EASY CALCULUS Introduction - Anyone with BASIC Math skills can understand….
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- เผยแพร่เมื่อ 21 ก.พ. 2022
- TabletClass Math:
tcmathacademy.com/
Introduction to Calculus, easy to understand for those that want to know what Calculus is. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at tcmathacademy.com/
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I was always bad in school. Was terrible at math. Barely got my diploma. In my mid 20s now and I study physics just for fun. Been having learning walls and knew I had to start here. I honestly cried at the end of this video. I could see the math visually and Understood it’s application so well. Never thought I’d see math in this way. Thank you so much. All the time I wasted in school. Feels terrible.
any advice ? im bad at math and the highest math for me is geometry in my sophomore year and im graduating highschool early. and im doing cal 1 and cal 2 in college next month
@@josem-wx7uz your Math skills are undeveloped for Calc.
@@plozar Yeah i started taking college algebra and i take trig next
YOUR PAST NEVER EQUALS YOUR FUTURE.....GOOD OR BAD. Keep breaking down the walls.
This was a very good explanation for 72 year old guy who flunked calculus in college once. You mentioned note taking. Note taking is incredibly difficult. If the student had a piece of paper in front of them showing the drawings and the formulas you presented it might be easier.
🙏
Note taking takes a lot of self discipline and skill
I'm 72, and i flunked College calculus 'cause i ran a Surf shop at the same time and found surfing more fun than math...
Southern Cal??
I’m 76 and found this explanation great, except what C was
At school I had terrible math teachers that put me off the subject for life. This did not stop me becoming a computer programmer for over 40 years. In all that time I never needed calculus, and only used algebraic equations a few times. Neverthless, your videos are good and will be useful for people that have to learn this subject.
Could you tell me what GCSE’s you did for this (if you live in the uk) and a levels for computer programmer cause I will not be doing calculus no way
You don’t really need calculus to become a software developer but you do need good logic plus the ability to copy and paste. Not forgetting AI code generators 🤔
Thank you for the video. Please do not stop and continue to create more in depth Calculus videos, and yes Calculus is a very fascinating subject or may be language. Love it.
totally agree
Mathematics is a language😊
Fr
Teaching starts at 5:48
whoever's skipping, i recommend watching it entirely
Quite helpful 😢
Thanks. I had no idea what I was trying to learn in Calculus and switched majors. I’m 75 , started tryin to refresh my algebra & found it’s kinda fun. BTW my major was in graphic design
It is said that working math problems may keep our brains in great condition in senior years.😊
Great tutorial really sooths some of the initial intimidation of complex math. considering that I am a 14-year-old boy who can't even focus on basic pre-algebra it is miraculous that this video actually made vauge sense to me and kept my attention for 20 minutes. this is one of the best math videos i have ever seen
A very brilliant math student once told me that if you want to learn something..teach it...😅
Excellent introduction to a seemingly-daunting topic. Thank you so much! I definitely feel more comfortable about calculus.
The first calculus class I took was one I dropped, because the professor hated tech so much, while a lot of my learning methods are tech heavy. This video did NOT disappoint in reinvigorating me to push my math skills to the max and be the game designer I've always dreamed of being.
I loved algebra in school and peaked there in math, because without understanding pre-calc it wasn't fun or easy anymore. I know I'm smart enough for it, but I wanted to learn other things. I graduated with an arts degree 10 years ago, and have been doing some deep soul-searching about going back to school to embark on a new career. This has led me to consider civil engineering as something I've always been passionate about, but the math terrifies me! I enrolled in some coursera classes to see how challenging it would be and gauge my learning deficit, but this video has made me feel SO much better about pursuing this! Thank you!
Thanks for the great videos. I’ve recently been self studying calculus. The books I’ve read explain how to solve calculus problems, but never showed how it applies to a graph with real numbers, step by step. Your videos have helped me conceptually understand what I’m doing when solving problems
Thanks I am horrible at math and I was looking into majoring in meteorology later on and becoming a storm chaser, and apparently it involves calculus and physics
I'm starting to really learn this a little earlier (I'm starting high school in two months) because I've heard the earlier you pick up the skills needed for meteorology, the better
YES! This is one of the best match courses/classes ever, thank you!!
Wow, you did a great job. I'm really impressed by the clarity.
That was an interesting re-introduction to calculus. I haven't used it since my engineering college days over 50 years ago and I dislike forgetting something I liked using in the past. So now onto the next stage and to work though some more examples.
