The lecture covers a number of mathematical concepts. The Taylor series is introduced and its properties discussed, supplemented by various examples. Complex numbers are explained in some detail, especially in their polar form. The lecture ends with a discussion of simple harmonic motion.

1. Course Introduction and Newtonian Mechanics
2. Vectors in Multiple Dimensions
3. Newton's Laws of Motion
4. Newton's Laws (cont.) and Inclined Planes
5. Work-Energy Theorem and Law of Conservation of Energy
6. Law of Conservation of Energy in Higher Dimensions
7. Kepler's Laws
8. Dynamics of a Multiple-Body System and Law of Conservation of Momentum
9. Rotations, Part I: Dynamics of Rigid Bodies
10. Rotations, Part II: Parallel Axis Theorem
11. Torque
12. Introduction to Relativity
13. Lorentz Transformation
14. Introduction to the Four-Vector
15. Four-Vector in Relativity
16. The Taylor Series and Other Mathematical Concepts
17. Simple Harmonic Motion
18. Simple Harmonic Motion (cont.) and Introduction to Waves
19. Waves
20. Fluid Dynamics and Statics and Bernoulli's Equation
21. Thermodynamics
22. The Boltzmann Constant and First Law of Thermodynamics
23. The Second Law of Thermodynamics and Carnot's Engine
24. The Second Law of Thermodynamics (cont.) and Entropy

This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.