I just noticed this video has 40 downvotes. How could anyone dislike these lectures? It's just ASTOUNDING how much education Dr. Susskind has online for FREE. It's an enormous contribution to the world.
Remember I felt a renewed interested in physics after 40 years and business career. Decided to go directly to m-theory course. Was lost after less than 10 minutes. Maybe those people felt like me at that time. Went back to 101 classical mech. and could hop right in. Seen most of Frof. Susskinds courses over a 9 year time and enjoyed most of them, and the professor always. He definitely needed a new printer at the time as it seemed to print his lecture notes in random order…
sta nford sta nford sta nford THE SAME thing 4th to church think about it Sir I'm NOT GOING TO THE same language a good day and it's really hard to tell the difference SIR ALEX IS THE AND to church by praying FOR YOU AND 4TH to church think about it Sir i will send you a draf draf draf example of a 4TH THE AND THE OTHER OTHER PEOPLE ARE NOT THE AND THE SAME thing 4th to church think about it is not to church think THAT THAT AND I have have have to use those years ago back in fresh an awkward silent then we can can I have seen the site sir i have finish designing the site exactly as you are ok with it Sir i have a weakness of it here in my country is the last i will do for this project js the project and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we can start now seeing your tight schedule for your kind of website are you thinking to have a ground based business skills to run my business and to be more certain about the completion in a way thar i will send it can touch every time there is a concepts and i will be waiting your response thank you for time thing but it is not to be a good plan if you thinking to have Sir I assure you that is the funny part of it here in my country is the last i will do for this project is a bit secure ans and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will be waiting your response thank you for your kind of website are you thinking to have Sir I assure you that is the differences between developers and clients in exceeding to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer it with in a few minutes of my frineds in my services and i will transfer it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in in my services and i will transfer it with in a few minutes of my frineds in my services and i will be you guys again for your kind interests in my services and i will transfer it with in the next time sew gar new eji the phone available after 5hrs and i will transfer it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and
@@bojohannesen4352 Well, I guess honestly I don't - at least not to a degree that's "critical to my life in any way." It's just a little sad to see such a lack of appreciation for the pursuit of knowledge. So yes, I "care," but no, it's not going to ruin my life or anything. I guess the way I look at it is a) this is good stuff and b) it's being offered for free, so why on Earth would anyone actually think it made sense to *criticize* it? It's a stellar example of "looking the gift horse in the mouth." So, there's that, which seems logical enough to me, and then there's just the sad fact that so few people really seem interesting in educating themselves. But I can't change it, and I'm doing fine, so I guess I'll just carry right along enjoying my own life.
I maybe understand about 20% of what this guy is talking about, but I still find it fascinating. Every now and then I'll catch a glimmer of understanding and that is enough for me right now.
Johnny, that is the way to do it. I've learned as a student of physics for 6 years now that the way to learn is to just dive in, learn maybe 10 percent of the subject, come back, try again, get like 30, go learn some more math, come back, learn about 60 percent, and then tenaciously stick with it and finally feel like you understand the subject. It's how I learned analytical mechanics, how I'm learning electromagnetism, and I am learning thermodynamics and quantum mechanics. Particle physics is a whole different beast, and I suspect I'll be studying for many years to come before I start to have a feeling of mastery, but that's the fun, the journey!
I started studying basic astrophysics when I was just 13 years old. Today I am 15 and I still have the notes from 2 years ago! I am now really interested into Classical Mechanics and I love the way Leonard Susskind does his explanations. Will try to follow these lectures as much as possible.
At least from a classical mech point of view, the principle of least action (and the minus sign) aren't that hard to understand. If KE is becoming PE, that means the object is getting slower. If PE is becoming KE, the object is getting faster. So, minimizing KE - PE means PE and KE try not to switch between each other...objects speed up and slow down as little as possible...ie., objects in motion stay in motion. objects at rest stay at rest. First law all over again.
Damn, didn't realize Michael from Breaking Bad had become a physicist. But in seriousness, loved Prof Susskind's introduction to calculus of variations. Very intuitive and eloquent.
I have a PhD I think Susskind is the best. I have mostly recovered from brain damage I am planning on going back to school. I agree with Susskind about the big bang postulate. Since kinetic E is made up of translational E. I expected the or knew from Stat. Mech. The way he teaches is very easy to follow. I have taught at U and Dr. Susskind is one of the best. You would consider me old. Exactly were is he fishing for compliments?
Right this is exactly what is going on. It is pretty clear when you study calculus actually. When you integrate something, you always have to add +C to the end. This represents your initial condition, which is the bit of information lost when you do the integral. F=ma, a=dv/dt, and v=dx/dt, since you have to integrate twice to get form position to acceleration, it isn't sufficient to know just the initial position, but you need to provide and initial velocity as well.
Actually, Newton formulated 2nd law in exactly F = dp/dt form: Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.
Also, Euclid's "Elements" helps dawn the logical process of the mind for more complex proofs (proofs are helpful in the realm of theoretical physics) and gives an understanding of basic geometry to better understand curved geometry and differential geometry. I also used this when I was younger... so when someone says Special Relativity and General Relativity does not follow Euclidean geometry, you want to know what the really means (particularly the "exclusion" of Euclid's 5th postulate).
@mascoteponto I figured it out. It took me about 1/2 hour, but Dr Susskind is right again. The d²F/dxdt term can be written as d/dx(dF/dt) = d/dx(dF/dx*dx/dt) = d²F/dx² * v + dF/dx * d/dt(dx/dx) but dx/dx = 1 and d/dt(1) = 0 So we get exactly what he said. QED
Feel the least action principle should be called the least conversion principle, which should be more intuitive, since what is really minimized is how much potential energy is converted to kinetic energy during the course of a trajectory.
Hi, I have an MPhil degree in Physics. I have taken six courses of Prof. Susskind which are "Classical Mechanics," "Quantum Entanglements Part 1," "Special Theory of Relativity," "General Theory of Relativity," "Cosmology," and "Statistical Mechanics". I have also taken handwritten notes of him in all the details and currently I'm typing his notes on Latex. Kindly let me know in the comments which lectures of him do you want the notes of and I will make them for you on Latex. Cheers!!