Thank you. ... Now, I am going to have to sit down and take some really clear notes so that I can fully understand the quirky steps needed to solve these kinds of problems. 👍
I appreciate that you took the time to create this video. I wish you had a versions of your explanation that stayed succinctly and absolutely on track with solving the problem in as few words as possible, leaving out all the extra verbosity 8:25 Maybe I'm not your target audience but I'd appreciate the availability of the speed course as a refresher. I took calculus in college back in '85 .
This was very well explained and I plan on taking this course. I had 2 horrible professors that made Data Management so unnecessarily difficult and they talked way too much about irrelevant things.
Thank you so much and don’t worry about your voice!
This will help me learn a lot more in school and get me to be an aeronautica engineer. Thank you so much, TabletClass Math.
I struggled through many calc classes in college. Imagine if I had TH-cam to help, what a difference that would have made!
I just started my Masters degree and it includes calculus. Thank you for these videos and hope your channel grows. btw subscribed today and cant want to learn more
Amazing introduction to Calculus. Thanks, man.
Very good. Most people that teach calculus don’t explain what you are really doing well enough.
Thank you for the introduction to Easy Calculus!
Thank you for making these videos it really helps dimestifyimg the subject.
This is fantastic, I really love it.
God bless u. I haven’t took calc. I will probably take it next semester or next year but I need to take the managerial calc. Idk if it’s because it’s almost 4:AM on a Thursday morning. But I understand this. Thank u I hope this is what calc looks like and doesn’t change for the love of god.
Good information! I love the detail - you explain the detail and assume we need explanations which is true for me.
Thank you so much! Very well explanation for a beginner.
Helpful Math videos. Nice to have an easy tutorial
Wonderful explaination. TH-cam is getting me the most needed videos in recommendation.
5:45 it really starts around here
Thank you! I'm beyond exasperated with the ridiculous blather! Maybe I'll hang on a bit.
Thank you!!! I understand why the intro was there, but that intro wasn't for me.
nice job very well explained Thank You So Much
Thanks!! Excellent explanation!
Great lesson! Im a year 10 and this was very clear and knowledgable
Thank you. Great job!
I’m in year 10 and 14 calculus is really really fascinating and interesting to me and you explained it very well thank you
I started smiling 🙂
I believe I'm going to understand this lesson,
The introduction is an interpretation of my mind 😢😂❤❤❤.
Ive been looking for this kind of video, God bless you🫶🏽👏🏽.
God bless you as well 😁💗
Such a big help for slow learner like me ty so much and godbless
It is wonderful, enriches understanding
This was really helpful. Thanks Prof.
Calculus AB is being taught to juniors in high school. So help is needed.
Thank you so much for this video and may you continue to make important lessons like this
Cool I am in 7th grade and haven't finished pre algebra yet and made 100% sense to me. I will take pre calculus in high school. It reminds me of slope of a line.
imagine 22mins video explain in details what ur teacher or lecture don't even do in the entire session 💯🙌
Very helpful to me Thanks.
I love your way of presenting math. Its super cool. Do you do slightly more advanced courses? Lagrangians, Fourier and Laplace transforms, Hamiltonian Operators, tensors, matrix mechanics?
are u with us 😂😂 or in the Pluto planent😂
Lol, sounds like you don’t need help.
The fact I can’t even tell if you’re speaking English or not says a lot 😭 lagrangians what now?
Thanks for everything 😊
Thank you very much!
Thanks for the video.
A big thank you 😊. Thank you very much.
Nice workframe that you created teaching Math. Got a lot of insights. Abou maths
It have seen self explanatory, but does takes a lot of practicing to get the hang of it
well explained thank you...
Thank you soo much. ❤❤❤
Thank you very much 🎉
great video thank you
When are you dropping pre calculus on your website?
Hello John: I enjoy your videos very much. I was born and educated in an English Grammar School back in the mid fifties to early sixties (yes I am ancient and left school in 1961). I find it puzzling when you mention
students taking cell phones to class ???. We were not allowed to take a calculator to class !!! Had we taken
one to an exam room, we would have been disqualified. The only thing we were allowed to carry was a slim
book of log tables. All calculations were made by hand. English kids were made to know multiplication tables
just like learning A.B.C.s at a very young age. Does England sound very Dickensian to you John?
Great class.. 👍🏽
Thank u soo much!
