1. The structure of mechanics : Kinematics and dynamics ; Average and instantaneous quantities ; Motion at constant acceleration
2. Motion in higher dimensions : Vectors in d=2 ; Unit vectors ; Choice of axes and basis vectors ; Derivatives of the position vector r ; Application to circular motion ; Projectile motion
3. Newton's laws I : Introduction to Newton's laws of motion ; Newton's second law ; Two halves of the second law ; Newton's third law ; Weight and weightlessness
4. Newton's laws II : A solved example ; Never the whole story ; Motion in d=2 ; Friction: static and kinetic ; Inclined plane ; Coupled masses ; Circular motion, loop-the-loop
5. Law of conservation of energy : Introduction to energy ; The work-energy theorem and power ; Friction and the work-energy theorem
6. Conservation of energy in d=2 : Calculus review ; Work done in d+2 ; Work done in d=2 and the dot product ; Conservative and non-conservative forces ; Conservative forces ; Application to gravitational potential energy
7. The Kepler problem : Kepler's laws ; The law of universal gravity ; Details of the orbits ; Law of conservation of energy far from the earth ; Choosing the constant in U
8. Multi-particle dynamics : The two-body problem ; The center of mass ; Law of conservation of momentum ; Rocket science ; Elastic and inelastic collisions ; Scattering in higher dimensions
9. Rotational dynamics I : Introduction to rigid bodies ; Angle of rotation, the radian ; Rotation at constant angular acceleration ; Rotational inertia, momentum, and energy ; Torque and the work-energy theorem ; Calculating the moment of inertia
10. Rotational dynamics II : The parallel axis theorem ; Kinetic energy for a general N-body system ; Simultaneous translations and rotations ; Conservation of energy ; Advanced rotations ; Conservation of angular momentum ; Angular momentum of the figure skater
11. Rotational dynamics III : Static equilibrium ; The seesaw ; A hanging sign ; The leaning ladder ; Rigid-body dynamics in 3d ; The gyroscope
12. Special relativity I: the Lorentz transformation : Galilean and Newtonian relativity ; Proof of Galilean relativity ; Enter Einstein ; The postulates ; The Lorentz transformation
13. Special relativity II: some consequences : Summary of the Lorentz transformation ; The velocity transformation law ; Relativity of simultaneity ; Time dilation ; More paradox
14. Special relativity III: past, present, and future : Past, present, and future in relativity ; Geometry of spacetime ; Rapidity ; Four-vectors ; Proper time
15. Four-momentum : Relativistic scattering
16. Mathematical methods : Taylor series of a function ; Examples and issues with the Taylor series ; Taylor series of some popular functions ; Trigonometric and exponential functions ; Properties of complex numbers ; Polar form of complex numbers
17. Simple harmonic motion : More examples of oscillations ; Superposition of solutions ; Conditions on solutions to the harmonic oscillator ; Exponential functions as generic solutions ; Damped oscillations: a classification ; Driven oscillator
18. Waves I : The wave equation ; Solutions of the wave equation ; Frequency and period
19. Waves II : Wave energy and power transmitted ; Doppler effect ; Superposition of waves ; Interference: double-slit experiment ; Standing waves and musical instruments
20. Fluids : Introduction to fluid dynamics and statics ; The hydraulic press ; Archimedes' principle ; Bernoulli's equation ; Applications of Bernoulli's equation
21. Heat : Equilibrium and the zeroth law: temperature ; Calibrating temperature ; Absolute zero and the Kelvin scale ; Heat and specific heat ; Phase change ; Radiation, convection, and conduction ; Heat as molecular kinetic energy
22. Thermodynamics I : Boltzmann's constant and Avogadro's number ; Microscopic definition of absolute temperature ; Statistical properties of matter and radiation ; Thermodynamic processes ; Quasi-static processes ; The first law of thermodynamics
23. Thermodynamics II : Cycles and state variables ; Adiabatic processes ; The second law of thermodynamics ; The Carnot engine
24. Entropy and irreversibility : Entropy ; The second law: law of increasing entropy ; Statistical mechanics and entropy ; Entropy of an ideal gas: full microscopic analysis ; Maximum entropy principle illustrated ; The Gibbs formalism ; The third law of thermodynamics.
