The Feynman Lectures on Physics
Feynman •
Leighton • Sands
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mainly mechanics,
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Richard
Feynman, Robert Leighton and Matthew Sands, talking with a teaching assistant after the
lecture on The Dependence of Amplitudes on Time, April 29,
1963.
Photograph by Tom Harvey. Copyright © California Institute of
Technology.
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Copyright © 1963, 2006, 2013 by the California Institute of Technology,
Michael A. Gottlieb, and Rudolf Pfeiffer
The Feynman Lectures on Physics, Volume I
Preface to the New Millennium Edition
Feynman's Preface
Add caption 
The special problem we tried to get at with these lectures was to maintain the interest of the very enthusiastic and rather smart students coming out of the high schools and into Caltech. They have heard a lot about how interesting and exciting physics isthe theory of relativity, quantum mechanics, and other modern ideas. By the end of two years of our previous course, many would be very discouraged because there were really very few grand, new, modern ideas presented to them. They were made to study inclined planes, electrostatics, and so forth, and after two years it was quite stultifying. The problem was whether or not we could make a course which would save the more advanced and excited student by maintaining his enthusiasm.
The lectures here are not in any way meant to be a survey course, but are very serious. I thought to address them to the most intelligent in the class and to make sure, if possible, that even the most intelligent student was unable to completely encompass everything that was in the lecturesby putting in suggestions of applications of the ideas and concepts in various directions outside the main line of attack. For this reason, though, I tried very hard to make all the statements as accurate as possible, to point out in every case where the equations and ideas fitted into the body of physics, and howwhen they learned morethings would be modified. I also felt that for such students it is important to indicate what it is that they shouldif they are sufficiently cleverbe able to understand by deduction from what has been said before, and what is being put in as something new. When new ideas came in, I would try either to deduce them if they were deducible, or to explain that it was a new idea which hadn't any basis in terms of things they had already learned and which was not supposed to be provablebut was just added in.
At the start of these lectures, I assumed that the students knew something when they came out of high schoolsuch things as geometrical optics, simple chemistry ideas, and so on. I also didn't see that there was any reason to make the lectures in a definite order, in the sense that I would not be allowed to mention something until I was ready to discuss it in detail. There was a great deal of mention of things to come, without complete discussions. These more complete discussions would come later when the preparation became more advanced. Examples are the discussions of inductance, and of energy levels, which are a first brought in in a very qualitative way and are later developed more completely.
At the same time that I was aiming at the more active student, I also wanted to take care of the fellow for whom the extra fireworks and side applications are merely disquieting and who cannot be expected to learn most of the material in the lecture at all. For such students I wanted there to be at least a central core or backbone of material which he could get. Even if he didn't understand everything in a lecture, I hoped he wouldn't get nervous. I didn't expect him to understand everything, but only the central and most direct features. It takes, of course, a certain intelligence on his part to see which are the central theorems and central ideas, and which are the more advanced side issues and applications which he may understand only in later years.
In giving these lectures there was one serious difficulty: in the way the course was given, there wasn't any feedback from the students to the lecturer to indicate how well the lectures were going over. This is indeed a very serious difficulty, and I don't know how good the lectures really are. The whole thing was essentially an experiment. And if I did it again I wouldn't do it the same wayI hope I don't have to do it again! I think, though, that things worked outso far as the physics is concernedquite satisfactorily in the first year.
In the second year I was not so satisfied. In the first part of the course, dealing with electricity and magnetism, I couldn't think of any really unique or different way of doing itof any way that would be particularly more exciting than the usual way of presenting it. So I don't think I did very much in the lectures on electricity and magnetism. At the end of the second year I had originally intended to go on, after the electricity and magnetism, by giving some more lectures on the properties of materials, but mainly to take up things like fundamental modes, solutions of the diffusion equation, vibrating systems, orthogonal functions, … developing the first stages of what are usually called "the mathematical methods of physics.'' In retrospect, I think that if I were doing it again I would go back to that original idea. But since it was not planned that I would be giving these lectures again, it was suggested that it might be a good idea to try to give an introduction to the quantum mechanicswhat you will find in Volume III.
