Teoretyczne minimum. Co musisz wiedzieć, żeby zacząć zajmować się fizyką

The Theoretical Minimum

by Leonard Susskind, George Hrabovsky, Joanna Skalska (Translator)

Książka, dzięki której poznasz smak prawdziwej fizyki.

Teoretyczne minimum to książka dla każdego, komu zdarzyło się żałować, że nie jest fizykiem, każdego, kto chciałby się przekonać i doświadczyć, w jaki sposób fizycy myślą i pracują. W przeciwieństwie do książek popularnonaukowych, które dają czytelnikowi przedsmak fizyki, „Teoretyczne minimum" Leonarda Susskinda uczy umiejętności niezbędnych, by naprawdę zająć się fizyką i móc o własnych siłach poszerzać wiedzę i poznawać bardziej skomplikowane tematy. Książka Susskinda to zestaw narzędzi, który umożliwia podjęcie tej wspaniałej intelektualnej wędrówki.

Genres: Science, Physics, Nonfiction, Mathematics, Popular Science, Stem, Textbooks

256 pages, Paperback

First published January 1, 2013

About the author

Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.

read more: http://en.wikipedia.org/wiki/Leonard_...

Reviews

[Vince · Rating 5 out of 5]

As someone squarely in the target audience for this book I found it to be right on the money. The audience is those who find themselves wishing popular physics books could be a little more technical at times. And, being technical means including the mathematics and the unifying concepts behind the theories. This book, and the online lectures it is a companion to, delivers on that count.

In order to get the most out of it you need to bring with you: some exposure to calculus (even if you are very rusty), some exposure to classical physics, access to the online lectures, and a willingness to do some hands on work with the math (including consulting outside resources if necessary).

As each new piece of mathematics is introduced (trig, derivatives and partial derivatives, integrals) you get a section describing the notation and how to work with it, but if you've literally never seen this stuff before, I think it is doubtful you'll completely 'get it' just from the book. Ditto with the physics. If you've never seen the equations for force or kinetic energy before you might be thrown off by the shotgun approach of seeing them introduced , almost out of the blue, as something to plug in to the calculus equations you are working with.

You will need to work with the math and the exercises in order to get the most out of the book. There are equations on every page; you probably aren't going to get a lot out of it just by reading the material and never doing it yourself.

The video lectures are a must. Sometimes the book is a little easier to follow, sometimes the lectures. It is much easier to review past material by looking it up in the book though.

One big shortcoming is that the book's companion site, http://madscitech.org/tm, doesn't provide links to the videos! You can find them by searching on YouTube for Susskind Classical Mechanics, however, there are two versions of the lectures, and a third set of lectures that are labeled "Theorectical Minimum" but are actually about quantum mechanics! I don't think it matters which of the two versions you watch. I watched the ones recorded in 2011. Here are a couple playlists to make it easier: Theoretical Minimum - Classical Mechanics - 2007 or Theoretical Minimum - Classical Mechanics - 2011.

The book excels at giving you insight into the conceptual underpinnings of theoretical physics. You'll learn what a space of states is and what properties the dynamical laws (laws of motion) that connect those states must have. You'll learn how to define the basic quantities of physics (velocity, acceleration) by using calculus. Things really start getting interesting though when the book covers topics such as the Lagrangian, the principle of least action, symmetry and conservation laws, the Hamiltonian, and Poisson brackets, all formulations and properties of the laws of physics with wide applicability even outside of classical mechanics.

If you've read much physics you've probably heard of a Lagrangian before. Now you get to find out exactly one is and why, together with the principle of least action, it is such a powerful way to formulate the laws of physics. The short answer is that they are easy to translate from one coordinate system to another (even coordinate systems of non-inertial reference frames). So, for example, translating the Lagrangian for Newton's force laws to a rotating reference frame (like being on a carousel) allows you to write out the laws of motion for that frame and out pops centrifugal force and the coriolis force. Very cool stuff, as was seeing the mathematical meaning of symmetries.

The writing is very good, if a little break-neck at times. I've seen some complaints about the formatting, especially of the math, but I don't see what the problem is. Admittedly I don't read mathematics texts often but I was able to read everything without any problems or confusion. It certainly isn't terrible as I saw someone say elsewhere.

I think the whole idea of writing this kind of book, not quite a textbook, not a popular account filled with nothing but analogies, is great. I read this as a 21 day loan from my local library, and I'll need to get it again to finish all the exercises in the later chapters, but I saw enough to know I loved it. I hope the series continues as planned.

[Jen · Rating 4 out of 5]

“A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.”

A quote from Susskind himself regarding the target audience of this project.

If you’re someone who has a (re)fresh(ed) foundation of algebra, trig, calc, has some enthusiasm for physics, and wants to become better acquainted with the mathematical relationships under the hood, this book is for you. It will help familiarize you with the techniques you’ll need to start engaging in foreplay with the universe. It is particularly effective if used in conjunction with Susskind’s online courses, which are freely available on YouTube. I strongly suggest you avail yourself of this supplement in order to achieve maximum epistemological virility. This is a multi-volume work, three of which are available at the time of my review, (This title, Quantum Mechanics, Special Relativity and Classical Field Theory) and it appears as though the maestro will have us ready to take the Cosmos itself up to our room to show off our etchings before he’s finished. So, If you feel like you’ve milked the popular science books for all their conceptual fluids and wish to get technical, this is an almost perfect primer for beginning your sexual dalliances with all things quantifiable.

