1. Approximation of arbitrary functions using Taylor polynomials
Taylor polynomials based at 0
Taylor polynomials based at an arbitrary point


2. Error in approximation using Taylor polynomials
The error in the approximation by a Taylor polynomial
The limit as the order of Taylor polynomial increases


3. Introduction to the infinite series


4. Tests for absolute convergence
The monotone convergence principle and absolute
Convergence
The ratio test
The root test
The proofs of the ratio test and the root test


5. An introduction to power series
The definitions
Convergence properties of a power series
Differentiation of functions defined by power series


6. Using termwise integration, multiplication and division to determine Taylor series
Termwise integration of power series
Arithmetic operations on Taylor series
The binomial series


7. Testing for absolute convergence with the integral and comparison tests
The integral test
Error estimates related to the integral test
Comparison tests


8. Using conditional convergence to determine alternating series
Alternating series


9. An introduction to the Fourier series
Fourier series of 2[pi]-periodic functions
Fourier series when the period is different from 2[pi]


Index.