I am actually a 7 th grader very interested in math ( actually idk why iam learning this in this age but 😅) . You teach very well 👏 l ,thankyou for your notes! 📝 😊
The 1>2 area is an approximate triangle. Why not figure the area of the triangle on each side, then subtract to figure the areas on each side of the curve?
Extremely useful but how you get the algorithm for it?
Such a great lead. Calculus demystified
THANK YOU....
THANK YOU
Good explanation
Yep. Nice. Gotcha! Thank you!
Im in grade 8 im looking for a boost and your explanations help me a lot
Thanks very much sir
Which application are you using for this Green board, pens, and colors?
A nit: proBlem not prolem. It's a very small nit. (30 years since I taught my last algebra class. 60 years since calculus. I still remember some. You are helping me slow cognitive decline. Thanks)
thank you .
I think it was very well explained, at least to a 72-year-old who flunked calculus once in college and got a D the second time around.
You did mention note taking. This is incredibly difficult for a young student or an old guy.
As far as I know there is real no class on note taking.
Now if the students had a handout on paper in front of them where they could kind of write little notes that might be of some use.
I also think that is very important to give students a real life use of why you would ever want to do a calculation like you should.
Something like when SpaceX launches the first the rocket. X could be the pressure building up on the rocket as it approaches Max Q
I agree that note-taking is hard in math. Maybe some handouts with mini-quizzes built into them.
I am studying in 7th grade but understood everything you said .
And is the answer 8.6 reoccurring for the last example
Thanks again.
Excuse me but if I may ask if you do anything with the "dx" part
My first ever calculus lesson. OH BOY !
Very helpful; Had a hard time with calculus back in high school days
Maybe I missed something here, but why did you plug a 2 in for the value of 'n' in the first equation? why not use 3 or 4 or anything else?
Specifically looking to solve the x squared(^2) function, see 10:06 into video
C represents a constant whose graph is a straight line and does not have area and therefore its area value is zero.
Very food boss very good seems like you actually care about students learning
Nice intro for use who are new to Calculus. I wish he would have given the answer for the definite integral of n=3 to n=1.
Which definite integral of n = 3 to n = 1 are you referring to? And it should be n = 1 to n = 3, not n = 3 to n = 1. That would give a negative answer and there no such thing as a negative amount of area, land, for instance! Area can be subtracted from another area, but in the case of a single area, such as here, there’s no such thing as negative area, or negative length, or negative time, etc. Those things do exist! It’s an existential truth ..can’t have -88 square acres of land …there is no such thing….?! If you mean this same parabola here, you’d simply do the same thing he does here with 0 to 2, or, as you say, n = 0 to n = 2 (these are called the “limits of integration,” 0 and 1 being the lower limits, and 2 and 3 being the upper limits), respectively; but for the “limits of integration” which you mention here, n = 1 to n = 3, you’d plug in 3 and 1 for x instead of plugging in 2 and 0 for x in the integral (x^3/3) - (x^3/3): (3^3/3) - (1^3/3) = (27/3) - (1/3) ≈ 9.000 - 0.333 ≈ 8.667 square units. Units being whatever is specified: feet, yards, meters, inches, etc. Here, nothing’s specified, so we use the most general term, square “units.”
As I'm new to Calculus I'm also new as to how to write about it. However, I can assure you that calculating a negative area can have a use. Up/down, right/left, matter/anti-matter.... LOL
@@tonymanns8249
My intent is not to say that we can’t subtract some particular amount of area from another, of course we can. Subtract 5 acres from 10 leaves 5 acres. So that it’s a mathematical as well as a real life possibility. The land exists. But, that’s just it, the land we subtract is real, it exists, it has to! In that sense, mathematically, it has a negative number, but the land itself exists.
When you set n = -1, you will get x^0/0, and you can't divide by 0 (zero).
But there is a function that works as the integral of x^-1 or 1/x
This is the natural logarithm of x + C.
At least, that's how I remember it from 43 years ago 😀
Una gran duda ¿por qué se restan las áreas en 0 a1? Si en el siguiente ejemplo 1, 3 ¿ Es lo mismo? si es así yo cometería el error sumando los dos rangos.
Don’t know if I am understanding your question correctly… If you integrate the function from 1 to 3 you would simply subtract 1 from 3 in doing the mathematical calculation after integrating. Here, the area of the function being integrated is from 0 to 2, so you would subtract 0 from 2 by that same process. If it were from 1/4 to 1/2, you would employ the very same process! Does that answer help any?