Susskind gives what he calls the 'theoretical minimum', i.e. everything you need to know to understand the subject without going in too much detail. A normal course would have several examples of the applications of the newtonian laws (like a particle falling with or without friction, for example). For a more complete knowledge of the subject I recomend 'Classical Dynamics of Particles and Systems' by Marion and Thornton and (for an advanced level) 'Classical Mechanics' by Goldstein.
This lecture is an exercise in trusting the process. The whole entire point is to show how energy is conserved and that a system path of least action/time that is defined by the integral of the lagrangian between 2 general coordinates of the system.
This is explained is Lecture 1 as well. If the motion equation were F(x) = mv, and all you knew was a particle's position x, then you could calculate the force using F(x). You can also calculate the velocity from v = F(x)/m. Then you could also find the acceleration of the particle using dF(x)/dt = mdv/dt ==> dF(x)/dx*dx/dt = ma ==> dF(x)/dx*v = ma. This gives you the equation a = dF(x)/dx * v / m. So knowing only the position also gave you the velocity and acceleration! (continued...)
It is difficult to explain using TH-cam's comment section, but try to imagine pulling the dx term out of the square root. You would have to find the term that you can multiply dx with that would result in sq(dx^2 + dy^2). You have to divide dy by dx so that when you multiply by dx you get just dy. You have to do this with the dx term as well, and dx/dx = 1, hence dx*sq(1+(dy/dx)^2).
From Dr Susskind's formula mj = (dF/dx)*a + (d²F/dx²)*v² 1st term --> (N/m)*(m/s²) = N/s² 2nd term --> (N/m²)*(m²/s²) = N/s² Your units from mj = (dF/dx)*a + (d²F/dxdt)*v 1st term --> (N/m)*(m/s²) = N/s² 2nd term --> (N/(m*s))*(m/s) = N/s² Yours works also but it still has a time derivative which we seek to eliminate to obtain an ODE rather than a PDE.
It's an incremental demonstration of why we have a 2-dimensional phase space in classical mechanics. If the laws of physics were based on f-mv then the phase space would be 1-space.
...cont: For example: If you drop something from a tower (and assue there is no air friction): the acceleration is always -g (-9.81 m/s2) but the time the particle will take to arrive on the ground will depend ALSO on the inital velocity v0. It makes a difference if you just let go of something or throw it down (giving it a initial velocity not equal to zero). From the integral of a you cannot get the initial velocity, hence you need to know both x AND v in the F=ma case.
in all seriousness, _jerk_ as da/dt is well taught - i remember my grade 13 (i grew up in ontario.) physics teacher explaining it as being essentially what it sounds like - a sharp change in acceleration, like you'd experience during turbulence. and, just about the only application i could imagine for further differentiation would in fact be in the field of low atmosphere air travel, in trying to understand the complex effects of gravity interfering with itself on a free-falling object.
so, imagine you're in a car that is constantly accelerating. if you change that by slowing down or speeding up the rate of acceleration, you're going to get thrown forwards or backwards (due to the third law), you're going to get jerked forward or backward, and that would be da/dt - just like it sounds like.
According to Wikipedia “Momentum” was defined by Jennings in 1721 in _Miscellanea_ as a rectangular area created by velocity and substance. This was published before Newton’s last edition. But newton used a name with an equivalent meaning “Quantitas motus”. Wikipedia does not define when first the word as used in speak.
Not gonna lie, first time he said there was a name for the derivative of a called "jerk" I laughed out loud. Then I reaized he was serious and looked it up.... guess there are some applications for it...
@QuaternionEM No, what you wrote there isn't even an operator and carries a suspicious similarity to the Lorentz factor used in the Lorentz transformations of special relativity... also, while it is true that conformal mapping exists as a map between complex functions, then even in that simple case it needs to conserve angles. In the case of conformal field theory it implies an additional symmetry of the lagrangian which in turn leads to the fields being massless, making the coupling constants
i don`t remember it was lecture 1 or 2, but when he told what the world would be like if we suppose f=mv, my brain and ear paused for 10 secs, it was the moment of truth.....thank you Proffesor
Wanseok Yang I'm a little confused at the moment. I've been enjoying Physics 8a over at Berk, but I'm not quite sure how F=MV proves anything... The law is F=MA isn't it?
Yeah, also he does mean d as in derivative. (delta x)/(delta t) will not give you velocity (v), but rather an average velocity over a time interval. This is not the same as an instantaneous velocity, which is what we mean when we say velocity.
Lol. Around 38:50 : « The principle of least action will contain all this junk. » The master acknowledge it is junk after all. (But useful junk though!) What do you do when you have junk? You replace the junk by a variable, the mathematical equivalent of sweeping dirt under the carpet. Then you have a nice clean equation. Yay! I love it.
I think you mean non-static, meaning acceleration changes with time. This is true, but a great many things do have static or constant acceleration, like projectile motion on the surface of the Earth. After you throw a ball, for instance, the only acceleration it experiences is the constant pull of gravity, which on the earth is about 9.8 m/s^2. For all these problems the a term is constant, and the kinematics equations derived by time derivatives are very useful.
This it the reference book for all theorems of "calculus of variation" included in Mr Leonard Susskind lectures: www.academia.edu/31560351/AN_INTRODUCTION_TO_LAGRANGIAN_MECHANICS
@QuaternionEM Now actually that's a good question - actually I've had about super-symmetry and Yang-Mills theory in my courses but not the conformal part (in the beginning there's quite some theory to read up on). To the best of my knowledge "conformal" implies preservation of angles under scalings of the energy which in turn means that the coupling constants are independent of the energy... since this adds additional symmetries to the Lagrangian density it also alters the commutation relations
+Kenny Duran. Sure. V=V(x(t)), where x(t) is the vector (x1(t), x2(t), x3(t)). The time derivative of x(t) is the velocity v(t)=(dx_1(t)/dt, dx_2(t)/dt, dx_3(t)/dt) also equal to (v_1(t), v_2(t), v_3(t)) whereas the derivative of V(x(t)) with respect to time is dV/dt = dV/dx_1*dx_1/dt + dV/dx_2*dx_2/dt + dV/dx_3*dx_3/dt You can check this is exactly the scalar product between the gradient of V, namely (dV/dx_1, dV/dx_2, dV/dx_3) and the velocity vector I mentioned before. The shorthand for it is the sum over i of dV/dx_i*v_i. I hope it helped.
