Limits & Continuity
A 17-module path through limits & continuity, in study order from foundations to the frontier.
Modules
- Limit Points and the Setting for Function Limits
- The Epsilon-Delta Definition of a Limit
- Uniqueness of Limits and Basic Examples
- Sequential Characterization of Limits
- The Algebra of Limits
- Proving Nonexistence of Limits
- One-Sided Limits
- Infinite Limits and Limits at Infinity
- Continuity at a Point
- Sequential Characterization of Continuity
- The Algebra of Continuous Functions
- Composition of Continuous Functions
- Continuity on Intervals and Sets
- The Intermediate Value Theorem
- The Extreme Value Theorem
- Uniform Continuity
- Classification of Discontinuities and Monotone Functions