The Book is Out!!!

Well, the book I wrote with Leonard Susskind, The Theoretical Minimum, is out and is a huge success! Thanks to all of you who have been following this! You can find the web site to support the book at www.madscitech.org/tm.

The Web Page for The Theoretical Minimum is Up!

The web page for The Theoretical Minimum is up and you can see it at: www.madscitech.org/tm.

More Information on the Book

I just finished working over the proofs for the publsher. It is now in their hands again. The next step is the Galleys, and then back to the publisher again. The book is scheduled to be out in January 2012.

Been Away Again

I have been away for a couple of months. In that time my co-author on the book, Leonard Susskind, and I have been working on the final draft of our book THEORETICAL MINIMUM: Claswsical Mechanics and hope to have it done in a few weeks.

MAST is working on developing education modules for basic science.

I have had a paper on numerical modeling of the diffusion equation accepted for publication in The Mathematica Journal.

I will be working on the show The Wonders of Physics this year.

I will be doing more in the coming days.

Book Deal

Today I received the executed book deal for my collaboration with Leonard Susskind on the book Theoretical Minimum: Classical Mechanics. The book will be published by Basic Books. We have until January of 2012 to finish it, but don't be surprised if we finish early.

Book News

Leonard Susskind and I have now signed a contract with Basic Books for the Theoretical Minimum: Classical Mechanics. This book is contracted to be completed by January of 2012 (don't be surprised if it is finished before then).

The Book Is DONE!!!

At 05:17 on Monday, 31 January 2011 I finished the first draft of the book Theoretical Minimum I: Classical Mechanics by Leonard Susskind and George Hrabovsky. This book was written in Mathematica 7 and Mathematica 8.

The Book is Almost Done!

I am almost done with the final two cahpters of the book I am writing with Leonard Susskind! I will be done by Sunday!

Book Project Update

Well here I am again. Sorry about the lengthy delay in posting, I am in a full-scale assault on the book to finish it by the end of this week. I have completed chapter 16, am finishing up chapter 15, and will finish 17 and 18 by week's end! The first draft is nearly done!

Here is the book now:

Lecture 1: Dynamical systems.

Interlude 1: Calculus.

Interlude 2: Newtonian mechanics.

Lecture 2: Conservation laws, the principle of least action, and the Lagrangian.

Interlude 3: Vectors and vector spaces.

Lecture 3: Conservation laws imply symmetry.

Interlude 4: Symmetry.

Lecture 4: Time translation symmetry, the conservation of energy, and the Hamiltonian.

Interlude 5: Transformations and matrices.

Lecture 5: Pendulums and springs.

Interlude 6: Complex numbers and ordinary differential equations. 

Lecture 6: The Hamiltonian method of mechanics. 

Interlude 7: Vector analysis.

Lecture 7: Liouville's Theorem and Information Conservation

Interlude 8: Thermodynamics (almost complete)

Lecture 8: Charged Particles in Electromagnetic Fields and an Introduction to Poisson Brackets

Interlude 9: Chaos (not done yet)

Lecture 9: Poisson Brackets and Canonical Transformations

Book Update

I have now completed 13 chapters out of 18!

Here is the chapter list so far:

Lecture 1: Dynamical systems.

Interlude 1: Calculus.

Interlude 2: Newtonian mechanics.

Lecture 2: Conservation laws, the principle of least action, and the Lagrangian.

Interlude 3: Vectors and vector spaces.

Lecture 3: Conservation laws imply symmetry.

Interlude 4: Symmetry.

Lecture 4: Time translation symmetry, the conservation of energy, and the Hamiltonian.

Interlude 5: Transformations and matrices.

Lecture 5: Pendulums and springs.

Interlude 6: Complex numbers and ordinary differential equations. 

Lecture 6: The Hamiltonian method of mechanics. 

Interlude 7: Vector analysis.

I am now working on Lecture 7: Liouville's Theorem and Information Conservation

Project Updates

Hello!

I have been insanely busy the last week. Had a great Thanksgiving!

Just completed Chapter 9 in the book project, this is a survey of linear algebra. I am about to start in on chapter 10, Leonard Susskind's classical mechanics Lecture 5.

I am also developing the program for the Institute for Scientific Computing Summer School program. I am also working on developing courses for teaching Mathematica 8 online.

That's all for now.

Book Project Milestone!

The classical mechanics book I am writing with Leonard Susskind has reached a milestone. As of now the page count stands at just over 100 pages! That is four chapters completed, the first two lectures, an introduction to calculus, and an introduction to Newtonian mechanics.

Blog Update

I have not posted for a couple of days because I am hard at work on transcribing Lecture 4 of Classical Mechanics. This is about symmetry and conservation laws.

I am also working on a book review for a book I received for review from CRC Press, Advanced University Physics.