He went from writing the expression for just the x component (x, y, z notation) of potential energy to writing the expression for the total potential energy (which is just the sum of the 3 components of potential energy) using the notation (x1, x2, x3). In doing so, the "x" in dU(x)/dt on the left hand side switched from being the "x" component to the vector X = (x1, x2, x3). It was a bit fast and he didn't really explain it so it was easy to miss.
@QuaternionEM No, his second term doesn't have velocity squared. :P By the way, I'm not criticizing him, just pointing out what I think is a honest mistake on his part. I'd love have a tenth of his knowledge. :)
There is a book on "Relativity" published for the sole purpose of educating individuals, like you, in the Theory of Relativity without the archaic insight in the complex mathematics (I got it at Barnes N' Noble for less than $10). Another book of interest is "A Brief History of Time", by Stephen Hawkings (also, an even simpler version called "A Briefer History of Time"). Plus, it doesn't hurt to build up your logic and simple proof-based concepts of geometry with Euclid's "Elements".
Personally I don't see the objection to this comment, at 17 you love this stuff, I think that's great! Wish I could get my son to pay more attention to it. He loves it too, just not enough to put down his xbox controller - rock on! Good to see people your age stepping up to learn this stuff!
Search google for the following: "classical mechanics" inurl:edu filetype:pdf Try to get the book and follow along with the syllabus. If you get lucky, you may come across a course that posts homework exercises and practice tests.
Or writing it in the opposite direction: sq(dx2 + dy2) = sq(dx2 + dy2 dx2/dx2) = sq(dx2 + dx2 (dy/dx)2) = dx sq(1 + (dy/dx)2) The important idea is dx = sq(dx2)!!
@p0pper no, you got it wrong. we deduce v from v=F/m and since F=F(x) we know everything we need to know. in the correct law besides x and F you need to know v to get the a because F=F(v(x)). Seems (maybe) that v is in the middle of the mathematical chain and thus unnecessary, but think of that this way - you pull something. you know F(x), m and try to tell the acceleration. Yes, you do it. Another guy looks at your data. He can't really tell whether object accelerated from 0 m/s or...
The word 'hypotenuse' has no plural form in English. The word is borrowed almost verbatim from the Latin 'hyptenusa', which is a femininine noun whose plural in Latin is 'hypetunae'. So if you use 'formulae' in English to express the plural form of the word 'formula', which has a similiar structure to 'hypotenusa', then you may use 'hypotenusae' as plural.
@QuaternionEM Hm, don't know the book by thornton, but try to look up some reviews (or just ratings 'n' comments on Amazon if nothing else's available... might give you an idea). The higher dimensions of super string theory are just spatial dimensions and I'm fairly certain that they are basically just an analytical continuation of the three spatial ones we know (i.e. instead of integrating over a 3D space its a 10D etc). I'm not really that into string theory though :-/.
You are just pulling the dx out of the square root. This happens a lot in simplifying square root expressions. dx sq(1 + (dy/dx)2) = sq(dx2*1 + dx2(dy/dx)2) = sq(dx2 + dy2).
Yes, the math is necessary for a full understanding of Special Relativity & General Relativity, but tell me is it at all possible for a 14 year old (like the person's comment I responded to) to completely understand Tensor Operations, Tensor Analysis, and Tensor Calculus without a background encompassing Vector Analysis or Multi-variable Calculus? This book (Relativity: The Special and General Theory) is for a conceptual overview (one I used when I was 14 yrs. old) of Einstein's theories.
When he says that force is causing the motion of a mass, does he actually mean that its energy? It seems to me that energy which is the phenomena which causes a mass to move and therefore create a velocity.
At 19:57 he says the derivative of v^2 is equal to 2v(dv/dt). According to the power rule, shouldn't the derivative of any variable squared be equal to two times the variable?
It depends with respect to what you are differentiating suppose you dv/dx of x^2 this will give u 2xdx/dx but we know dx/dx is equal to 1 therefore we ends up with 2x. Whereas if we were differentiating with respect to the above it would have been 2xdx/dt in this case the dx/dt remains. But what really intrigues me is his calculus in differentiating df/dx with respect to time which am not getting the d^f/dx^2v^2
v is a vector and the v_i's are the components of that vector. the components depend on the the actual vector v(t) so the components are v_i(v(t)) so d/dt(v_i^2(v(t))) = 2(v_i(v(t))) d/dt(v_i(v(t))). If we hide the dependencies of v_i on v(t) we get 2 * v_i * d/dt(v_i). You can also yield the same result by doing a directional derivative in the direction of v
Yes but notice its not a derivative with respect to v its a derivative with respect to time, since v is a function of time we must apply the chain rule which gives 2v dv/dt
Wait a minute - there should be no intuition that says the action would be the integral of kinetic energy plus potential energy. That's just the total energy and it's CONSTANT, so it would be the same regardless of trajectory. All "possible" trajectories would have that same energy, so choosing a different one wouldn't change anything - there's no "minimization" to be done there.
You CANNOT know v from knowing x. The point of the F = mv exercise is that if the equation were true, just knowing x for a particle and not knowing its v would still allow you to fully predict all future (and past) locations of the particle. This is not possible in nature; you need to know not only the particle's position but how it is moving (velocity) in order to see where it will wind up. See my reply to p0pper.
Korcan Kanoglu Yes! It's called "The Theoretical Minimum: What You Need to Know to Start Doing Physics" By Leonard Susskind and George Hrabovsky. It was written specifically for these lectures. It's not very long, but it's full of great information.
@paigerocks884 Yes, he's demonstrating mathematical logic, I believe. He's giving you an instant where you can see that the math is flawless, but the physical law is nevertheless flawed. Aristotle's mechanics were actually along those lines, I believe.
@QuaternionEM You're probably right about the first part - I've just started doing my thesis about conformal super-symmetrical Yang Mills theories (theoretical particle physics in case you're wondering), so I guess this IS a bit of a waste of time... but it's okay to watch while eating or cleaning ;-). My comment of course was made in comparison to when I had classical mechanics myself and not my current level. Way to be judgemental btw - what do you do for a living?
