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.