Sequences & Series of Functions
A 14-module path through sequences & series of functions, in study order from foundations to the frontier.
Modules
- Pointwise Convergence of Sequences of Functions
- Failure of Property Preservation under Pointwise Convergence
- Uniform Convergence
- The Cauchy Criterion for Uniform Convergence
- The Uniform Limit of Continuous Functions
- The Weierstrass M-Test
- Uniform Convergence and Integration
- Uniform Convergence and Differentiation
- Equicontinuity of Families of Functions
- The Arzelà-Ascoli Theorem
- The Stone-Weierstrass Theorem
- Fourier Series: Rigorous Foundations
- Orthogonality and Bessel's Inequality
- Convergence of Fourier Series