I am looking for non inertial reference frames , rigid bodies, rotational motion and euler angles. I am going over prof. Susskind's videos any one know which videos cover that? Thanks
@QuaternionEM You are absolutely correct. Every time I looked at it, I put it on the 7:30 mark, at which the expression was still incomplete. My apologies. =P
You're getting your symbols mixed up. The d is for delta, not derivative. As in "change in". F(x) = m (change in x)/(change in t). Acceleration is defined as change in position divided by change in time... therefore... F, in terms of position, is equal to mass times acceleration... F=ma.
No this is incorrect, a=dv/dt not dx/dt v=dx/dt or change in position/ change in t. Velocity is the time derivative of acceleration, and position is the time derivative of velocity.
@DigitizedSelf Yang Mills...yeah...THAT's the ticket! Tell me some original awesome math details about your thesis. What specifically is the conformal part?
Hey, great lecture! i' currently wachting to whole playlist of modern physics. i was confused when i saw quantum mechanics before theory of relativity. Is the order chosen intentionally? best wishes
Perhaps in terms of difficulty, but I believe they are quite unrelated until a very advanced level (In which case it's all theoretical stuff which is not proven I believe apart from perhaps Quantum field theory), so you don't need to know relativity before doing quantum.
Heres something thats confusing me. How do we assume that F is a function of X. For Aristotle's law it might make sense cuz V is a function of X and T (and T is initially 0). This isnt so for Newton's law. Any ideas?
@DigitizedSelf I'm unsure why a minimum of 10 dimensions are required though, but it is my impression that its related to internal symmetry of the theory (in what way however I don't know). Sooo, having basically said I know almost nothing about string theory here's another revelation: What are the dimensions of electromagnetism? (haven't ever heard of dimensions specific to EM...)
Man i wanna go back to highschool and actually do good, so i could take advantage of the opertunities out in the world. like learning from ppl like this!
@DigitizedSelf I'm noticing that one of the biggest differnces between physics and EE is the nomenclature. Have you ever read "Classical Dynamics" by Thornton? I have a copy. I'm wondering if it's considered a good text or not. Here's a good question: What, mathematically, are the higher dimensions of string theory? Are they similar to electro- magnetic dimension or are they actual spatial dimensions. What equations describe them? Thanks.
Something i don't get : he says aristote's is a one dimensional space because it only needs x. Following its logic, I would (humbly) describe it as a 2 dimensional one : you need the position, and the force that moves things around. And since F=mv, that means you need x and v. X alone doesn't tell you what force is being applied to it (no matter how you describe it). dx/dt tells you, but that means you need a "pair" of x. That's two dimensional to me... Anyone ?
@BarbaraPloyer333 Don't forget to learn calculus too. It's EXTREMELY important. I mastered it at your age and it's nowhere near as hard as it seems. Just look up some pdfs on google.
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I just noticed this video has 40 downvotes. How could anyone dislike these lectures? It's just ASTOUNDING how much education Dr. Susskind has online for FREE. It's an enormous contribution to the world.
Because these people realized they reached their pons asinorum
Some people think knowledge is from the devil
Remember I felt a renewed interested in physics after 40 years and business career. Decided to go directly to m-theory course. Was lost after less than 10 minutes. Maybe those people felt like me at that time. Went back to 101 classical mech. and could hop right in. Seen most of Frof. Susskinds courses over a 9 year time and enjoyed most of them, and the professor always. He definitely needed a new printer at the time as it seemed to print his lecture notes in random order…
sta nford sta nford sta nford THE SAME thing 4th to church think about it Sir I'm NOT GOING TO THE same language a good day and it's really hard to tell the difference SIR ALEX IS THE AND to church by praying FOR YOU AND 4TH to church think about it Sir i will send you a draf draf draf example of a 4TH THE AND THE OTHER OTHER PEOPLE ARE NOT THE AND THE SAME thing 4th to church think about it is not to church think THAT THAT AND I have have have to use those years ago back in fresh an awkward silent then we can can I have seen the site sir i have finish designing the site exactly as you are ok with it Sir i have a weakness of it here in my country is the last i will do for this project js the project and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we can start now seeing your tight schedule for your kind of website are you thinking to have a ground based business skills to run my business and to be more certain about the completion in a way thar i will send it can touch every time there is a concepts and i will be waiting your response thank you for time thing but it is not to be a good plan if you thinking to have Sir I assure you that is the funny part of it here in my country is the last i will do for this project is a bit secure ans and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will be waiting your response thank you for your kind of website are you thinking to have Sir I assure you that is the differences between developers and clients in exceeding to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer it with in a few minutes of my frineds in my services and i will transfer it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in in my services and i will transfer it with in a few minutes of my frineds in my services and i will be you guys again for your kind interests in my services and i will transfer it with in the next time sew gar new eji the phone available after 5hrs and i will transfer it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in a few days ago back in fresh an awkward silent then we use it for replacements and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and night to finish it with in the next time sew gar new eji the phone available after 5hrs and i will transfer as ordered a good day and
@@bojohannesen4352 Well, I guess honestly I don't - at least not to a degree that's "critical to my life in any way." It's just a little sad to see such a lack of appreciation for the pursuit of knowledge. So yes, I "care," but no, it's not going to ruin my life or anything.
I guess the way I look at it is a) this is good stuff and b) it's being offered for free, so why on Earth would anyone actually think it made sense to *criticize* it? It's a stellar example of "looking the gift horse in the mouth."
So, there's that, which seems logical enough to me, and then there's just the sad fact that so few people really seem interesting in educating themselves. But I can't change it, and I'm doing fine, so I guess I'll just carry right along enjoying my own life.
I maybe understand about 20% of what this guy is talking about, but I still find it fascinating. Every now and then I'll catch a glimmer of understanding and that is enough for me right now.