If you’re mathematically illiterate and you’re a tad curious what this whole physics hoopla is about, this is not the book for you. This slim beauty achieved its figure by shedding all but the most essential descriptive elements. Yet I have seen several people suggesting that this would be fine for someone just becoming interested in physics. I disagree. I think those reviewers are underestimating the difficulty for people in those situations, and how effective most math/science teachers are at producing lifelong enemies of their respective fields. I’m not sure how they’re recommending it without the minimum (theoretical) proviso; you’ll have to learn the math. And since this book assumes mathematical knowledge, and functions okay as a refresher, but terribly as a crash course, I think you’d be better served by establishing that foundation before jumping in here. Although it wouldn’t be impossible to read through this while learning the math in tandem, I can’t judge how pleasurable that experience would be personally. But, bringing my considerable powers of imagination to bear, I envision demoralization and hair loss.

The following are somewhat apocryphal stories from a variety of people whose lives have been improved by physics.

Mitch from Flintcock Idaho writes:

As a college football lineman, the application of force is very important to me. I learned from this book the crucial components needed to make someone literally shit themselves from a tackle. That’s mass and acceleration. I decided to work on both. Dirty bulking with burritos the size of my forearm makes it easy to obtain caloric surpluses despite my busy schedule, coupled with heavy strength training to make sure portions of that beef are going toward muscle hypertrophy, and finally, plyometric exercises to condition my CNS for maximal fast twitch fiber recruitment to enhance my explosiveness. Thanks to Newton, I’m a goddamn terminator on the field now. The other day, during practice, I hit a guy so hard that he sounded like an asthmatic panther violently wheezing into a megaphone. Coach Bartleby ran up slicing the air with his hands and turning purple from whistle blowing. He says: “Shit fire, hoss! Did somebody step on a duck?!” The dude had shat himself.

Randy from Shittledick Indiana writes;

This book saved me from trying out a pair of knuckle dusters one of my schoolmates had fashioned out of flimsy alloys. Ricky comes up to me by the lockers, glancing this way and that before fishing in his duffel bag. He says: “Look at these sumbitches, Randy. I made these last night. If Chad messes with me again today... BOOM.” He says, smacking the DIY duster into his palm. “I’ll crow hop and stove him. See if I don’t. It’ll leave a mark on him and all his descendants. Right here.” He says, indicating a spot between his eyes. “From, like, Lamarckian inheritance ‘n shit. Right in his germ line, dude. BOW!” He punches the air. “Here, try ‘em on this locker.” Hesitating due to equal and opposite reactions, I draw upon my vigorous study of great oration to urge restraint:

“We build a fire in a powder magazine, then double the fire department to put it out. We inflame wild beasts with the smell of blood, and then innocently wonder at the wave of brutal appetite that sweeps the land as a consequence.”

“Pussy.” He scoffs. “These are better than brass knucks. Check this out!” KABLAAM! He wallops a locker with bad intentions. The locker, walloping back, crimps the metal around his fingers like a vicious waffle iron. “Eeeeeeeeeeeeeee!’ He shrieks. Holding this frantic note impossibly long as he sprints through the halls. Holding his hand in front of him like a live bomb. Fingers protruding like from the mouth of the mangled duster like microwaved franks. “Eeeeeeeeeeeeeeee eeeeeeeeeee eeeeeeeeee...” Off into the distance.

[Roy Lotz · Rating 4 out of 5]

I’ve heard people wonder aloud (insofar as writing comments on the internet can be considered “aloud”) whether a layperson could understand this book. Well, take it from me, a certified layman, that it can be done; it is difficult, but doable.

Before the review, some advice. This book pushes forward quickly; the reader, especially the struggling reader, will be left far behind if she isn’t careful and thorough. The beginning lectures, up until about the middle of the book, I found fairly easy; S&H even give the mathematically rusty reader some refreshers on trigonometry, calculus, and a bit of linear algebra, too. (These ten-page “interludes” will likely be insufficient for those doing calculus for the first time; I used Khan academy to brush up on some math beforehand.) The second half, however, gets hairy fast—especially if, like me, this is the first time you’ve done physics since high school.

Here’s my advice if you find yourself struggling with a chapter. First, read it through to the end, even if you don’t understand it. This way, by skimming through the material, you at least know what they’re trying to teach you. Next, if you’re really stumped, look up the pertinent lecture online, and watch it. (Note that the #s of the lectures online don’t necessarily match the #s of the chapters in the book.) After you’re done with the lecture, go through the chapter slowly, taking careful notes. You’ll recognize the exercises as things Susskind did during his lectures, and you should be in familiar waters after seeing how Susskind solved them.

Now for the review.

The title of this book should have the word “Minimum” underlined twice and in bold font; they really mean to teach you the absolute minimum, and nothing more. This gives the book a strange, somewhat disorienting, breathless feel—like they’re sprinting through the material just to get to the end. Often, a fundamental concept will be explained in a single sentence; complex mathematical relationships will be taught in a few pages. (The last chapter was particularly daunting, as they compressed the final two of Susskind’s online lectures into a twenty-page dash to the finish line.) Just when you feel like you finally half-understand what they’re talking about, they’re off to the next thing. I’m really not sure why they felt such a need to rush. (I often got the impression that the book was aimed less at teaching Classical Mechanics, than at laying the groundwork for Quantum Mechanics; maybe Susskind finds CM a little boring?) This book is a skimpy 220 pages; and, what with the large margins, large font, and wide spacing, there isn’t much writing per page. In short, this book is short—maddeningly short.

In fact, the aforementioned difficulty of this book was hardly at all due to the mathematics—which were surprisingly easy, even for me—and much more due to how quickly they were explained. Why not elaborate? Just a little? The one-sentence explanations of things often took on a distressingly Delphic quality; I felt like I was trying to read meaning into the oracular utterances of the authors.

