorithms of information , and in order to come up with new ones (if you have an R&D job in a place like apple or Samsung for example) you have to derive math equations that represent or sometimes even invent new algorithms to achieve such a goal. You would then use something like Matlab to test the math you just derived.
CFD can have a lot of math. And if you want to be a good CFD engineer, you MUST understand the math behind: calculus 1 2 3, dif equations, linear algebra and numerical methods + the physics behind (heat transfer thermo and fluids) FEA too.
Though you probably need a MS/PhD for most positions.
You couldn't be more accurate.
Actually my Thesis is in ANSYS about CFD and is exactly as you said all the equation's are ready and you just give instruction to the software how to solve it you don't solve nothing on your own like in math.
Really nice video and hope People don't drop out because they are afraid of Math.
Third year MechE here, thank you man these videos that keep it real motivates me
Great video as always man! You have helped me with my choice to become a mechanical engineer in the future.
From my own experience so far, I've used iterative root-finding algorithms, fair bit of curve fitting to create surrogate models (tends to get a bit creative for funky multi-dimensional data), transforms for converting between different coordinate frames of reference, vector-matrix operations, some basic statistical analysis, and had to brush up on comprehending quaternions. Bit of a variety of different tasks/projects, but very satisfying to be able to apply so much of what I learned (& taught) and to learn and apply concepts beyond what I ever studied. Really depends on the field and the type/stage of business though. If I worked at a massive well-established engineering giant, I suppose I'd rarely do much outside of using common engineering software packages and picking through spreadsheets.
If you are truly employed as an engineer, and by that i dont mean truly in a gatekeeping way but more so in a not manager type way, you should know your math. Yes you wont use those mathematical skills literally but you build all your understanding on it. And i also believe that your degree to which you use math depends on how well you where able to master it in the first place
there are valid points. obviously, modern day engineers rely (too much) on software to compute unbelievably hard problems quickly and accurately. this is undertaken to such an extreme, in some cases, that many engineers are reduced to specific program operators, such as simulators and design/manufacturing tools.
Ah, the rocket equation. The stuff my brain thinks of when I can't fall asleep at night.
This might be true for mechanical engineers. In electrical engineering you atleast do loads of diff-eq
@@WissamSeif Maybe not purely hand-calculations, but definitely a quite a bit of math as you need to calculate all sorts of things like power, resistance, capacitance, frequency response, filters, etc to properly design your circuit.
I've learned this also really depends on what and where your job is. My title is Electrical Engineer but I'm more of an industrial automation engineer using off-the-shelf parts like relays, power supplies, and servo drives. Also do a lot of programming for the controls of what ever the machine is. I do very little math in my job but I wish I had opportunity to need to do more.
@@vex123 this is true of any discipline if anything mechanical and civil *more*. Your entire job is calculating in order to design. The point of the video is you don’t actually plug these numbers into a calculator anymore, and use software for most of the hard stuff like multi variable calculus that we learned in school
This will probably be lost in the comments, but I think that it is much more important to understand the underlying principle and the way the numerical solution works than to find a rigorous analytical solution to very simple problems. This due to the fact that once the problem gets hard enough you won't get an analytical solution anymore or it's not worth it to spend the time to obtain it. don't get me wrong, the analytical solution to a simplified is indeed useful, but only as a very rough estimate for comparison purposes.
He is so right. i have been in aeronautical engineering for years, G650, G600, SLS, 787,767,more. the only math crunching is by stress engineers for the most part. most companies have standards to follow. there are some math needed to deviate for custom elements but usually the creates of the documents are super smart and leave formulas in in the documents. So basically the company standard documents are a great guide. however software does most of the work these days. and wait till AI is full incorporated into everything. but like he states math is important to understand whats going on.
This is all so cool! Want to learn that.
Amazing video. Stuff like this makes me excited for university
Asked this question to you a few months ago. You told me not liking maths was taking the easy way out. 🙃
@@WissamSeif completely agreed
As an aerospace systems engineer, I use ZERO math at work. My job consists in looking at documents and organizing meetings. And I am not even a manager. Truth is, the modern workplace has a LOT of paper pushing (certain industries even more than others). Be aware of that, if you are just starting. It may be your future career (but it's not guaranteed).
@@WissamSeif yeah I think a lot of the misconception comes from the fact that universities mostly teach the design and analysis stuff, so people might expect the job to be like that. But in reality there is a lot that is glossed over: documentation management, procurement, sales, project management... And these jobs can be done, and are often done, by engineers.
I wish I could have a job like that since Im good at organizing and directing. Im not that good at working with softwares...