I'm 16 old and have studied all these
Johnny, that is the way to do it. I've learned as a student of physics for 6 years now that the way to learn is to just dive in, learn maybe 10 percent of the subject, come back, try again, get like 30, go learn some more math, come back, learn about 60 percent, and then tenaciously stick with it and finally feel like you understand the subject. It's how I learned analytical mechanics, how I'm learning electromagnetism, and I am learning thermodynamics and quantum mechanics. Particle physics is a whole different beast, and I suspect I'll be studying for many years to come before I start to have a feeling of mastery, but that's the fun, the journey!
Mathematics Fanatic - I’m 15 and I’ve studied and forgotten it so here I am again... 😂
@@pphilosophy2156 this is actually a very deep truth that took me many years of self studying to figure out!
@@skye.s2515 how is it going now? What are you studying? Are you still on the series?
"s" as distance comes from German: "Strecke", meaning path
Maurice A echt?😂
Ohhh.... thank you!!
Another possible origin is "Spatium" according to hsm.stackexchange.com/questions/7138/why-is-distance-sometimes-abbreviated-s
I started studying basic astrophysics when I was just 13 years old. Today I am 15 and I still have the notes from 2 years ago! I am now really interested into Classical Mechanics and I love the way Leonard Susskind does his explanations. Will try to follow these lectures as much as possible.
Ig u are doing things in the wrong order.. Isn't it classical first then the rest of physics..
@Anubhav Mahapatra like the life of a star and stuff?
Are you studying physics at university now?
position
velocity
acceleration
jerk
snap
crackle
pop
The derivatives of position with respect to time
😂😂
Whoo! I finally understand what a Lagrangian is! Thank you Susskind and Stanford!
At least from a classical mech point of view, the principle of least action (and the minus sign) aren't that hard to understand.
If KE is becoming PE, that means the object is getting slower. If PE is becoming KE, the object is getting faster.
So, minimizing KE - PE means PE and KE try not to switch between each other...objects speed up and slow down as little as possible...ie., objects in motion stay in motion. objects at rest stay at rest. First law all over again.
Wow that's the bestest explanation
the world is so lazy that it even does not want to convert ke to pe and vice versa
Explained very clearly!
This guy explains analytical mechanics in a clearer way than I have ever heard from a professor or read in any textbook. Just perfect ;)
Damn, didn't realize Michael from Breaking Bad had become a physicist. But in seriousness, loved Prof Susskind's introduction to calculus of variations. Very intuitive and eloquent.
Jesus he faked his own death. After Walt left the river he got up.
34:35 Assumption: The Forces act along the line joining the particles.
I have a PhD I think Susskind is the best. I have mostly recovered from brain damage I am planning on going back to school. I agree with Susskind about the big bang postulate. Since kinetic E is made up of translational E. I expected the or knew from Stat. Mech. The way he teaches is very easy to follow. I have taught at U and Dr. Susskind is one of the best. You would consider me old. Exactly were is he fishing for compliments?
Right this is exactly what is going on. It is pretty clear when you study calculus actually. When you integrate something, you always have to add +C to the end. This represents your initial condition, which is the bit of information lost when you do the integral. F=ma, a=dv/dt, and v=dx/dt, since you have to integrate twice to get form position to acceleration, it isn't sufficient to know just the initial position, but you need to provide and initial velocity as well.
I'm 16 y.o. Ukrainian and my English is good for marvel but not for physics eehh books.
but I understand him. lil bit proud of myself..
Actually, Newton formulated 2nd law in exactly F = dp/dt form:
Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.
Shooting
Also, Euclid's "Elements" helps dawn the logical process of the mind for more complex proofs (proofs are helpful in the realm of theoretical physics) and gives an understanding of basic geometry to better understand curved geometry and differential geometry. I also used this when I was younger... so when someone says Special Relativity and General Relativity does not follow Euclidean geometry, you want to know what the really means (particularly the "exclusion" of Euclid's 5th postulate).
@mascoteponto
I figured it out.
It took me about 1/2 hour, but Dr Susskind
is right again. The d²F/dxdt term can be written as
d/dx(dF/dt) = d/dx(dF/dx*dx/dt) = d²F/dx² * v + dF/dx * d/dt(dx/dx)
but dx/dx = 1 and d/dt(1) = 0
So we get exactly what he said.
QED
Thanks for explaining I am watching this lecture in October, 2019
Feel the least action principle should be called the least conversion principle, which should be more intuitive, since what is really minimized is how much potential energy is converted to kinetic energy during the course of a trajectory.
6:32 inertia 6:54 the constant
Would probably be helpful to learn calculus before watching these.
Makes no difference
That's exactly what I was thinking haha
Your comment convinced me to take calculus last year. Now I'm back to watch these videos. Thanks. And screw integrals.
Calculus is useful in a lot of different fields.. Good choice.
Ehh the basic principles would do too
@Escaladist It's a course from the Stanford Continuing Studies Program.
Hi, I have an MPhil degree in Physics. I have taken six courses of Prof. Susskind which are "Classical Mechanics," "Quantum Entanglements Part 1," "Special Theory of Relativity," "General Theory of Relativity," "Cosmology," and "Statistical Mechanics". I have also taken handwritten notes of him in all the details and currently I'm typing his notes on Latex. Kindly let me know in the comments which lectures of him do you want the notes of and I will make them for you on Latex. Cheers!!
Hey, i would love to have your 'Classical Mechanics' notes.
Likewise, your notes on classical mechanics would be wonderful
I love how he says "due to two") 31:04
Susskind gives what he calls the 'theoretical minimum', i.e. everything you need to know to understand the subject without going in too much detail.
A normal course would have several examples of the applications of the newtonian laws (like a particle falling with or without friction, for example).
For a more complete knowledge of the subject I recomend 'Classical Dynamics of Particles and Systems' by Marion and Thornton and (for an advanced level) 'Classical Mechanics' by Goldstein.
This lecture is an exercise in trusting the process. The whole entire point is to show how energy is conserved and that a system path of least action/time that is defined by the integral of the lagrangian between 2 general coordinates of the system.
what i learnt from this lecture:
the plural of hypotenuse is hippopatmusses 1:9:03
if anybody is interested.. the derivative of jerk is jounce :) wat a nice word
after jounce is snap, crackle and pop xD
hahaha
physicists naming their derivatives
Jounce is another word for snap.