Aside from the rushed style of the mathematical explanations, there is a complete lack of discussion in the book. How do these equations apply to reality? I haven’t a clue. Even the equations themselves stay at a very abstract level; he never plugs numbers into his equations in order to demonstrate how they might be used in a concrete situation: they remain abstract summaries of relationships, and nothing more. The unwary reader might get the impression that physics is not a science at all, but is simply a bunch of algebraic manipulation. This is concerning.

A third flaw of this book is perhaps trivial, but perhaps diagnostic: it’s sloppy. One can look up an enormous errata file for the hardcover version of this book online. Thankfully, in my paperback, most of these have been corrected. Even so, some odd errors remain. Consider this marred sentence (I’ve given part of the preceding one for context):

… there are two separate concepts: mechanical momentum and canonical momentum. Mechanical momentum is what you learn about in elementary mechanics (Momentum equals mass times velocity) and in advanced mechanics (Canonical momentum equals derivative of the Lagrangian with respect to velocity).

Does that sentence make you scratch your head? How does that second parenthetical relate to the sentence at all? Without the parentheticals, the sentence only mentions the mechanical momentum; the explanation of canonical momentum comes out of the blue. It’s obviously missing something. Let me fix it:

… there are two separate concepts: mechanical momentum and canonical momentum. Mechanical momentum is what you learn about in elementary mechanics (Momentum equals mass times velocity) and canonical momentum is what you learn about in advanced mechanics (Canonical momentum equals derivative of the Lagrangian with respect to velocity).

That sounds better, right?

I’m not just being pedantic; there are many little errors like that which I caught, some within the actual mathematics. (The exercise solutions online are much, much worse.) This is very annoying if you’re in a position like me: forced to read the book with extreme care, in order to keep up with the relentlessly fast pace.

I believe the following is the explanation for all of the above flaws: Susskind merely handed Hrabovsky his lecture notes, and asked him to turn them into a book. In his lectures, Susskind himself comes across as (to put it mildly) not detail-oriented. Hrabovsky, who assembled the garbled solutions to the exercises online, must also be a bit messy. Perhaps this is a common foible of mathematical physicists. In any case, the quick pace, the lack of discussion, and the sloppiness of the book are, I think, due to its genesis as lecture notes.

So why, then, am I still giving it four stars? Well, for one, I just like a challenge; and believe me, understanding a book so Delphic, so fast-paced, and so mathematically-oriented was a challenge for someone with my background.

But, challenge aside, I think this book also has a valuable place in the spectrum of books available for the layperson. This is because what Susskind does, he does very well—namely, teaches the fundamental mathematical relationships. For all it lacks in thoroughness and ease of use, this book makes up for in elegance: it gets to the heart of the matter, without wasting a single word.* Susskind is impressed, infatuated even, with the mathematical symmetry and balance of the structure, by the interconnectedness of its parts, and by the ease with which complex systems can be summed up in a few symbols and variables. This love of elegance is infectious; and the dutiful student will find herself, during brief flashes of insight, with a similar admiration for this elegance. And, perhaps even more impressive, Susskind manages to make it all look easy!**

[On to Volume II!]


*Sometimes, this makes Susskind have to be a bit vague and imprecise with the math; there were some mathematical manipulations in here that would have made a strict mathematician go red in the face.

**Though Susskind does have the bad habit, deplorable in a pedagogue, of calling things 'easy' or 'obvious'. When he does so, the struggling student is doubly distressed—"this is supposed to be easy? obvious?" Teachers should refrain from calling things 'easy'; it's the students who decide that.

[WarpDrive · Rating 5 out of 5]

This is a great book.
- Perfect level of detail: the book provides an accurate and elegant quantitative description of advanced classical mechanics based on the actual mathematics, but without being bogged down into un-necessary detail.
- The authors provide a rigorous mathematical treatment of the subject, but they manage, always, to beautifully highlight the elegance of the main concepts: for example, they make the reader thoroughly appreciate the beauty of the Lagrangian and Hamiltonian approaches, and the sheer elegance and power of the Poisson Brackets. These were all concepts I was already familiar with, but the authors in this book made me really appreciate them in their full splendour.
- This book is a great support to the legendary and enormously popular online continuing-education course lectures by the main author (series of courses called "The Theoretical Minimum"), but it can also very easily used as a stand-alone book.
- Overall, this book has been for me a continuing source of intellectual pleasure. Highly recommended to anybody who loves physics and mathematics. A great introductory / intermediate-level step.
- Only a couple of small annoyance: 1) a few typos (but they have been addressed in the supporting website http://www.madscitech.org/tm/). 2) And a couple of hand-waving sentences that an orthodox mathematician would likely take exception to.
- And, finally, let's briefly describe the main author, Susskind himself: I am a fan of him, he has the most impressive background and he is clearly a genius; moreover, he is a great teacher, an inspiration, and a generous individual willing to publicly share his knowledge.

[John Gribbin · Rating 5 out of 5]

Are you one of those people who enjoyed science at school or college, but ended up with a different career, still wondering what makes the Universe tick? Maybe you subscribe to Scientific American, follow news stories about black holes, and read reviews of science books in WSJ without quite finding enough meat to satisfy you. If so, The Theoretical Minimum is the book for you. The subtitle “what you need to know to start doing physics” sets out the authors’ stall, and the “minimum” referred to in the title is the minimum amount of knowledge you need about classical physics (that is, everything except quantum mechanics) to proceed to “the next level”, which would be freshman physics at university.