@@Andrea-pe2iw have you tried looking into the management career path?
@@abaddonavav its too late for that, Im completing my mechanical engineering degree
@@Andrea-pe2iw you can try going for a management path at your future workplace, event if you are an engineer
3:53 And that is EXACTLY what it is all about!
I use a huge amount of math in my day-to-day work as an electronic engineer. Plenty of math graduates excel in electronic engineering and (in my specific line of work) I would rather hire a strong math graduate with no engineering background than any engineering graduate who struggles with math. It's virtually impossible to say anything general about "engineers" because engineering is such a vast and diverse field, encompassing countless industries, each requiring their own skillsets.
I study at a Dutch university and all these at 0:43 I took in my first year alone. We get way more math than that, like way more.
Its not about to use it, but have the basic understandment of the possibilitys. You know its possible to calculate a optimal design by variation and a FEM simulation. A mechanic wouldnt go for that approach since he doesnt know what the FEM simulation even does.
In 15 years:
High school algebra: I do a lot of back of the hand calculations for heat transfer, material stress, electrical calculations, etc. I do a lot of design work so this happens frequently. Maybe every other day.
Differential calculus: Rarely. It happens once in a while that I need to differentiate something. Maybe every 6 months?
Integral calculus: Rarely. Annually? Less?
Differential Equations / Partial Differential Equations: Never. Not once. I have literally never used this. I visualize gradients almost non-stop in my head. Lets call that daily, if not more frequently. Put math behind the ideas? Never. I doubt I could even remember how to do it at this point.
Wow, that’s interesting
@@WissamSeif All over the place. Manufacturing, then oil and gas, then mining, then forestry. I was project manager on a few medium-big construction projects. Now I have a small tech company building very oddball industrial robots.
Which is more difficult health sciences or computer engineering technology? Please advise needed
Great channel and content! This would have been useful in high school before choosing a career!
wow, such a great video. Gj man, from an italian engineer!
having just had a homework on deriviving equations using Navier-Stokes equations in Aerodynamics, i happy to hear that the computer takes care of that for me from now on,, but i wasted my time
Glad you back bro. Needed the insight on this one lol
I'm an electrical engineer and I've been lucky enough to use a decent amount of math, both for understanding, and an electromagnetics calculations.
I must say you are absolutely amazing, I HAVE got much more help from you. 🤗🤗🤗🤗
Great video, thanks
watching this while in the engineering mathematics lecture
Nuc Eng. Same same. I do hand calcs to verify software outputs... and by hand calcs I mean I use excel or code.
Hey wissam!
I love your videos, i would really appreciate a video showing us how to get better grades in university for the more intense physics courses.
Thank you for the info!
Is it ok if I don’t remember the projectile motion? It’s been awhile since I took Physics.
Thanks for the Talk....good job
I read it as how much meth do engineers really use 😭😭. Great vid btwww
wait, your university doesn't require its engineers to take 3 semesters of meth?
I am a year13 student in England and I am doing my first year of foundation what things in math do you think I should read up on to prepare
You should teach Mechanics or Physics I instead of these professors who hardly teach.
I’ve contemplated this fact, and I’ve talked to my good buddy who takes the same classes as me, we find the material and info the teachers give us is normally not so helpful, (30% of teachers are good and help). But honestly we were quite upset that teachers act like they know everything but expect us to learn so much on our own. You could argue you should read your textbook more, but after having internships and real jobs, there is a lot of learning on your own, so yes the struggle sucks but I think it makes for a stronger individual in the future
The Yankees hat sitting on top of the exercise ball is a nice touch
Amazing video!!!
Not only do computers handle a lot of the math used in industry, but you have to also remember that most of that math concepts being used in even the most technical applications are hundreds of years old now and very well understood, so it's not going to be a source of stress.
6:48 wouldnt the trajectory be elliptical not parabolic?
@@WissamSeif for the trajectory of the rocket upon renentry.
@@WissamSeif According to kepler's laws all trajectories are elliptical ignoring drag.
@@WissamSeif I thought it was only parabolic if you assume constant gravity.
The TH-cam channel Science Asylum has a video on Orbits which explains this.
I have a question. I like to build things and I think that engineering is interesting but I am not good at math do you still recommend engineering.
Great video. Thanks
I’m glad you mentioned Katherine Johnson lol. Hidden Figures is one of my favorite movies (the movie talks about this mission)
Great video. Engineering major tier list next??
Your thumbnails are always so funny 👁👄👁
Hey! I love your videos. Love from🇧🇩
The best engineering channel!