For better and greater clarity, perhaps, let’s use a simpler more straightforward geometrical figure, a rectangle, and suppose you integrated the shaded area of the function y = 2. “Its integral would be 2x.” And let us suppose that the boundaries of the function were the x-axis from x = 0 to x = 4, the y-axis from y = 0 to y = 2, the line x = 4, from y = 0 to y = 2, and the line y = 2 from x = 0 to x = 4. Now, we already know, even before doing any calculus at all, that area has to be a rectangle with a length of 4 units and a width of 2 units, and that the product of those dimensions must give us an area of 8 units^ 2. Now if you integrated that area, which should give the integral of 2 from 2 to 3 to get 2x from 2 to 3 by subtracting 2 from 3 you should get 1/4 the area, which would be 2 units ^2. Whereas on integrating the same function from 0 to 4, which is the entire area of the rectangle, by subtracting 0 from 4 in doing the math you should get 8 units^2, which, again, is the entire area. That’s how it’s done… Hope that clarifies things somewhat rather than confuses you even more.
No sé si entiendo bien tu pregunta... Si integras la función de 1 a 3, simplemente restarás 1 de 3 al realizar el cálculo matemático mientras integras. Aquí, el área de la función que se está integrando es de 0 a 2, por lo que restarías 0 de 2 mediante el mismo proceso. ¡Si fuera de 1/4 a 1/2, emplearías exactamente el mismo proceso! ¿Esa respuesta ayuda en algo?
Para mayor claridad, tal vez usemos una figura geométrica más simple y directa, un rectángulo, y supongamos que integra el área sombreada de la función y = 2. “Su integral sería 2x”. Y supongamos que los límites de la función fueran el eje x de x = 0 a x = 4, el eje y de y = 0 a y = 2, la recta x = 4, de y = 0 a y = 2, y la recta y = 2 desde x = 0 hasta x = 4. Ahora, ya sabemos, incluso antes de hacer cualquier cálculo, que esa área tiene que ser un rectángulo con una longitud de 4 unidades y un ancho de 2 unidades. , y que el producto de esas dimensiones debe darnos un área de 8 unidades ^ 2. Ahora, si integraste esa área, lo que debería dar la integral de 2 de 2 a 3 para obtener 2x de 2 a 3 restando 2 de 3, debería obtener 1/4 del área, que serían 2 unidades ^2. Mientras que al integrar la misma función de 0 a 4, que es el área completa del rectángulo, al restar 0 de 4 al hacer los cálculos deberías obtener 8 unidades ^ 2, que, nuevamente, es el área completa. Así es como se hace... Espero que esto aclare un poco las cosas en lugar de confundirte aún más.
Makes me want to watch Good Will Hunting!
I just watched this video to realize I know all of basic calculus but I never realized it because I’m not in english language country and nobody ever told me that’s what it is. I think I could say we just called it derivatives of a function/mathematical analysis but that’s not really the best translation for that
One of the problems with trying to explain this calculus is there is no reference to the real world what would you ever use this formula or calculus for? A good example might be when SpaceX launches a rocket. The narrator is explaining as the rocket accelerates it’s approaching Max Q.
Maybe the students could calculate how much pressure that really might be.
It’s used in computer science.
That was fun.
5:30 For my use
this helped me too much
Skip the intro /commercial (25% of video) and go to 5:40.
Okay, how do you end up with the units squared?
@ William Rudman
Which “units” are you referring to? If you mean x^2, he simply chose 2 arbitrarily to substitute for n. In other words, he, or you, could’ve chose any number (power), he could’ve chosen 1, or 4, for instance. X^n is the general formula or form that allows us to choose any number in the place of n, the n simply allows us to choose the number (power) we’ll replace it with to find the area under the particular curve our choice gives us. If the formula was x^5, say, that would be fixed and final; we couldn’t substitute any number for 5, we could only use 5; n is an unknown, it’s variable and therefore allows us to do our own choosing as to what number it’ll be. 5, on the other hand, or any other number, for that matter, is fixed and final and a done deal and allows us to do nothing other than use it. Therefore we could never use it to find areas under curves raised to different powers other than 5. It would be useless for anything else but itself! But general formulas using unknown values such as n allows us to arbitrarily choose what we want, we could make n 2, 4, whatever! In other words, if we say f(x) = 2x + 1, just for example of the importance of variability, we could choose an infinite number of values for x. But if we limited x to only equal 4 what useful value would such a formula be to us when we wanted to find f(x) at all values other than 4? Well that’s what’s going on here with n! It allows us to pick a value in its place, is all… n simply says, go on why don’t ya, have fun, create your own graph by plugging in a number substituted for me, is all! But if you mean the expression x^3/3 - x^3/3 from 0 to 2, he simply followed the rule for integrating functions: x^n goes to x^(n + 1)/n + 1, which gives, when we follow the rule, and when we choose n to equal, or said another way, to be 2, for instance, and as done here, x^2 becomes x^3/3. Then we evaluate that expression from 0 to 2 since the area under the curve that we’re trying to find is bounded by the curve f(x) = x^2 and x = 0, and x = 2. Then he takes that integrated expression, x^3/3 and evaluate it from 0 to 2 like so: x^3/3 - x^3/3 becomes 2^3/3 - 0^3/3 = 8/3 - 0/3 = 8/3 - 0 = 8/3 ≈ 2.67.