This is explained is Lecture 1 as well. If the motion equation were F(x) = mv, and all you knew was a particle's position x, then you could calculate the force using F(x). You can also calculate the velocity from v = F(x)/m. Then you could also find the acceleration of the particle using dF(x)/dt = mdv/dt ==> dF(x)/dx*dx/dt = ma ==> dF(x)/dx*v = ma.
This gives you the equation a = dF(x)/dx * v / m. So knowing only the position also gave you the velocity and acceleration! (continued...)
I haven't seen the calculus of variation for a while. Great exposition and pedagogy Dr. Susskind--I'm very grateful for the simply incredible lecture!
It is difficult to explain using TH-cam's comment section, but try to imagine pulling the dx term out of the square root. You would have to find the term that you can multiply dx with that would result in sq(dx^2 + dy^2). You have to divide dy by dx so that when you multiply by dx you get just dy. You have to do this with the dx term as well, and dx/dx = 1, hence dx*sq(1+(dy/dx)^2).
From Dr Susskind's formula mj = (dF/dx)*a + (d²F/dx²)*v²
1st term --> (N/m)*(m/s²) = N/s²
2nd term --> (N/m²)*(m²/s²) = N/s²
Your units from mj = (dF/dx)*a + (d²F/dxdt)*v
1st term --> (N/m)*(m/s²) = N/s²
2nd term --> (N/(m*s))*(m/s) = N/s²
Yours works also but it still has a time derivative which we seek to eliminate
to obtain an ODE rather than a PDE.
It's an incremental demonstration of why we have a 2-dimensional phase space in classical mechanics. If the laws of physics were based on f-mv then the phase space would be 1-space.
I'm a zygote and I love this
I am a gamete, and also love this.
28:55
38:49
46:41
54:45
1:00:21
1:13:24
...cont:
For example: If you drop something from a tower (and assue there is no air friction): the acceleration is always -g (-9.81 m/s2) but the time the particle will take to arrive on the ground will depend ALSO on the inital velocity v0. It makes a difference if you just let go of something or throw it down (giving it a initial velocity not equal to zero).
From the integral of a you cannot get the initial velocity, hence you need to know both x AND v in the F=ma case.
in all seriousness, _jerk_ as da/dt is well taught - i remember my grade 13 (i grew up in ontario.) physics teacher explaining it as being essentially what it sounds like - a sharp change in acceleration, like you'd experience during turbulence. and, just about the only application i could imagine for further differentiation would in fact be in the field of low atmosphere air travel, in trying to understand the complex effects of gravity interfering with itself on a free-falling object.
so, imagine you're in a car that is constantly accelerating. if you change that by slowing down or speeding up the rate of acceleration, you're going to get thrown forwards or backwards (due to the third law), you're going to get jerked forward or backward, and that would be da/dt - just like it sounds like.
1. Principle of Least Action [52:22]
these are a great set of videos! haven't done maths in a while so i've had to go out and buy 'calculas for dummies' to keep up...........
I bought it too:)
i bet that "calculas for dummies" lives up to it's name, along with "biologee for burnouts" and "fysics for fools".
calcalculas for dummies is actually a pretty good book, I like the witty style
F can be a function of x since there exist such forces. One of them is the harmonic oscillator for which the force law is F= -kx
Thank you Stanford, thank you mr. Susskind!
According to Wikipedia “Momentum” was defined by Jennings in 1721 in _Miscellanea_ as a rectangular area created by velocity and substance. This was published before Newton’s last edition. But newton used a name with an equivalent meaning “Quantitas motus”. Wikipedia does not define when first the word as used in speak.
The fourth derivative of the position vector, with respect to time, is called Jounce!
In my field we call it snap: velocity, acceleration, jerk, snap, crackle, pop.
Not gonna lie, first time he said there was a name for the derivative of a called "jerk" I laughed out loud. Then I reaized he was serious and looked it up.... guess there are some applications for it...
We all know the change of jerk over time is just called character development
@QuaternionEM No, what you wrote there isn't even an operator and carries a suspicious similarity to the Lorentz factor used in the Lorentz transformations of special relativity... also, while it is true that conformal mapping exists as a map between complex functions, then even in that simple case it needs to conserve angles. In the case of conformal field theory it implies an additional symmetry of the lagrangian which in turn leads to the fields being massless, making the coupling constants
Healthy use of the speed control and pause button. watching at higher speed and pausing every 5 minutes or so is much better way to watch.
i don`t remember it was lecture 1 or 2, but when he told what the world would be like if we suppose f=mv, my brain and ear paused for 10 secs, it was the moment of truth.....thank you Proffesor
It was lecture 1 :)
Wanseok Yang I'm a little confused at the moment. I've been enjoying Physics 8a over at Berk, but I'm not quite sure how F=MV proves anything... The law is F=MA isn't it?
Robert Wilson III He was just showing what would happen in that (Aristotelian) case.
Robert Wilson III In the SI system you write F, m, a and v . M is reserved for moment - torque - A refer to an area, and V to volume.
Wayne Adams ah. Well that makes perfect sense. Thanks
How does a light ray has momentum if it has no mass?
Wow, it was just a brilliant teacher at his best.
Yeah, also he does mean d as in derivative. (delta x)/(delta t) will not give you velocity (v), but rather an average velocity over a time interval. This is not the same as an instantaneous velocity, which is what we mean when we say velocity.
Lol. Around 38:50 : « The principle of least action will contain all this junk. » The master acknowledge it is junk after all. (But useful junk though!) What do you do when you have junk? You replace the junk by a variable, the mathematical equivalent of sweeping dirt under the carpet. Then you have a nice clean equation. Yay! I love it.
I think you mean non-static, meaning acceleration changes with time. This is true, but a great many things do have static or constant acceleration, like projectile motion on the surface of the Earth. After you throw a ball, for instance, the only acceleration it experiences is the constant pull of gravity, which on the earth is about 9.8 m/s^2. For all these problems the a term is constant, and the kinematics equations derived by time derivatives are very useful.