It is perfectly clear that students who will major in physics can wait until their third year for quantum mechanics. On the other hand, the argument was made that many of the students in our course study physics as a background for their primary interest in other fields. And the usual way of dealing with quantum mechanics makes that subject almost unavailable for the great majority of students because they have to take so long to learn it. Yet, in its real applicationsespecially in its more complex applications, such as in electrical engineering and chemistrythe full machinery of the differential equation approach is not actually used. So I tried to describe the principles of quantum mechanics in a way which wouldn't require that one first know the mathematics of partial differential equations. Even for a physicist I think that is an interesting thing to try to doto present quantum mechanics in this reverse fashionfor several reasons which may be apparent in the lectures themselves. However, I think that the experiment in the quantum mechanics part was not completely successfulin large part because I really did not have enough time at the end (I should, for instance, have had three or four more lectures in order to deal more completely with such matters as energy bands and the spatial dependence of amplitudes). Also, I had never presented the subject this way before, so the lack of feedback was particularly serious. I now believe the quantum mechanics should be given at a later time. Maybe I'll have a chance to do it again someday. Then I'll do it right.
The reason there are no lectures on how to solve problems is because there were recitation sections. Although I did put in three lectures in the first year on how to solve problems, they are not included here. Also there was a lecture on inertial guidance which certainly belongs after the lecture on rotating systems, but which was, unfortunately, omitted. The fifth and sixth lectures are actually due to Matthew Sands, as I was out of town. The question, of course, is how well this experiment has succeeded. My own point of viewwhich, however, does not seem to be shared by most of the people who worked with the studentsis pessimistic. I don't think I did very well by the students. When I look at the way the majority of the students handled the problems on the examinations, I think that the system is a failure. Of course, my friends point out to me that there were one or two dozen students whovery surprisinglyunderstood almost everything in all of the lectures, and who were quite active in working with the material and worrying about the many points in an excited and interested way. These people have now, I believe, a firstrate background in physicsand they are, after all, the ones I was trying to get at. But then, "The power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous.'' (Gibbon)
Still, I didn't want to leave any student completely behind, as perhaps I did. I think one way we could help the students more would be by putting more hard work into developing a set of problems which would elucidate some of the ideas in the lectures. Problems give a good opportunity to fill out the material of the lectures and make more realistic, more complete, and more settled in the mind the ideas that have been exposed.
I think, however, that there isn't any solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teachera situation in which the student discusses the ideas, thinks about the things, and talks about the things. It's impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned. But in our modern times we have so many students to teach that we have to try to find some substitute for the ideal. Perhaps my lectures can make some contribution. Perhaps in some small place where there are individual teachers and students, they may get some inspiration or some ideas from the lectures. Perhaps they will have fun thinking them throughor going on to develop some of the ideas further.