Leonard Susskind is a Professor of Physics at Stanford University, and more widely known as the author of The Black Hole War and The Cosmic Landscape. George Hrabovsky got sidetracked from a possible career in science, but even without a science degree ended up running a technological research center, Madison Area Science and Technology.

Their book grew out of a course taught by Dr Susskind at Stanford University, for local people in what he calls “the nonacademic community”. He found that these students, eager to learn but with no need to worry about grades or exams, wanted “the real thing -- with equations”. And he gave it to them. But don’t be scared by that word “equations”. If you understand stock market derivatives or futures trading there is nothing here to worry about -- provided you start at the beginning and follow the story methodically.

That is where Susskind, aided by Hrabovsky, is so good. Their relationship began when Hrabovsky viewed Susskind’s lectures online, and sent Susskind an email suggesting that the course should be turned into a book. The resulting collaboration between master and pupil follows the structure of the lectures themselves, and is perfect for getting the message across. The beginning is disarmingly simple. It doesn’t start with anything as complicated as a coin toss, but with a coin glued to the table so that it always shows the same face uppermost. What could be simpler? But by the end, the committed reader will be familiar with Maxwell’s equations of electricity and magnetism, and have a thorough understanding of the force of gravity and its influence on planetary orbits, the work for which Isaac Newton is justly famous. Along the way you get beautifully clear explanations of famously “difficult” things like differential and integral calculus, what physicists mean by symmetries, and conservation laws. In spite of the emphasis here on classical physics, this actually takes the reader to the edge of an introduction to quantum mechanics; we can only hope that this will be the theme of the team’s next book.

More subtly, along the way the authors expound what might be called the philosophy of science, making it clear why physics contains deep truths about the Universe. The job of classical mechanics, they say, “is to predict the future,” which it does with far more success than alternatives such as astrology or the I Ching. They explain what scientists mean by terms such as “system” and “reversibility”, and are not afraid to spell out the limits of precision. Even if some of the equations do pass over the heads of some readers, this is a powerful exposition of why science is “real”, and a counter to the kind of wishful thinking employed by people who, for whatever reason, reject the scientific world view.

At the heart of this book, both physically and metaphorically, is the principle of least action, the most important idea in physics. It can be summed up in the phrase “the Universe is lazy”, and among many other things, the principle underpins the reason why light moves in straight lines, and how light “knows” which angle to turn through when it moves from one medium (such as air) to another (such as glass). It can be used to describe the parabola followed by a thrown baseball, and indeed, to derive Newton’s laws. If I had my way, all of physics would be taught starting with the principle of least action and working outwards from there; The Theoretical Minimum comes close to realising my dream.

Which brings me to the audience for the book. It most definitely hits the spot for the kind of mature, committed “nonacademic” that the authors have in mind. Equally, it is certainly not for the dilettante science watcher happy with the kind of “pop science” accounts” that deal as far as possible in words and images without worrying about the equations -- not that I am knocking that kind of book; I write them myself. But it is also just the right book for a much younger audience than the mature people with careers behind them who filled the classes at Stanford. It is spot on for any young student of science to read up before heading off to university to study physics seriously, and I shall certainly be recommending it in that connection. It should also be required reading for our politicians and lawmakers -- but that is probably hoping for too much.

This review first appeared in a slightly different form in the Wall Street Journal.

[Sean · Rating 3 out of 5]

While physics does indeed boil down to these basics, the reader needs to come into this book with both a serious physics background and multiple semesters of calculus (partial derivatives, differential equations).
Ch 1 does Simple Dynamical Systems and the Space of States. (I think the word 'simple' simply appears too many times in this book). Ch 1 has a math Interlude to quickly review/teach Spaces, Trigonometry and Vectors (vector notation, add/sub, lengths in 3-d, dot product).
Ch 2 does motion, but you need to be casual about always seeing 'a', acceleration, written as the 2nd order derivative of displacement, or the first derivative of velocity. The math Interlude starting on page 47 teaches Integral Calculus. We're ready to start Ch 3, and we've covered ~2 semesters of calculus review and expressed motion in its purely differential form.
Yes - all this is true. But I've taught AP C High School Physics, and this book would scare them out of wanting to major in this field that I love. These lectures might work for a very sharp university incoming freshman class who all got 4's and 5's on the AP C Physics (both Mechanics and the E&M).
Ch 3 is Dynamics (F=ma, but the last page in the chapter has the 2nd order differential equation for simple harmonic motion: d2x/dt2 = -(omega)^2 x, followed by an Exercise: "Show by differentiation that the general to this equation is given in terms of two constants A and B by x(t) = A cos wt + B sin wt. Determine the initial position and velocity at time t=0 in terms of A and B".
This is easy for me - but I'm a physics major/teacher. This would crush 99+% of people.
Actually, I'm tutoring a 10th grader right now that could do this problem in 8th grade (when I finished tutoring him completely through the entire Giancoli AP B textbook). He kept asking additional calculus questions, which he learned to master quickly.
To help you in this chapter 3, the "Interlude" covers Partial Differentiation (using 3 dimensions).
Exercise 1: Computer all first and second partial derivatives - including mixed derivatives - of the following functions(x/y)e^(x^2+y^2), e^x cos y.
Again, piece of cake if you taught AP C Calculus, like I have.
The subsequent chapters on Lagrange and Hamiltonian are just as simply great. And if you loved physics and calculus and remember it, you will like these chapters.
The name of the book should not have the 2nd part of the title: "What you need to know to start doing physics". (or reword this)
These concepts in this book are completely covered by the third semester of college physics (1:Mechanics, 2:Electricity & Magnetism, 3:Analytic Mechanics (Lagrange/Hamiltonian).
I will actually actually show this book to this 10th grader (who is destined for MIT), and he will enjoy it. But someone picking up the library book will most likely put it back on the shelf.
I would give 5 * if this book was titled to be picked up by the proper SERIOUS physics student. I have to give 3 because the content does NOT match the "start doing physics" in the title.

