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 of 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. Motion in d=2 -- Friction : static and kinetic -- Inclined plane -- Coupled masses -- Circular motion, loop-the-loop -- 5. Law of conservation of energy. The work-energy theorem and power -- Friction and the work-energy theorem -- 6. Conservation of energy in d=2. Work done in d=2 and the dot product -- Conservative and non-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. 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 -- 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 -- 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.