# Advanced Calculus

- Author:
- Kevin Hopkins

- Topic:
- Calculus

Worksheets and illustrations used in Advanced Calculus. Transitioning the information from https://sites.google.com/site/collegealgebraworksheets/advanced-calculus-illustrations to GeoGebratube.
Some of the topics discussed in Advanced Calculus were first introduced in Calculus. In this case, the sections numbers given correlate to the section in the Stewart Calculus textbook. In Advanced Calculus we look at them more to determine why a theorem is true (or what might need to be changed if we adjust the assumptions somewhat).
Some of the topics (especially fractals) came up as we were looking at sequence, especially recursive sequences. Most of the fractal worksheets are not my own creation (you can see who created them at the bottom of the worksheet).

## Table of Contents

### For Advanced Calculus specifically

- Section 2.1-Sequences-Approximating Pi
- Section 2.3-Epsilon X Game
- Section 2.4-Subsequences
- Section 2.5-Monotone Convergence Theorem
- Section 1.7-Formal Definition of the Limit
- Section 1.8-Intermediate Value Theorem
- Section 1.8-Bisection Method-Related to Intermediate Val Thm
- Section 1.8-Secant Method-Related to Intermediate Value Thm
- Section 4.2-Antipodal Points Theorem
- Section 6.1-Differentiability
- Section 2.2-Sketching Graph of Derivative
- Section 3.2-Mean Value Theorem
- Section 6.6-Blancmange Function
- Section 5.1-Limit of Compositions
- Section 5.3-Epsilon Delta Definition of Limits
- Section 1.2-Precise definition of the limit
- Section 7.1-Riemann Integral
- Random Polynomials

### From Calculus

### Fractals