This it the reference book for all theorems of "calculus of variation" included in Mr Leonard Susskind lectures:
www.academia.edu/31560351/AN_INTRODUCTION_TO_LAGRANGIAN_MECHANICS
@QuaternionEM Now actually that's a good question - actually I've had about super-symmetry and Yang-Mills theory in my courses but not the conformal part (in the beginning there's quite some theory to read up on). To the best of my knowledge "conformal" implies preservation of angles under scalings of the energy which in turn means that the coupling constants are independent of the energy... since this adds additional symmetries to the Lagrangian density it also alters the commutation relations
59:00
Does anyone know why he was adding the three components of potential energy at 21:55?
+Kenny Duran.
Sure.
V=V(x(t)), where x(t) is the vector (x1(t), x2(t), x3(t)).
The time derivative of x(t) is the velocity
v(t)=(dx_1(t)/dt, dx_2(t)/dt, dx_3(t)/dt)
also equal to
(v_1(t), v_2(t), v_3(t))
whereas the derivative of V(x(t)) with respect to time is
dV/dt = dV/dx_1*dx_1/dt + dV/dx_2*dx_2/dt + dV/dx_3*dx_3/dt
You can check this is exactly the scalar product between the gradient of V, namely (dV/dx_1, dV/dx_2, dV/dx_3) and the velocity vector I mentioned before. The shorthand for it is the sum over i of dV/dx_i*v_i.
I hope it helped.
He went from writing the expression for just the x component (x, y, z notation) of potential energy to writing the expression for the total potential energy (which is just the sum of the 3 components of potential energy) using the notation (x1, x2, x3). In doing so, the "x" in dU(x)/dt on the left hand side switched from being the "x" component to the vector X = (x1, x2, x3). It was a bit fast and he didn't really explain it so it was easy to miss.
@QuaternionEM
No, his second term doesn't have velocity squared. :P
By the way, I'm not criticizing him, just pointing out what I think is a honest mistake on his part. I'd love have a tenth of his knowledge. :)
Why at 17:00 he says he has done it last time? Are there videos of "last time" on youtube?
th-cam.com/play/PL6i60qoDQhQGaGbbg-4aSwXJvxOqO6o5e.html
4 years too late but still
looks very difficult. i‘m a Chinese student. i can't understand the course very well. oh
张宏亮 这个很容易，没那么难，起码能听懂
There is a book on "Relativity" published for the sole purpose of educating individuals, like you, in the Theory of Relativity without the archaic insight in the complex mathematics (I got it at Barnes N' Noble for less than $10). Another book of interest is "A Brief History of Time", by Stephen Hawkings (also, an even simpler version called "A Briefer History of Time"). Plus, it doesn't hurt to build up your logic and simple proof-based concepts of geometry with Euclid's "Elements".
I think that for 51:08, x = -4/3, not -8/3. 2x = -8/3, so x = -8/6 = -4/3.
Maan these are real gems
Personally I don't see the objection to this comment, at 17 you love this stuff, I think that's great! Wish I could get my son to pay more attention to it. He loves it too, just not enough to put down his xbox controller - rock on! Good to see people your age stepping up to learn this stuff!
@superfahd We are looking at the special case where it is X, it could be a function of something else.
you can think of the derivative as the change in velocity, thats how it relates to Newtons equations.
Search google for the following:
"classical mechanics" inurl:edu filetype:pdf
Try to get the book and follow along with the syllabus. If you get lucky, you may come across a course that posts homework exercises and practice tests.
Or writing it in the opposite direction:
sq(dx2 + dy2) = sq(dx2 + dy2 dx2/dx2) = sq(dx2 + dx2 (dy/dx)2) = dx sq(1 + (dy/dx)2)
The important idea is dx = sq(dx2)!!
At 16:17: if F = -∇U(x, y)
Shouldn't it be: Fx = - ∂U(x, y)/∂x
If i compare it to this: en.wikipedia.org/wiki/Del
Thanks in advance :)
∂_x is a shorthand notation for ∂/∂x . (I dont know how to write subscripts here, so "_x" means "subscript x" )
ok cool, ty!
@p0pper no, you got it wrong. we deduce v from v=F/m and since F=F(x) we know everything we need to know. in the correct law besides x and F you need to know v to get the a because F=F(v(x)). Seems (maybe) that v is in the middle of the mathematical chain and thus unnecessary, but think of that this way - you pull something. you know F(x), m and try to tell the acceleration. Yes, you do it. Another guy looks at your data. He can't really tell whether object accelerated from 0 m/s or...
@mascoteponto
Yes, his second term does have the velocity squared.
Here it is in black and white at 8:05.
Just own your mistake and quit crying.
sqrt(dx^2 + dy^2) = sqrt(dx^2(1+dy^2/dx^2) = dx sqrt(1 +dy^2/dx^2) tho i believe the rigorous formulation of arc length is more complicated
The word 'hypotenuse' has no plural form in English. The word is borrowed almost verbatim from the Latin 'hyptenusa', which is a femininine noun whose plural in Latin is 'hypetunae'. So if you use 'formulae' in English to express the plural form of the word 'formula', which has a similiar structure to 'hypotenusa', then you may use 'hypotenusae' as plural.
@QuaternionEM Hm, don't know the book by thornton, but try to look up some reviews (or just ratings 'n' comments on Amazon if nothing else's available... might give you an idea).
The higher dimensions of super string theory are just spatial dimensions and I'm fairly certain that they are basically just an analytical continuation of the three spatial ones we know (i.e. instead of integrating over a 3D space its a 10D etc). I'm not really that into string theory though :-/.
You are just pulling the dx out of the square root. This happens a lot in simplifying square root expressions.
dx sq(1 + (dy/dx)2) = sq(dx2*1 + dx2(dy/dx)2) = sq(dx2 + dy2).
Yes, the math is necessary for a full understanding of Special Relativity & General Relativity, but tell me is it at all possible for a 14 year old (like the person's comment I responded to) to completely understand Tensor Operations, Tensor Analysis, and Tensor Calculus without a background encompassing Vector Analysis or Multi-variable Calculus? This book (Relativity: The Special and General Theory) is for a conceptual overview (one I used when I was 14 yrs. old) of Einstein's theories.
@BenBen2351 with on exception you forgot that f it istelf is f(x) it's depentant only on x so if you know x then you know f
When he says that force is causing the motion of a mass, does he actually mean that its energy? It seems to me that energy which is the phenomena which causes a mass to move and therefore create a velocity.