Richard P. Feynman
June, 1963
Copyright © 1963, 2006, 2013 by the California Institute of Technology,
Michael A. Gottlieb, and Rudolf Pfeiffer
Foreword
Chapter 1. Atoms in Motion
11 Introduction
12 Matter is made of atoms
13 Atomic processes
14 Chemical reactions
Chapter 2. Basic Physics
21 Introduction
22 Physics before 1920
23 Quantum physics
24 Nuclei and particles
Chapter 3. The Relation of Physics to Other Sciences
31 Introduction
32 Chemistry
33 Biology
34 Astronomy
35 Geology
36 Psychology
37 How did it get that way?
Chapter 4. Conservation of Energy
41 What is energy?
42 Gravitational potential energy
43 Kinetic energy
44 Other forms of energy
Chapter 5. Time and Distance
51 Motion
52 Time
53 Short times
54 Long times
55 Units and standards of time
56 Large distances
57 Short distances
Chapter 6. Probability
61 Chance and likelihood
62 Fluctuations
63 The random walk
64 A probability distribution
65 The uncertainty principle
Chapter 7. The Theory of Gravitation
71 Planetary motions
72 Kepler’s laws
73 Development of dynamics
74 Newton’s law of gravitation
75 Universal gravitation
76 Cavendish’s experiment
77 What is gravity?
78 Gravity and relativity
Chapter 8. Motion
81 Description of motion
82 Speed
83 Speed as a derivative
84 Distance as an integral
85 Acceleration
Chapter 9. Newton’s Laws of Dynamics
91 Momentum and force
92 Speed and velocity
93 Components of velocity, acceleration, and force
94 What is the force?
95 Meaning of the dynamical equations
96 Numerical solution of the equations
97 Planetary motions
Chapter 10. Conservation of Momentum
101 Newton’s Third Law
102 Conservation of momentum
103 Momentum is conserved!
104 Momentum and energy
105 Relativistic momentum
Chapter 11. Vectors
111 Symmetry in physics
112 Translations
113 Rotations
114 Vectors
115 Vector algebra
116 Newton’s laws in vector notation
117 Scalar product of vectors
Chapter 12. Characteristics of Force
121 What is a force?
122 Friction
123 Molecular forces
124 Fundamental forces. Fields
125 Pseudo forces
126 Nuclear forces
Chapter 13. Work and Potential Energy (A)
131 Energy of a falling body
132 Work done by gravity
133 Summation of energy
134 Gravitational field of large objects
Chapter 14. Work and Potential Energy (conclusion)
