The Taylor Series, Complex Numbers, and Simple Harmonic Motion - Lecture 16

Explore advanced mathematical concepts in this comprehensive lecture from Yale University's Fundamentals of Physics course. Delve into the Taylor series, understanding its derivation and properties through various examples. Examine functions with invalid Taylor series and learn to develop series for common functions like cosine and exponential. Discover how to derive trigonometric functions from exponential functions. Investigate complex numbers, focusing on their properties and polar form. Conclude with an in-depth look at simple harmonic motion, including its relationship to the law of conservation of energy and harmonic motion due to torque. This 1-hour 14-minute video provides a thorough exploration of these crucial mathematical concepts, essential for a deeper understanding of physics.

- Chapter 1. Derive Taylor Series of a Function, f as [Σ (0, ∞)fnxn/n!].
- Chapter 2. Examples of Functions with Invalid Taylor Series.
- Chapter 3. Taylor Series for Popular Functions(cos x, ex,etc).
- Chapter 4. Derive Trigonometric Functions from Exponential Functions.
- Chapter 5. Properties of Complex Numbers.
- Chapter 6. Polar Form of Complex Numbers.
- Chapter 7. Simple Harmonic Motions.
- Chapter 8. Law of Conservation of Energy and Harmonic Motion Due to Torque.