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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 -- |