141 Work
142 Constrained motion
143 Conservative forces
144 Nonconservative forces
145 Potentials and fields
Chapter 15. The Special Theory of Relativity
151 The principle of relativity
152 The Lorentz transformation
153 The MichelsonMorley experiment
154 Transformation of time
155 The Lorentz contraction
156 Simultaneity
157 Fourvectors
158 Relativistic dynamics
159 Equivalence of mass and energy
Chapter 16. Relativistic Energy and Momentum
161 Relativity and the philosophers
162 The twin paradox
163 Transformation of velocities
164 Relativistic mass
165 Relativistic energy
Chapter 17. SpaceTime
171 The geometry of spacetime
172 Spacetime intervals
173 Past, present, and future
174 More about fourvectors
175 Fourvector algebra
Chapter 18. Rotation in Two Dimensions
181 The center of mass
182 Rotation of a rigid body
183 Angular momentum
184 Conservation of angular momentum
Chapter 19. Center of Mass; Moment of Inertia
191 Properties of the center of mass
192 Locating the center of mass
193 Finding the moment of inertia
194 Rotational kinetic energy
Chapter 20. Rotation in space
201 Torques in three dimensions
202 The rotation equations using cross products
203 The gyroscope
204 Angular momentum of a solid body
Chapter 21. The Harmonic Oscillator
211 Linear differential equations
212 The harmonic oscillator
213 Harmonic motion and circular motion
214 Initial conditions
215 Forced oscillations
Chapter 22. Algebra
221 Addition and multiplication
222 The inverse operations
223 Abstraction and generalization
224 Approximating irrational numbers
225 Complex numbers
226 Imaginary exponents
Chapter 23. Resonance
231 Complex numbers and harmonic motion
232 The forced oscillator with damping
233 Electrical resonance
234 Resonance in nature
Chapter 24. Transients
241 The energy of an oscillator
242 Damped oscillations
243 Electrical transients
Chapter 25. Linear Systems and Review
251 Linear differential equations
252 Superposition of solutions
253 Oscillations in linear systems
254 Analogs in physics
255 Series and parallel impedances
Chapter 26. Optics: The Principle of Least Time
261 Light
262 Reflection and refraction
263 Fermat’s principle of least time
264 Applications of Fermat’s principle
265 A more precise statement of Fermat’s principle
266 How it works
Chapter 27. Geometrical Optics
271 Introduction
272 The focal length of a spherical surface
273 The focal length of a lens
274 Magnification
275 Compound lenses
276 Aberrations
277 Resolving power
Chapter 28. Electromagnetic Radiation
281 Electromagnetism
282 Radiation
283 The dipole radiator
284 Interference
Chapter 29. Interference
291 Electromagnetic waves
292 Energy of radiation
293 Sinusoidal waves
294 Two dipole radiators
295 The mathematics of interference
Chapter 30. Diffraction
301 The resultant amplitude due to n equal oscillators
302 The diffraction grating
303 Resolving power of a grating
304 The parabolic antenna
305 Colored films; crystals
306 Diffraction by opaque screens
307 The field of a plane of oscillating charges
Chapter 31. The Origin of the Refractive Index
311 The index of refraction
312 The field due to the material
313 Dispersion
314 Absorption
315 The energy carried by an electric wave
316 Diffraction of light by a screen
Chapter 32. Radiation Damping. Light Scattering
321 Radiation resistance
322 The rate of radiation of energy
323 Radiation damping
324 Independent sources
325 Scattering of light
Chapter 33. Polarization
331 The electric vector of light
332 Polarization of scattered light
333 Birefringence
334 Polarizers
335 Optical activity
336 The intensity of reflected light
337 Anomalous refraction
Chapter 34. Relativistic Effects in Radiation
341 Moving sources
342 Finding the “apparent” motion
343 Synchrotron radiation
344 Cosmic synchrotron radiation
345 Bremsstrahlung
346 The Doppler effect
347 The ?, k fourvector
348 Aberration
349 The momentum of light
Chapter 35. Color Vision
351 The human eye
352 Color depends on intensity
353 Measuring the color sensation
354 The chromaticity diagram
355 The mechanism of color vision
356 Physiochemistry of color vision
Chapter 36. Mechanisms of Seeing
361 The sensation of color
362 The physiology of the eye
363 The rod cells
364 The compound (insect) eye
365 Other eyes
366 Neurology of vision
Chapter 37. Quantum Behavior
371 Atomic mechanics
372 An experiment with bullets
373 An experiment with waves
374 An experiment with electrons
375 The interference of electron waves
376 Watching the electrons
377 First principles of quantum mechanics
378 The uncertainty principle
Chapter 38. The Relation of Wave and Particle Viewpoints
381 Probability wave amplitudes
382 Measurement of position and momentum
383 Crystal diffraction
384 The size of an atom
385 Energy levels
386 Philosophical implications
Chapter 39. The Kinetic Theory of Gases
391 Properties of matter
392 The pressure of a gas
393 Compressibility of radiation
394 Temperature and kinetic energy
395 The ideal gas law
Chapter 40. The Principles of Statistical Mechanics
401 The exponential atmosphere
402 The Boltzmann law
403 Evaporation of a liquid
404 The distribution of molecular speeds
405 The specific heats of gases
406 The failure of classical physics
Chapter 41. The Brownian Movement
411 Equipartition of energy
412 Thermal equilibrium of radiation
413 Equipartition and the quantum oscillator
414 The random walk
Chapter 42. Applications of Kinetic Theory
421 Evaporation
422 Thermionic emission
423 Thermal ionization
424 Chemical kinetics
425 Einstein’s laws of radiation
Chapter 43. Diffusion
431 Collisions between molecules