Loved the video, keep it up. What are your thoughts on getting internships in college? Thanks
They suck, you know nothing and struggle on the problem you are assigned.
If you don't want to spend years looking for a job when you graduate, they are essential, in my opinion. We hire the best interns as full engineers the day they graduate. The average is 3.2 years before they seek another job, but they are off and running to be able to have a successful career. I know someone right now who focused on grades and working at Walmart. He is on his 2nd year of looking for an engineering job. Even with a reference letter from me, HR threw his resume in the trash upon receiving it. I told him, man you screwed yourself by not interning. No way to turn back time now. Every year you delay, the worse it gets.
Are there finite element analysis packages that take corrosion into account? Like ... if you had a beam under mechanical stress in a saline environment like a river or ocean
I dont thing you can solve corrosion via final element analysis, but i would guess you could do it with final volumen methode and couple it to the final element
method to simulate the stress :)
A tight slap for people who say maths don't help in real world
Not sure if you made a video on this yet, but what are good books or literally anything for a future mechanical engineering student. I want to prepare myself before I even start my engineering program. I am barely doing my calculus courses.
Learn some CAD and coding.
Mathematical justification is the main reason why engineers would dare design a 150 plus storey building or a plane that can carry more than 500 people although nobody had ever done them before the Burj Khalifa or the A380, and on the frontiers of the field mathematics is usually all there is, so engineers can never know an excess of mathematics.
Is love for math one of the reason why you got into poker? Do you still play to this day?
I have used math constantly over my 39 year engineering career. My focus has mostly been on electronics and software for autonomous mobility (incorporating AI), and many years of military vehicles and robot sw in the defense industry, so maybe I'm an odd case. As an example, the other day I was working out the partial derivatives (Jacobians) for a Kalman filter. I use trig constantly for translating between multiple coordinate systems used in physical systems. It is quite apparent that many of my engineering coworkers often don't have a clue about the math I'm doing. I see their eyes glaze over in my presentations, but perhaps that's why I'm a top engineer most places I go. I constantly had to work out battle damage calculations and equations of motion for projectiles, quite frequently, while working on defense systems.
@@WissamSeif First I had to study the physical tests/experiments that had been performed with real military projectiles and vehicles, with detailed damage metrics taken, with regard to damage caused by various projectiles that hit at various points and angles on the vehicle. I could classify different bounding boxes on and around the vehicle, that if hit with a projectile of a certain type, different damage would occur at each rough location, and at different angles. This is usually some floating point number that represents a damage percentage. I can't say a lot about that without exposing IP, but I can say that 'spall' and the placement of critical systems is a major consideration. This was all done in a 3D simulation environment with 6DOF motion simulators. Man that was a very fun time as an engineer. We developed all of that from scratch over years.
So I knew I needed a data structure that would allow me to break up the vehicle into an multi-dimensional array of battle damage percentages based on where and at what angle, and of what type, would cause a certain amount of damage. Then, using trig, you build an overall bounding box, so anything outside of it get's ignored. Anyway, anything about where is best to hit a vehicle or anything like that is strictly classified and I would never consider getting into that kind of thing. Most modern video game engines do all the work for you now, so much so that they are used across the industry. No sense in creating a framework for it from scratch, like we did back then!
Sorry, I'm off topic. As for math, well a lot of knowledge trig is very good to do cheap and efficient checks. Always start with broad checks, and narrow down and down until you do that final calcs of actual damage on only relevant interactions. The projectile might hit the ground near to the vehicle, and still do damage. So a lot of trig is very important to work out of the physics of it all. I like, and regularly use, law of sins, law of cosines, heron's formula, cross products, dot products, linear algebra. Also a formula as simple as Pythagoras theorem, can be applied in many interesting ways. One is: Everyone knows that A^2 + B^2 = C^2, but if you express a line in standard form (Ax + By + C = 0), not slope/intercept, and plug in a point for x and y, that A^2 + B^2 > C^2 vs less than C^2, then one can determine if the point is left or right of the line. In standard form, the line is more of a vector because it has a direction vs in slope/intercept it has no direction. There is a ton of tricks like that to check bounds very quickly.
Edit to add: As far as hand-calcs, only drawing diagrams to get the math right and a couple spot checks, as when the computer does millions of calcs to make decisions, it's obvious pretty quickly that the calcs are wrong. Most multi-dimensional lookup tables are used as confidences based on empirical data.