Lots on my plate this week.

Book project update

I have just completed a 15 page chapter on calculus that covers limits, derivatives, integrals, differential equations, infinite series, and partial derivatives. This chapter is for the proposed classical mechanics book I am working on with Leonard Susskind.

I took a very minimalist approach to the subject. If you want to see how I crammed so much into so little, wait for the book... :-)

Actually, some of this material will likely find its way into my column (and I took some of it from my existing columns).

Secret Weapons of The Theoretical Physicist

Tonight I am thinking about a set of the most powerful techniques of the theoretist, classically called back-of-the-envelope calculations. These consitute two broad categories of methods.

The first is the method of estimation, where you use some basic reasoning abilities to determine a rough estimate of the quantities you are considering. For example, you want to estimate the number of hairs on someone's head. You think about it and decide that if you knew the area of the part of the head covered by hair, then knew the average area of a hair, you could figure it out. Then you make the necessary assumptions about the quantities (either by looking up the information, or by figuring it out for yourself).

The second is the ability to check the correctness of equations and to derive new equations by studying the relevant units of the quantities. All terms of any equation must have the same units. When you chaeck the terms, any that do not have the correct units are just wrong. By including powers of each quantity in each term and making sure all of the units come out the same, you invent a system of algebraic equations that can be solved. This gives you the necessary powers of each variable and shows you the structure of each term within a factor of a constant of proportionality. In this way you can learn what each term must look like. This allows you to invent new equations if you know the units involved. This is called dimensional analysis.

I will be writing about these ideas in my column in the coming weeks. I will also be discussing this in the Classical Mechanics book I am writing with Leonard Susskind.

Book Review: Mechanics, by Landau and Lifshitz

It is my intent to review every book in my store, below, so I will start with the first book in the store. You can purchase this book at my book store below.

This is the first volume of the classic Course of Theoretical Physics due to Lev Landau and the Landau Institiute of Theoretical Physics in Russia. These ten volumes were the subject of what Landau belived to be the required preparation in physics for any theoretical physicist.

This volume begins with a touching introduction to Lev Landau and his philosophy. It also lays out the prerequisites for this volume. To quote: "...ability to solve any indefinite integral that can be expressed in terms of elementary functions and to solve any ordinary differential equation of the standard type, knowledge of vector analysis and tensor algebra as well as the principles of the theory of functions of a complex variable (theory of residues, Laplace method). If you need this ackground I recommend Hassani, Mathematical Methods for Students of Physics and Related Fields, Second Edition.

The first chapter describes Lagrange's equations of motion from the starting point of generalized coordinates. This lays the ground work for a very nice presentation of the least action principle. Then there is a nice section of the Galilean transformations; it is important to realize that there is no discussion of special relativity in the book. The book then describes the Lagrangian of a free particle in Cartesian, spherical, and cylindrical coordinates. The final section of the first chapter not only discusses the Lagrangian of a system of particles, but nicely links Lagrange's equations to Newtonian theory.

The second chapter presents one of the most important aspects of theoretical physics, the conservation laws. This begins with a unified treatment of integrals of the motion, the conservation of energy, how conservation of energy implies the homogeneity of time, and conservative systems. This leads into the conservation of momentum, how the conservation of momentum implies the homogeneity of space, generalized momenta, and generalized forces. There is a brief discussion of systems of particles, the center of mass, and internal energy. This leads to a section on the conservation of angular momentum, how this implies the isotropy of space, and the idea of the central field. The final section deals with a couple of different topics such as the behavior of the equations of motion under transformations and the virial theorem.

The third chapter is a very practical one about applying the equations of motion to specific situations. This begins with one dimensional motion and a discussion of energy diagrams and oscillations. This leads into a discussion of how to interpret energy diagrams and derive the potential from a specific period of oscillation. The next topic covered is the beginning of the two-body problem in the form of the reduced mass of a system. The two-body problem is then reduced to a one-body problem in a central field in a very clear presentation. This leads to a nice discussion of the Kepler problem for bound and unbounded orbits.

Chapter four is an important discussion of the classical theory of particle scattering. This begins by the idea that particles can break up, this also introduces the lab and center-of-mass frames of reference. Then the authors describe elastic collisions in quite intuitive way. Then the notions of impact parameters and scattering-cross sections are covered. As an example of scattering due to fields, there is a section on Rutherford scattering. The chapter ends with small-angle scattering.