432 The mean free path
433 The drift speed
434 Ionic conductivity
435 Molecular diffusion
436 Thermal conductivity
Chapter 44. The Laws of Thermodynamics
441 Heat engines; the first law
442 The second law
443 Reversible engines
444 The efficiency of an ideal engine
445 The thermodynamic temperature
446 Entropy
Chapter 45. Illustrations of Thermodynamics
451 Internal energy
452 Applications
453 The ClausiusClapeyron equation
Chapter 46. Ratchet and pawl
461 How a ratchet works
462 The ratchet as an engine
463 Reversibility in mechanics
464 Irreversibility
465 Order and entropy
Chapter 47. Sound. The wave equation
471 Waves
472 The propagation of sound
473 The wave equation
474 Solutions of the wave equation
475 The speed of sound
Chapter 48. Beats
481 Adding two waves
482 Beat notes and modulation
483 Side bands
484 Localized wave trains
485 Probability amplitudes for particles
486 Waves in three dimensions
487 Normal modes
Chapter 49. Modes
491 The reflection of waves
492 Confined waves, with natural frequencies
493 Modes in two dimensions
494 Coupled pendulums
495 Linear systems
Chapter 50. Harmonics
501 Musical tones
502 The Fourier series
503 Quality and consonance
504 The Fourier coefficients
505 The energy theorem
506 Nonlinear responses
Chapter 51. Waves
511 Bow waves
512 Shock waves
513 Waves in solids
514 Surface waves
Chapter 52. Symmetry in Physical Laws
521 Symmetry operations
522 Symmetry in space and time
523 Symmetry and conservation laws
524 Mirror reflections
525 Polar and axial vectors
526 Which hand is right?
527 Parity is not conserved!
528 Antimatter
529 Broken symmetries
Copyright © 1963, 2006, 2013 by the California Institute of Technology,
Michael A. Gottlieb, and Rudolf Pfeiffer
Chapter 1. Atoms in Motion
11 Introduction
12 Matter is made of atoms
13 Atomic processes
14 Chemical reactions
Chapter 2. Basic Physics
21 Introduction
22 Physics before 1920
23 Quantum physics
24 Nuclei and particles
Chapter 3. The Relation of Physics to Other Sciences
31 Introduction
32 Chemistry
33 Biology
34 Astronomy
35 Geology
36 Psychology
37 How did it get that way?
Chapter 4. Conservation of Energy
41 What is energy?
42 Gravitational potential energy
43 Kinetic energy
44 Other forms of energy
Chapter 5. Time and Distance
51 Motion
52 Time
53 Short times
54 Long times
55 Units and standards of time
56 Large distances
57 Short distances
Chapter 6. Probability
61 Chance and likelihood
62 Fluctuations
63 The random walk
64 A probability distribution
65 The uncertainty principle
Chapter 7. The Theory of Gravitation
71 Planetary motions
72 Kepler’s laws
73 Development of dynamics
74 Newton’s law of gravitation
75 Universal gravitation
76 Cavendish’s experiment
77 What is gravity?
78 Gravity and relativity
Chapter 8. Motion
81 Description of motion
82 Speed
83 Speed as a derivative
84 Distance as an integral
85 Acceleration
Chapter 9. Newton’s Laws of Dynamics
91 Momentum and force
92 Speed and velocity
93 Components of velocity, acceleration, and force
94 What is the force?
95 Meaning of the dynamical equations
96 Numerical solution of the equations
97 Planetary motions
Chapter 10. Conservation of Momentum
101 Newton’s Third Law
102 Conservation of momentum
103 Momentum is conserved!
104 Momentum and energy
105 Relativistic momentum
Chapter 11. Vectors
111 Symmetry in physics
112 Translations
113 Rotations
114 Vectors
115 Vector algebra
116 Newton’s laws in vector notation
117 Scalar product of vectors
Chapter 12. Characteristics of Force
121 What is a force?
122 Friction
123 Molecular forces
124 Fundamental forces. Fields
125 Pseudo forces
126 Nuclear forces
Chapter 13. Work and Potential Energy (A)
131 Energy of a falling body
132 Work done by gravity
133 Summation of energy
134 Gravitational field of large objects
Chapter 14. Work and Potential Energy (conclusion)
141 Work
142 Constrained motion
143 Conservative forces
144 Nonconservative forces
145 Potentials and fields
Chapter 15. The Special Theory of Relativity
151 The principle of relativity
152 The Lorentz transformation
153 The MichelsonMorley experiment
154 Transformation of time
155 The Lorentz contraction
156 Simultaneity
157 Fourvectors
158 Relativistic dynamics
159 Equivalence of mass and energy
Chapter 16. Relativistic Energy and Momentum
161 Relativity and the philosophers
162 The twin paradox
163 Transformation of velocities
164 Relativistic mass
165 Relativistic energy
Chapter 17. SpaceTime
171 The geometry of spacetime
172 Spacetime intervals
173 Past, present, and future
174 More about fourvectors
175 Fourvector algebra
Chapter 18. Rotation in Two Dimensions
181 The center of mass
182 Rotation of a rigid body
183 Angular momentum
184 Conservation of angular momentum
Chapter 19. Center of Mass; Moment of Inertia
191 Properties of the center of mass
192 Locating the center of mass
193 Finding the moment of inertia
194 Rotational kinetic energy
Chapter 20. Rotation in space
201 Torques in three dimensions
202 The rotation equations using cross products
203 The gyroscope
204 Angular momentum of a solid body
Chapter 21. The Harmonic Oscillator
211 Linear differential equations
212 The harmonic oscillator
213 Harmonic motion and circular motion
214 Initial conditions
215 Forced oscillations
Chapter 22. Algebra
221 Addition and multiplication
222 The inverse operations
223 Abstraction and generalization
224 Approximating irrational numbers
225 Complex numbers
226 Imaginary exponents
Chapter 23. Resonance
231 Complex numbers and harmonic motion
232 The forced oscillator with damping
233 Electrical resonance
234 Resonance in nature
Chapter 24. Transients