At 19:57 he says the derivative of v^2 is equal to 2v(dv/dt). According to the power rule, shouldn't the derivative of any variable squared be equal to two times the variable?
It depends with respect to what you are differentiating suppose you dv/dx of x^2 this will give u 2xdx/dx but we know dx/dx is equal to 1 therefore we ends up with 2x. Whereas if we were differentiating with respect to the above it would have been 2xdx/dt in this case the dx/dt remains. But what really intrigues me is his calculus in differentiating df/dx with respect to time which am not getting the d^f/dx^2v^2
Finally I got it after a few trial
v is a vector and the v_i's are the components of that vector. the components depend on the the actual vector v(t) so the components are v_i(v(t)) so d/dt(v_i^2(v(t))) = 2(v_i(v(t))) d/dt(v_i(v(t))). If we hide the dependencies of v_i on v(t) we get 2 * v_i * d/dt(v_i). You can also yield the same result by doing a directional derivative in the direction of v
Yes but notice its not a derivative with respect to v its a derivative with respect to time, since v is a function of time we must apply the chain rule which gives 2v dv/dt
Wait a minute - there should be no intuition that says the action would be the integral of kinetic energy plus potential energy. That's just the total energy and it's CONSTANT, so it would be the same regardless of trajectory. All "possible" trajectories would have that same energy, so choosing a different one wouldn't change anything - there's no "minimization" to be done there.
Exactly
You CANNOT know v from knowing x. The point of the F = mv exercise is that if the equation were true, just knowing x for a particle and not knowing its v would still allow you to fully predict all future (and past) locations of the particle. This is not possible in nature; you need to know not only the particle's position but how it is moving (velocity) in order to see where it will wind up. See my reply to p0pper.
Is there any textbook that can accompany those lectures?
For me, I used John Taylor's.
Korcan Kanoglu Yes! It's called "The Theoretical Minimum: What You Need to Know to Start Doing Physics" By Leonard Susskind and George Hrabovsky. It was written specifically for these lectures. It's not very long, but it's full of great information.
@mcgilson007 He mentions the force law later, but it was kind of in passing. That could have been clearer
@paigerocks884 Yes, he's demonstrating mathematical logic, I believe. He's giving you an instant where you can see that the math is flawless, but the physical law is nevertheless flawed. Aristotle's mechanics were actually along those lines, I believe.
@QuaternionEM You're probably right about the first part - I've just started doing my thesis about conformal super-symmetrical Yang Mills theories (theoretical particle physics in case you're wondering), so I guess this IS a bit of a waste of time... but it's okay to watch while eating or cleaning ;-). My comment of course was made in comparison to when I had classical mechanics myself and not my current level.
Way to be judgemental btw - what do you do for a living?
I am looking for non inertial reference frames , rigid bodies, rotational motion and euler angles. I am going over prof. Susskind's videos any one know which videos cover that?
Thanks
It is unfortunate that most of the writings on the white board are out of focus, sometimes blurred, specially when the camera moves backwards.
@QuaternionEM
You are absolutely correct. Every time I looked at it, I put it on the 7:30 mark, at which the expression was still incomplete. My apologies. =P
You're getting your symbols mixed up. The d is for delta, not derivative. As in "change in". F(x) = m (change in x)/(change in t). Acceleration is defined as change in position divided by change in time... therefore... F, in terms of position, is equal to mass times acceleration... F=ma.
No this is incorrect, a=dv/dt not dx/dt v=dx/dt or change in position/ change in t. Velocity is the time derivative of acceleration, and position is the time derivative of velocity.
@DigitizedSelf
Yang Mills...yeah...THAT's the ticket!
Tell me some original awesome math details about your thesis.
What specifically is the conformal part?
@Psychosmurf547
I thought you would have already figured it out, considering that you have mastered all of calculus.
Oh. I think it's because x and v is fundamental to describing the physical world. right?
At 50 minutes he just completely demystifies partial derivative. Check it out!
Hey, great lecture!
i' currently wachting to whole playlist of modern physics.
i was confused when i saw quantum mechanics before theory of relativity.
Is the order chosen intentionally?
best wishes
Perhaps in terms of difficulty, but I believe they are quite unrelated until a very advanced level (In which case it's all theoretical stuff which is not proven I believe apart from perhaps Quantum field theory), so you don't need to know relativity before doing quantum.
Heres something thats confusing me. How do we assume that F is a function of X. For Aristotle's law it might make sense cuz V is a function of X and T (and T is initially 0). This isnt so for Newton's law.
Any ideas?
@DigitizedSelf I'm unsure why a minimum of 10 dimensions are required though, but it is my impression that its related to internal symmetry of the theory (in what way however I don't know). Sooo, having basically said I know almost nothing about string theory here's another revelation: What are the dimensions of electromagnetism? (haven't ever heard of dimensions specific to EM...)
If I remember correctly, I think important equations come out of string theory when you state it in 11 dimensions
Man i wanna go back to highschool and actually do good, so i could take advantage of the opertunities out in the world. like learning from ppl like this!
@DigitizedSelf
I'm noticing that one of the biggest differnces
between physics and EE is the nomenclature.
Have you ever read "Classical Dynamics" by
Thornton? I have a copy. I'm wondering if it's
considered a good text or not.
Here's a good question:
What, mathematically, are the higher dimensions
of string theory? Are they similar to electro-
magnetic dimension or are they actual spatial
dimensions. What equations describe them?
Thanks.
Really Interesting, mind-boggling last 30 mins !!!! :D
Something i don't get : he says aristote's is a one dimensional space because it only needs x.
Following its logic, I would (humbly) describe it as a 2 dimensional one : you need the position, and the force that moves things around. And since F=mv, that means you need x and v. X alone doesn't tell you what force is being applied to it (no matter how you describe it). dx/dt tells you, but that means you need a "pair" of x.
That's two dimensional to me...
Anyone ?
@BarbaraPloyer333 Don't forget to learn calculus too. It's EXTREMELY important. I mastered it at your age and it's nowhere near as hard as it seems. Just look up some pdfs on google.
Thank you very much
@BenBen2351 we are taking the force law as a given