16. The Taylor Series and Other Mathematical Concepts
For more information about Professor Shankar's book based on the lectures from this course, Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics, visit http://bit.ly/1jFIqNu.
Fundamentals of Physics (PHYS 200)
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.
00:00 - Chapter 1. Derive Taylor Series of a Function, f as [Σ (0, ∞)fnxn/n!]
14:21 - Chapter 2. Examples of Functions with Invalid Taylor Series
17:30 - Chapter 3. Taylor Series for Popular Functions(cos x, ex,etc)
23:31 - Chapter 4. Derive Trigonometric Functions from Exponential Functions
31:41 - Chapter 5. Properties of Complex Numbers
42:40 - Chapter 6. Polar Form of Complex Numbers
50:04 - Chapter 7. Simple Harmonic Motions
01:03:07 - Chapter 8. Law of Conservation of Energy and Harmonic Motion Due to Torque
Complete course materials are available at the Yale Online website: online.yale.edu
This course was recorded in Fall 2006.