241 The energy of an oscillator
242 Damped oscillations
243 Electrical transients
Chapter 25. Linear Systems and Review
251 Linear differential equations
252 Superposition of solutions
253 Oscillations in linear systems
254 Analogs in physics
255 Series and parallel impedances
Chapter 26. Optics: The Principle of Least Time
261 Light
262 Reflection and refraction
263 Fermat’s principle of least time
264 Applications of Fermat’s principle
265 A more precise statement of Fermat’s principle
266 How it works
Chapter 27. Geometrical Optics
271 Introduction
272 The focal length of a spherical surface
273 The focal length of a lens
274 Magnification
275 Compound lenses
276 Aberrations
277 Resolving power
Chapter 28. Electromagnetic Radiation
281 Electromagnetism
282 Radiation
283 The dipole radiator
284 Interference
Chapter 29. Interference
291 Electromagnetic waves
292 Energy of radiation
293 Sinusoidal waves
294 Two dipole radiators
295 The mathematics of interference
Chapter 30. Diffraction
301 The resultant amplitude due to n equal oscillators
302 The diffraction grating
303 Resolving power of a grating
304 The parabolic antenna
305 Colored films; crystals
306 Diffraction by opaque screens
307 The field of a plane of oscillating charges
Chapter 31. The Origin of the Refractive Index
311 The index of refraction
312 The field due to the material
313 Dispersion
314 Absorption
315 The energy carried by an electric wave
316 Diffraction of light by a screen
Chapter 32. Radiation Damping. Light Scattering
321 Radiation resistance
322 The rate of radiation of energy
323 Radiation damping
324 Independent sources
325 Scattering of light
Chapter 33. Polarization
331 The electric vector of light
332 Polarization of scattered light
333 Birefringence
334 Polarizers
335 Optical activity
336 The intensity of reflected light
337 Anomalous refraction
Chapter 34. Relativistic Effects in Radiation
341 Moving sources
342 Finding the “apparent” motion
343 Synchrotron radiation
344 Cosmic synchrotron radiation
345 Bremsstrahlung
346 The Doppler effect
347 The ?, k fourvector
348 Aberration
349 The momentum of light
Chapter 35. Color Vision
351 The human eye
352 Color depends on intensity
353 Measuring the color sensation
354 The chromaticity diagram
355 The mechanism of color vision
356 Physiochemistry of color vision
Chapter 36. Mechanisms of Seeing
361 The sensation of color
362 The physiology of the eye
363 The rod cells
364 The compound (insect) eye
365 Other eyes
366 Neurology of vision
Chapter 37. Quantum Behavior
371 Atomic mechanics
372 An experiment with bullets
373 An experiment with waves
374 An experiment with electrons
375 The interference of electron waves
376 Watching the electrons
377 First principles of quantum mechanics
378 The uncertainty principle
Chapter 38. The Relation of Wave and Particle Viewpoints
381 Probability wave amplitudes
382 Measurement of position and momentum
383 Crystal diffraction
384 The size of an atom
385 Energy levels
386 Philosophical implications
Chapter 39. The Kinetic Theory of Gases
391 Properties of matter
392 The pressure of a gas
393 Compressibility of radiation
394 Temperature and kinetic energy
395 The ideal gas law
Chapter 40. The Principles of Statistical Mechanics
401 The exponential atmosphere
402 The Boltzmann law
403 Evaporation of a liquid
404 The distribution of molecular speeds
405 The specific heats of gases
406 The failure of classical physics
Chapter 41. The Brownian Movement
411 Equipartition of energy
412 Thermal equilibrium of radiation
413 Equipartition and the quantum oscillator
414 The random walk
Chapter 42. Applications of Kinetic Theory
421 Evaporation
422 Thermionic emission
423 Thermal ionization
424 Chemical kinetics
425 Einstein’s laws of radiation
Chapter 43. Diffusion
431 Collisions between molecules
432 The mean free path
433 The drift speed
434 Ionic conductivity
435 Molecular diffusion
436 Thermal conductivity
Chapter 44. The Laws of Thermodynamics
441 Heat engines; the first law
442 The second law
443 Reversible engines
444 The efficiency of an ideal engine
445 The thermodynamic temperature
446 Entropy
Chapter 45. Illustrations of Thermodynamics
451 Internal energy
452 Applications
453 The ClausiusClapeyron equation
Chapter 46. Ratchet and pawl
461 How a ratchet works
462 The ratchet as an engine
463 Reversibility in mechanics
464 Irreversibility
465 Order and entropy
Chapter 47. Sound. The wave equation
471 Waves
472 The propagation of sound
473 The wave equation
474 Solutions of the wave equation
475 The speed of sound
Chapter 48. Beats
481 Adding two waves
482 Beat notes and modulation
483 Side bands
484 Localized wave trains
485 Probability amplitudes for particles
486 Waves in three dimensions
487 Normal modes
Chapter 49. Modes
491 The reflection of waves
492 Confined waves, with natural frequencies
493 Modes in two dimensions
494 Coupled pendulums
495 Linear systems
Chapter 50. Harmonics
501 Musical tones
502 The Fourier series
503 Quality and consonance
504 The Fourier coefficients
505 The energy theorem
506 Nonlinear responses
Chapter 51. Waves
511 Bow waves
512 Shock waves
513 Waves in solids
514 Surface waves
Chapter 52. Symmetry in Physical Laws
521 Symmetry operations
522 Symmetry in space and time
523 Symmetry and conservation laws
524 Mirror reflections
525 Polar and axial vectors
526 Which hand is right?
527 Parity is not conserved!
528 Antimatter
529 Broken symmetries
Copyright © 1963, 2006, 2013 by the California Institute of Technology,
Michael A. Gottlieb, and Rudolf Pfeiffer
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