Chapter Five is on the theory of oscillations. Naturally, this begins with free oscillations in one dimension. The book then turns its attention to forced oscillations and resonance. Then the authors treat the idea of oscillations in more than one degree of freedom, including eigenfrequences and normal modes. This is then applied to the classical theory of molecules. Then damped oscillators are covered along with a discussion of dissipative functions in Lagrangian dynamics. The next section introduces dissipation and damped and driven oscillations. At this point the book leaves the realm of simple oscillating systems and goes into parametric oscillations and the Mathieu equation. There is a discussion of nonlinear oscillators, laying the ground-work for the study of chaos, this also includes a section of the resonance of nonlinear oscillators—introducing the Duffing oscillator without calling it that. Finally, there is an interesting section on the motion of a particle in a rapidly oscillating field.

Chapter six is a thorough treatment of rigid body dynamics. This begins with a discussion of the kinematics of rigid bodies. Then the authors introduce the inertia tensor. Indeed, this is one of the few sections in the book with more than a few problems (there are nine here). The section on angular momentum uses the axes of inertia to define angular momentum. Then the equations of motion for a rigid body are derived. This leads to the notion of Euler angles, which in turn leads to the Euler equations. These notions are then applied to the motion of a top. Then they shift gears a little and discuss rigid bodies in contact. Finally, and I think this might have done better at the beginning of the chapter, is a section on motion in noninertial frames, specifically rotating frames. This chapter seems very conventional, though it must be remembered that the first version of it came out in 1960, so a lot of other books are based on material found in here.

The final chapter is an overview of Hamiltonian theory. This begins, reasonably enough, with Hamilton's canonical equations of motion and relates the Hamiltonian and the Lagrangian in the normal way. The Routhian has its own section. Then they address the extremely important topic of the Poisson brackets. The next section establishes the idea of a functional without using those words. Then the authors discuss the principle of Maupertuis. Then they discuss canonical transformations and link them to Poisson brackets, and discuss conjugate variables, laying some of the groundwork for quantum mechanics. The authors next introduct the idea of phase space through a discussion of Liouville's theorem. The next section discusses the Hamilton-Jacobi equation and the idea of general and complete integrals. This is followed by a treatment of the method of separation of variables. Then the authors have an excellent and clear discussion of adiabatic invariants, a subject with applications in plasma physics. Then they discuss action-angle variables. Then the authors turn to the validity of the adiabatic invariant. The chapter, and the book, ends with a section on conditionally periodic motion.

The book, with all problems included, is just 167 pages long and comprises a total of 52 sections. This is something you could easily cover in two months of dedicated study. I think the book could use an update, but it's a classic as it is and its choice of topics are pretty good. I like it a lot, even if it doesn't really cover chaos in any meaningful way.

Brief on Calculus and Appreciation to Leonard Susskind for his Lectures

Hello everyone!

I have been working on the book project with Leonard Susskind. I just completed an 11-page overview of calculus with detailed material on limits, derivatives (including a short table of derivatives), integrals (with another short table of integrals), differential equations (covering mostly separation of variables), and Taylor series.

I am thinking of adding sections on partial derivatives, maxima and minima, and maybe curvature.

Of course, Leonard has not committed to anything yet; I certainly have not produced enough material to do more than whet his appetite for more. It is possible that something could happen to prevent me from finishing, and he probably does not want to stick his neck, or his reputation, out for someone who is not too well known.

I am having great fun writing this material. It is extremely challenging to develop short and clear explanations for these topics. My olf Mind of a Theorist column is good for this, the philosophy that Iadopted for the column is the same the Leonard has in the lectures.

To quote from the introduction, "What is this course about? Who am I teaching to? While undergraduate or graduate students will be able to read this, it is mostly designed for people who are interested in getting into the meat of physics right away. This is not a standard physics course. This is the real deal, theoretical physics at full scale! We use equations, and sometimes hard equations, but we try to use the simplest equations that will do the job. Basically, we try to keep it minimal. The goal here is to get to the basic ideas fast. So we will be telling you what you really, really, need to know to get to the next level. Sometimes the basics can be hard; we will do them anyway, but will only spend the minimum time required to get them right. And here we mean getting them really right, not by metaphors or analogies, but equations when necessary."

I am dazzled by the structure of the video lectures. In lecture one he introduces the ideas of dynamical systems, phase space, and conservation laws with no mathematics; just some diagrams and very clear explanations. Wonderful!

Wonderful Opportunity

I have begun converting Leonard Susskind's video lecture series on Modern Physics to book form. I have just completed Lecture 1 of the video course Modern Physics: Classical Mechanics and am now working on a chapter on calculus.

So far, so good. These are still early days, but I plan to convert them all in time.

Whether it becomes anything is, at this point, up in the air; we will see how it goes.

I am honored to be working with someone so passionate about providing a good resource on theoretical physics to enthusiasts. I am honored that he didn't just slam the door in my face! I am having a great time in converting these lectures, not only because I get to work with one of the giants of theoretical physics; but also because I am forced to think deeply about the meaning of the lectures and their context. It is a wonderful opportunity.

Thanks, Leonard!