[BetseaK · Rating 2 out of 5]

This book is useful if you want to refresh the pre-existing knowledge but it is not an effective learning tool for “anyone who has ever regretted not taking physics at college”. Namely, this is not the book for someone who wants to learn from scratch.

[Jack Laschenski · Rating 3 out of 5]

Despite my education, far beyond my ken.

However, the book has caused me to start studying calculus again at the Khan Academy!!

[Tomislav · Rating 4 out of 5]

In physics, I have found the word “classical” to be relative. While the entire content of this book is classical mechanics, that would mean everything before quantum mechanics and relativity. What I previously thought of as classical mechanics was what I had learned in engineering school many years ago - as done with that sort of calculus devised by Leibniz and Newton. However, that is preparatory, and before quantum mechanics, there is a necessary recasting of physical principles into Lagrangian and Hamiltonian mechanics. So, the first half of the book was review as I expected – but the second half was new and more challenging. There have been two follow-up Theoretical Minimum books since this was published – Quantum Mechanics: The Theoretical Minimum, and Special Relativity and Classical Field Theory: The Theoretical Minimum, which I have not read and for which it is now obvious this is a prerequisite. They are all advertised as learning books, but I found them to be too densely packed for that in the sections that were new for me. I can follow the new material, but retain and use for problem solving? I need a more overtly instructional approach for that.

However, the half that was review for me worked well as a refresher, and I expect the same could be true in the second half for readers further educated than myself in this field. The folksy introductions tell you how to think about what you about to dive into, but were sometimes distracting. There are exercises that are more than practice problems; they develop topics not covered didactically. Read them and solve them! I came to this book, tired of the kind of “physics” books that explain through analogy, and conceptual debates that seem more like belief systems. Refreshing the math has been a pleasant experience, but it takes quite a bit of time – and I have a distance to go before I reach the juicy stuff. I recommend the book to the appropriate audience, but knock it down a bit for the misleading advertising. Here’s the table of contents.

1 The Nature of Classical Physics
2 Motion
3 Dynamics
4 Systems of More Than One Particle
5 Energy
6 The Principle of Least Action
7 Symmetries and Conservation Laws
8 Hamiltonian Mechanics and Time-Translation Invariance
9 The Phase Space Fluid and the Gibbs-Liouville Theorem
10 Poisson Brackets, Angular Momentum, and Symmetries
11 Electric and Magnetic Forces
Appendix 1 Central Forces and Planetary Orbits

There is a companion website for this book at http://www.madscitech.org/tm/, which contains Solutions to Exercises of Lectures 1-6 and Errata for both the 2013 and 2014 editions. The errors in the 2013 edition are extensive, so I recommend the 2014 edition. The PDFs are good enough to determine if this book is something you want to get into, but to best view the CDF solutions, you should download and install the free Wolfram CDF Viewer from http://www.wolfram.com/cdf-player/

In addition, you can watch lectures by Leonard Susskind from a related course at Stanford for free at http://www.theoreticalminimum.com/cou.... The first half of the book is covered in just the first two ninety-minute lectures, and then they jump up for remaining eight lectures.

[Dale · Rating 5 out of 5]

This is a book I've wanted for a long time. Being many years out of college, and having forgotten everything I once knew about theoretical physics (which, sadly, was not nearly as much as I thought I knew), I have been looking for a way to refresh my knowledge. This little book is that way.

It's intended for people who have some mathematical background, and it is definitely not easy going, despite the lighthearted style of the book. You really do need to do the exercises, and it helps to watch the lectures online. And I guess it wouldn't hurt to supplement this book with an actual physics text if you plan to pursue the subject further. But as a guide to the actual mathematics of physics, this book is superb.

The book intersperses "mathematical interludes" with the physics. The interludes are short-form introductions to the necessary mathematics (derivatives, integrals, partial derivatives, etc.). By the end of the book you will be introduced to Hamiltonian mechanics and Poisson brackets - pretty advanced stuff, I think, for an introductory classical physics book!

[Rama Rao · Rating 5 out of 5]

An easy guide to learn classical mechanics

This is one of the best books to learn the math behind classical physics. Written beautifully by Stanford University Professor Lenny Susskind, and George Hrabovsky, it provides strong introduction to classical dynamics/Newtonian physics for college-level students of physics, chemistry, engineering, philosophy, and others interested in understanding the physical reality.

This book begins at the simplest level. It develops the basics and reinforces fundamentals, ensuring a solid foundation in the principles and methods like calculus. Vectors, integral calculus, and partial differentiation (dynamics) is introduced at the basic level. It is very well explained to do math. The highlight of the book includes space and time (coordinates), particles (matter), energy (kinetic and potential), motion in spacetime coordinates, momentum, electric & magnetic forces, force of gravity, acceleration, and energy. Application of Newton’s laws of physics, principles of least action, symmetries, conservation laws, Hamiltonian mechanics and invariance of time-translation are fascinating. You have everything you need to get mathematical perspectives of classical physical reality.