Engineers almost never need to solve diff eq by hands just model something and run it through the computer
So how does one make a model of the system without understanding the fundamentals of diff eq??? Please enlighten me. When I open Simulink, to make the model, I have to understand the physics that goes into the equations and the relationship between the real world and the math, how can I even lay out the integrator and differentiator blocks on the screen? You can't just plop down a bunch of random 1/S blocks and connect them up randomly to make a real time control system. Right?
Where are you from wissam?
First year of engineering this fall. Any advice lmao?
Study hard, don’t underestimate any class. Your GPA in your first 2 years is important to maintain because it’s very unstable at the start
I hope you don't like sleep. I worked part time in my first 2 years, and almost full time my 2nd two years. I also maintained a social life. I got about 2 hours a night and slept until at least noon on Saturdays. It is sometimes that way when you are working too. I worked from 7am until 8pm today working on something hot to meet a deadline. It's good practice for working 12 hour days for 8 hours of pay. What? Did you think they pay you more than 100k for 40 hours of work?! Ummm no. Not the best jobs anyway.
What type of engineer are you? I am thinking of becoming an engineer one day, and right now am taking engineering classes
I'm not sure if I want to do it, so I'm taking a computer science class as well as advanced math (algebra 2 honors).
If possible, I might take accounting or other math related course.
But right now I'm hoping engineering is for me
عظيم .. اللهم بارك
Me in dynamics class: pain
I'm relieved about not Doing too much math
Try EE
7:40 I hate you 🤣🤣🤣
Got to tell the truth to viewers. How much math do engineers really use? My answer is ALL THE MATH. Starting from Algebra up to how good engineer you want to be.
How you are supposed to use CAD (p.s) if you don't understand Trig. How you are supposed to give any kind of input to computer if you don't understand how to look and understand geometric shapes and master calculus. Long story short. Math is not about solving equations but to develop the analytical thinking and problem solving. If you don't understand math, you are not a problem solver. Not a problem solver = not an engineer. So, you better go and learn that math. All of it!
I missed the word "math" in the title, so I read how much to engineers actually use? And I was a lot. Smart people tend to use. 😂
Yes, but engineers are being hired in the belief that the work is too easy for them to make stupid mistakes, and can get quickly up to speed in a week. Whereas hiring someone bright but without the engineering background might take months in comparison and then having to deal with their mistakes.
Hello physicist here I'm here to comment
π = 3 lol
Guess who is back ❤️
So you’re telling me we are learning matrices just for FEA software to do it themselves 🗿
@@WissamSeif ahh fair enough
20%
How much math do engineers study? Not a lot.
How much math do engineers use? Very few, in average.
(I'm a mathematician)
Math in engineering, is basically just ratios and relationships.
Math is useful eventhough you never use it.
Some of the worst math I encountered was in my chemistry minor, while doing Chem E, PCHEM is a weed out course of the highest order for Chem students, and I can honestly say it’ll give an engineer a run for their money, it was a god awful class.
So all the tiring math they force us to learn from high school and beyond comes down to the push of a button? 🤦♂️ So why bother everyone like that? I just do not understand. Something here does not make sense
Well first you may have to model a complex physical system into a computer using the equations you have learned. Then you push a button and it does all the math in real time. It's not like you're getting out a blue book and working the equations down to the final answer. But you have to understand how and why the equations actually work, to model a system using them, before that 'button' can be pushed. Does that make sense? That's why you have to work through them painfully, at least once in your life, or you wouldn't even know what equations to start using to solve a problem.
Lmao the right answer is just... Excel :v
PI=3 that's it.
I'm watching this instead of practicing for my calculus test😂
Disagree, DSP engineers use a ton of math on the job. Maybe not hand calculations but if you don’t understand the math you are implementing into the computer, you might as well be throwing shit at a wall. Don’t speak for all disciplines, Electrical ain’t Mechanical.
You guys mainly deal in free body diagrams, of course you guys don’t need a ton of math for that.
You are late by 65 days
This video would probably give a flat earther a brain hemorrhage.
Doing math??? That’s what Matlab was made for 😂
None.
Do engineers use math?!?
Read the comments and you'll see that many of us do, but a lot of people are also just mindless drones that push paper, manage bills of materials or people. If that's what you want to do, then no, you won't use much more than arithmetic done by a spreadsheet. On the other hand, if you want to work in R&D and design a state of the art real-time control system, you may use a ton of higher math. I prefer the positions of the later variety. I know a lot of people who went to school for engineering, and graduated, but knew deep down they were no good at it. There are many positions for trainers, sales people, project managers, and other that will never work an equation a single day in their careers and are paid very well.
I like how engineers think they do 'complex math' what a joke.
Hell economists do more real maths than engineers
Most engineers are just software operators.