Or perhaps in asking how does he end up with the units squared, the answer you’re looking for is because the size of an area is found by multiplying the lengths of two sides of something. For instance, a board that measures 3ft. X 4ft. = 12 ft.^2, or 12 square feet… the units square because ft. X ft. = ft.^2, just as b • b = b^2. For the same reason, volume is given in cubic units because in that case the lengths of 3 sides are multiplied together to give units^3, that is, ft. • ft. • ft. = ft^3!
Now… if you didn’t ask for all that, then, my apologies.
guys is it always x*2 or does it change?
nice, solving integrals is so much fun
😮
you do not even need that to compute it. The y - coordinate of the point x = 2 , is y = 4.
so the area of a rectangle formed by using the x and y axes is 2 * 4 = 8.
since it is y = x^2, that means the ratio of (the area above the curve / the area below the curve) = 2 / 1
Therefore, the area under the curve is [1 / ( 2 + 1 ) * 8 ] = 8 / 3
yeah but he's showing us how to use calculus to find the solution. Algebra's great but this is a calculus video.
@@carloskruut423 but many Times in class you will not use calculus to determine thé answer.
I need help understanding, please send me your information so I can get a better understanding
I don't understand how they came up with this formula as bein the formula for the area under the parabola/line? I can accept it as being so but by what reasoning did they derive the formula???
@ Robert Fanfalone
Geometrical argument and analysis in trying to find the areas of odd shapes that have no equations but are built through geometrical analysis and scientific investigation and observation that began with the Greeks, especially with Archimedes, who lived around 287-212 B.C. A brief research of the topic of “The Quadrature of Parabola” of Archimedes will give you some insight and mental grasp into how the formula came about centuries ago with Archimedes’ discovery and development of the formula x^3/3 + C through his work by way of geometrical analysis of the quadrature problem. And it is said that had Archimedes known the things learn in the later centuries he would’ve discovered the calculus… way back then! Geometry, algebra, geometrical analysis, trigonometry, to name a few, and of course scientific investigation all serve as the origin and foundation not only calculus, but also functions as the one seen here. This stuff goes way back for centuries. There’s a scientific video series by Cal State titled “The Mechanical Universe and Beyond” which debuted around 1985 or so. And it’s done in a most wonderful narrative form as the narrator goes through the history of the sciences and mathematics from the earliest recorded time in history up to the mid to late 1980’s! It has 56 episodes of roughly 30 minutes each! Check it out here on TH-cam! It gives you the history of all mathematics, all the sciences and brief biographies of all the great mathematicians and scientists, especially, it’s narrates the history of the efforts of proclaimed inventors of the calculus, Newton and Liebnitz, and the little spat and beef over the race between them to be the first to invent the calculus, interesting, it narrates the discovery of “The Law of Falling Bodies” which maps out the path of a parabola and discovered by Galileo, as well as his life trials and other discoveries, a genius he was, as well as the others, but he’s one of my favorites, if not my favorite… sometimes it’s Newton, though. And it gives you both the origin and the process of developing mathematical functions, and the likes. And to top things off, it teaches calculus and physics as you go through the entire series! Incomparably valuable resource… don’t miss it! And you’ll never regret it!
@@ndailorw5079
Great info Robert! Thank you for sharing the details.
Where's the 8 cones from ? I would think is 6/3?
X^3/3 becomes 2^3/3 when 2 is substituted for x to become 2^3/3 which becomes 2•2•2/3 which becomes 8/3. 2 times 2 times 2 = 8. You don’t add the 2’s, you multiply them!
at what age do u use this. i learned this now and im 14