I read the book from beginning to end; and revised a second time, I got a much better understanding of the calculus. There are companion videos on YouTube from Lenny Susskind which is helpful. Mechanics and calculus are also described by many other physicists on YouTube that also assist in your learning experience. You can do this at your own pace. This book is enjoyable to read, and it is highly recommended.

[Giulio Ciacchini · Rating 4 out of 5]

A tough read, but accessibile
It is a fascinating attempt to bridge the gap between popular science and real physics. Unlike most accessible physics books that stop at metaphors or thought experiments, this one aims to teach you the math and logic you actually need to start “doing” theoretical physics, hence the title “Theoretical Minimum.”
The book starts from the ground up: what is a state, what does it mean to observe something, how do we describe motion. Then, slowly and clearly, it gets complicated and it builds up to the machinery of Lagrangian and Hamiltonian mechanics, the real backbone of modern physics. He doesn’t hide the math behind analogies or metaphors.

It’s definitely not a light read. You’ll need to stop, think, and probably re-read a few passages with a pencil in hand. But the effort pays off, once you start seeing how these ideas fit together, physics begins to look less like a mess of equations and more like a deeply logical, almost poetic structure.

The key topics covered include:
The mathematical language of physics - calculus, differential equations, and how they describe change.
Newtonian mechanics reinterpreted through energy principles.
The Lagrangian and Hamiltonian formalisms, which are the backbone of modern physics.
Phase space, symmetry, and conservation laws (Noether’s theorem in essence).

P.S. the last chapters were a bit too complicated for my knowledge

[Myat Thura Aung · Rating 5 out of 5]

This book is a condensed version of the Standford lectures on classical mechanics by Leonard Susskind. (The videos are available on Youtube.) It offers you the minimal theoretical knowledge to advance to the next step, quantum mechanics. If you are dissatisfied with what most pop science books are offering you but can't afford time and energy to read fat textbooks, then this is definitely for you. It might be quite challenging if you're not so familiar with math. But if you really wanna get serious, then don't you shy away.

[Murray Cumming · Rating 4 out of 5]

If I had read this at 18 it would have driven me to continue studying mathematics and physics. Instead I had no idea what might come next. All this time I've been oblivious to the Lagrangian and Hamiltonian (deep abstractions that apply to all physical laws including quantum mechanics), and had never heard of the vector potential (gauge fields). This book isn't perfect but I'm grateful to the authors for enlightening me. Maybe there are better books that cover the same stuff and maybe I'll find them now.

I'd studied Mathematics, Further Mathematics and Physics (and others) at (British) A Level, and I've revised the maths a couple of times over the years. But I was still missing some linear algebra (dot products and cross products of vectors - not the same as regular matrix multiplication) needed to understand the ideas of divergence and curl in the last chapter about electric and magnetic fields. Luckily Khan Academy had a useful video:
https://www.khanacademy.org/math/line...
and I found a helpful video about gradients, divergence and curl from the Open University:
https://www.youtube.com/watch?v=ynzRy...

There are some unnecessarily sudden jumps from equation to equation, without showing the steps. So it took me a few tries to get through the initial Principle of Least Action chapter that introduces the Langrangian, with repeated views of the source lectures on YouTube:
https://www.youtube.com/watch?v=h96SW... (and the next one)
I would have liked more hand-holding.

The reasoning also seemed rather circular at times, which makes sense when showing that an idea is consistent, but I think it should have had a clearer focus on when it's trying to prove an idea, leaving the mere exercising of the ideas as secondary.

Unfortunately, the formatting in the Kindle version is almost intolerable. Every formula, and many single symbols, are tiny faint inline graphics. I would have gotten through this book more quickly without having to struggle with them.

[Jsrott · Rating 3 out of 5]

This is not a book for the physics "enthusiast." It runs through some pretty hefty mathematical mechanics in pretty short order, but does a decent job of that. Most of the time I was reading I was thinking "gee, I remember being able to do that at one time," and "oh yeah, I remember learning about that." I wish they had provided solutions to the exercises they gave in each chapter, if only to verify you actually did understand how it works. It's short on explanation and the bigger picture, but from the ending I suspect there's going to be an additional volume coming out that perhaps finishes what this book starts. Unless you've had training in advanced calculus, I'd probably recommend going somewhere else for an introduction to physics. If you have, it's a pretty decent summary.

[Guillaume Belanger · Rating 3 out of 5]

Interesting, but I would never qualify the book as accessible. I studied Physics in my first degree. Then did a masters in Particle Physics, and then a PhD in high energy Astrophysics, and there are things in there that I had never encountered. So, just to say, I liked it because it was a nice review of things I studies a long time ago, but I can't imagine anyone without a technical background reading this book and understanding much. In addition, I found some of the "simple" explanations confusing and overly complicated. I bought his book on Quantum Mechanics at the same time, and will read that one as well. We'll see...

[Jake · Rating 5 out of 5]

As an undergraduate in computer science/data science having to take classical mechanics was quite a slog. Nothing about the logic of classical mechanics in aggregate was intuitive to how I think about the world, unlike many of my peers. I thought I was doomed to think this way about the rest of physics. Instead I've found that after Classical Mechanics, EM and GR is coming much more organically. I began reading this after doing much reading on EM and a bit of GR. This book was a simple review of much of what I'd learned up to this point in physics but with new notation I was unfamiliar with. The first new material for me started in lecture 6, after a bit of work it made a lot of sense, after that my knowledge was sparse so it was nice getting to some new material.

I did reading of this book along side the set of lectures by the same name by Leonard, which can be found here. The book was more of a resource for those with rusty calculus and little CM knowledge I found, but as an undergraduate who is forced to run the calculus gauntlet it was quite enjoyable and simple to follow. The lectures have much more linear algebra and statistics, which seems to be a disconnect with much of the pedagogy surrounding STEM fields in general.

My big take away from this book is that my brain is geared toward thinking about QM much more than CM. I gained many insights from this book and set of lectures that are not only applicable to physics but my career I'm pursuing. Susskind's first postulate for instance is something anyone taking linear algebra should be taught. It is one of those things that the entire subject seems to be funneling toward, that is an immediate simple check that anyone doing math in the modern world should be able to do and should do. I also learned who Emmy Noether was from reading this book which was a delight.

I highly recommend this book but with the caveat of the lectures along side it. It was well written, succinct about a subject and field where that is not the norm. I would particularly recommend it for those, like myself who do not like Classical Mechanics. It might just help change your view that there is a much more modern way of thinking about this beautiful subject. I also recommend it for those looking for a thought process or method of thinking about difficult problems in productive ways. Read the book, watch the lectures, "deal" with the notation, and do the exercises.✌

[Angie Reisetter · Rating 4 out of 5]

An elegant, well-written book. In the first 50 pages or so, Susskind introduces integral and differential calculus, as well as multi-variable calculus, so that he can conduct his discussion of classical mechanics on a high level, so that its beauty and simplicity is clear. I really appreciate this approach.

What baffles me is that this was a NYT bestseller. Who's reading this? The introduction to calculus is cursory -- I imagine it serves best as a review for those who have seen it before. And there are pages of equations that must be slowly worked through to understand what he's getting at, if you don't already know. So it breaks all the rules of a popular science book. Is it really for engineers hoping to brush up on their basic science? Those who have taken calculus and physics, but it was a long time ago, so they want to revisit it? Are there enough of those people to make it a best seller?

Hey, I'm not complaining. This book is at the advanced undergraduate/beginning graduate level of classical mechanics, and if Susskind can make that popular, more power to him. That's fantastic. And from a physicist's point of view, this is really a beautiful book. I'm just not sure what all those folks out there are getting from it. Hopefully enough for them to see some beauty in the math and science. And maybe, just maybe, this is proof that people aren't as adverse to math as we like to think? I'm not sure.

[Thomas B · Rating 3 out of 5]

What is the theoretical minimum of understanding a text necessary to log it as “read” on goodreads without lying?

I can tell you that my eyes touched every word in this book. I can’t tell you how many of the typed elements penetrated the various parts of my eyeballs and how many of the equations were lost on their way through my nerves and into my brain. I was not a strong maths student, and never had a pre-Calculus class let alone Calculus. So, many of the equations in this book were essentially static to me.

I read all of the prose(?). But much of this prose broke down the equations—unfortunately not in a way that could make much sense to me. I thrived on the parts of the book that explored concepts more than the parts focusing on calculus.

As it turns out, the theoretical minimum to start doing physics is more than the practical maximum of my maths competency. The fault lies with me, not the book. I do think with a primer to *Calculus*, I could figure this out, but not in this form.

[Douglas Ross · Rating 4 out of 5]

Let's be clear, I will never be able to "do" Physics at anything even remotely approaching Susskind's level. But, what I loved about this book are the little nuggets of common sense interspersed in the mathematics that help (me at least) understand Physics better conceptually. The book reminded me of the good fortune I had in the 1960's to be introduced to Physics by Dr. Robert Packard, the much beloved Physics professor at Baylor University for over fifty years. Dr. Packard taught us that the really important principles of Physics are usually "elegantly simple" ideas despite the chaos and complexity involved in proving them. It may not have been his intention but Susskind has done something similar with this book.

[Rachael · Rating 5 out of 5]

Yes! This book is awesome. I borrowed it from the library, but I believe I will buy a hardcopy and get the next one on QM as soon as it comes out late this month. The Theoretical Minimum has elegantly overviewed the basics of classical mechanics, through a focus on the Lagrangian and Hamiltonian, equations of motion, symmetries, in a way that is clearly preparatory for QM. I have a new appreciation for how many concepts tie together in a way that were left un-unified before.

That being said, this isn't really a book for beginners. If you really like physics, have had some previous exposure, and know some calculus, you can do this. Problems are included and should be worked through as you go along.

[Santiago Ortiz · Rating 4 out of 5]

This is not a book to be read in 4 days (I read this book in 4 days).

[z · Rating 3 out of 5]

I'll come back to this after I revise math :( dnf but it's not you baby it's me

update: ok but now that I look at an actual textbook this book is way too compressed from the lagrangian onwards

[Midiam Daniela · Rating 4 out of 5]

No creo que este sea como tal un libro de divulgación científica, pues el lenguaje es un poco más técnico e introduce material que se encuentra en tratados escritos a un nivel más avanzado en el espacio de unas pocas páginas e incluye ejercicios manejables (de los cuales puedes encontrar pistas y soluciones detalladas en el sitio web del libro), sin embargo no hay que suponer que para estos no se necesita ningún esfuerzo, si requerirá cierta familiaridad con las matemáticas y la física que el autor introduce a lo largo del libro.
Lo que más me parece que es lo atractivo de este es que te da una apreciación de las formulaciones más generales de la física clásica que son inestimables para los científicos en general. Claramente no te convertirás en un físico teórico sólo con leer este y los otros dos que siguen, pero si te interesa la física (no sólo la teórica), el libro te informará sobre los conceptos utilizados en la física, cómo los físicos los manipulan y cómo los físicos hacen matemáticas.

[Matthew Emery · Rating 5 out of 5]

I wish there were more books like the Theoretical Minimum. I have a bit of a background in mathematics, and I've always been interested in physics. I have often found myself frustrated by popular physics that attempt to hand-wave the mathematical reasoning behind some physical phenomena. It usually leads me to more confusion.

The Theoretical Minimum is not that type of book. In a short amount of time, Susskind builds from the basics of Newtonian mechanics to more advanced concepts like Lagranian and Hamiltonian mechanics. If those terms scare you, they shouldn't! They are just another way of looking at a physical system. I would recommend that people reading this book have a solid background in first-year calculus and maybe a little bit of linear algebra and probability theory. Even if you don't, you will likely gain from struggling with this book than you would from breezing through 3 or 4 books in a similar genre.

A tip: there are accompanying (and entertaining) lectures by Susskind available here: https://youtu.be/ApUFtLCrU90 They are helpful, especially near the back half.

[Robert Hare · Rating 5 out of 5]

Incredibly eye-opening. I’ve taken quite a few physics classes, but this book single-handedly taught me more about classical mechanics than any class I’ve ever taken. If this is what you’re into, I would definitely recommend it.

[James F · Rating 4 out of 5]

This is definitely not all that you need to know to do physics, but it helps in understanding it. It is based on an online video course, which I haven't looked at; this is just about the book as it is in print. The premise is the same as that of Penrose's The Road to Reality which I finished a few months ago, to teach enough math along the way to actually understand the physics rather than just some quantitative concepts as in most "popular" science books. This book is much less technical than Penrose (although to be fair this is only the "classical" volume and the quantum physics volume will undoubtedly be more technical), and explains things in a more step by step way; where to really understand Penrose you need to already know a lot of the math, this really starts from what most people already have, high school algebra and trig and explains what you need -- the minimum of derivatives, integrals, and partial derivatives, then explaining the physics. Only the last few chapters went a little too fast for me -- from vector spaces through gradients, divergence and curl. Perhaps because my college calculus course rushed through these at the very end and so they were basically new, where the rest was more review.

When I took first year (classical) physics in college, there was one older student in the class who kept complaining that the course was described as "calculus-based" and really wasn't; I didn't understand at the time what he meant, because compared to my non-calculus high school physics class it was using derivatives and integrals and even partial derivatives toward the end. But after reading this, I understand the difference -- he meant there were no Lagrangians, no Hamiltonians, no concept of Action. This is a whole different way of looking at physics than I was taught. Unlike after reading the Penrose book, after reading this I feel that I (mostly) got it. I intend to go on to read the second book on quantum physics (there doesn't seem to be a printed book covering the lectures on relativity.) I would suggest reading these first, then trying Penrose. But as with the Penrose book, it mainly inspired me to get on with the project of reviewing my math and trying to teach myself more from actual textbooks -- from these books I think I have some idea of what pathway to follow. (I'm thinking: review college calculus; real analysis; complex analysis; topology; vector calculus; [start physics here]; group theory; tensor calculus; calculus of variations . . . if someone who has majored in math or science could correct me before I get too far down the wrong path, it would be appreciated!!) Of course, at my age I probably won't get to the physics at all, but it may help stave off the mental decline for a few years.

[Tom Schulte · Rating 3 out of 5]

...This work presents classical mechanics including conservation laws, Hamiltonian mechanics, and planetary orbits. Such focus is appropriate for a book under two hundred fifty pages. There are little to no mentions of relativity, quantum mechanics, and string theory. This allows room for the clear description of advanced classical physics concepts. Somewhat surprising, the authors also use that room for the breezy and humorous. I challenge anyone to show me a book that can skip from a groaner joke about George and Lennie from Of Mice and Men discussing physics to Poisson brackets in a single page. This is an excellent work for its intended audience and the authors succeed in making the material concise and easy to read. I am very glad to see that future volumes are promised. I do have to say that in the age of LaTeX typesetting is at times surprising how careless some of the mathematical typography is. Dots notating differentiation are absolutely untethered from their function and exponents drift about in a disconcerting manner.

[See my entire review at MAA Reviews]

[João Ritto · Rating 4 out of 5]

Books for non-physicists on the subject may vary in style but typically have one thing in common: they skip the math. This is precisely what this book tries to make up for. In a few hundred pages the authors attempt to give an introduction of physics for a lay reader not sparing the use of equations.

If your field is not physics but you are relatively comfortable with calculus (my field is economics, for example, and I could skip most of the mathematical appendices), this book may give you some understanding of the math behind this challenging, yet intriguing and fascinating subject.

Personally, I found that in the second half of the book, it went a little too far in its focus in math. Because it wanted to be short, the last chapters, from Lagragean mechanics onwards lacked a little bit of discussion of concepts, results and intuition and though I wanted the math I also wanted a better understanding of things, which I found hard to get... Perhaps I wanted too much from a book that was not long enough. Good treatment of the subject, either way, and a good start (at least) for a lay reader interested in the math of physics.

[Maya · Rating 1 out of 5]

I am not sure what the point of this book is. It claims to introduce the necessary material of a first course in physics, including the relevant mathematics, but it instead seems to cram two years of math into ~200 pages and then go straight to advanced mechanics. While it's supposedly appropriate for a dedicated lay reader, how anyone who doesn't already have a STEM background is expected to make sense of this book is a mystery--I have taken calculus, diff eq, analysis, etc. and I was completely lost after 80 pages or so. Newton's Laws of Gravitation get a passing mention in the appendix. If this is a "first course," I suppose there must be some zeroth course lurking about that they expect you to take first. Either that, or the book is really meant as a textbook to go with the online lectures from which it was originally derived.