Advanced Calculus
1. For Advanced Calculus specifically
1. Section 2.1-Sequences-Approximating Pi
2. Section 2.3-Epsilon X Game
3. Section 2.4-Subsequences
4. Section 2.5-Monotone Convergence Theorem
5. Section 1.7-Formal Definition of the Limit
6. Section 1.8-Intermediate Value Theorem
7. Section 1.8-Bisection Method-Related to Intermediate Val Thm
8. Section 1.8-Secant Method-Related to Intermediate Value Thm
9. Section 4.2-Antipodal Points Theorem
10. Section 6.1-Differentiability
11. Section 2.2-Sketching Graph of Derivative
12. Section 3.2-Mean Value Theorem
13. Section 6.6-Blancmange Function
14. Section 5.1-Limit of Compositions
15. Section 5.3-Epsilon Delta Definition of Limits
16. Section 1.2-Precise definition of the limit
17. Section 7.1-Riemann Integral
18. Random Polynomials
2. From Calculus
1. Appendix A-Really an overview of ideas for the entire course
2. Graphing Functions-Section 1.1
3. Section 11.8-Power Series
4. Section 11.10-More Complicated Taylor Series
5. Section 11.10-Taylor Series
6. Section 11.10-More Complicated Taylor Series
3. Fractals
1. Sierpinski Triangle
2. Foldable Fractal
3. Foldable Fractal 2
4. Menger Sponge: Stage 1
5. Mandelbrot Visualization
6. Koch Snowflake 1

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Advanced Calculus

Kevin Hopkins, Aug 23, 2014

Worksheets and illustrations used in Advanced Calculus. Transitioning the information from [url]https://sites.google.com/site/collegealgebraworksheets/advanced-calculus-illustrations[/url] 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).

For Advanced Calculus specifically
1. Section 2.1-Sequences-Approximating Pi
2. Section 2.3-Epsilon X Game
3. Section 2.4-Subsequences
4. Section 2.5-Monotone Convergence Theorem
5. Section 1.7-Formal Definition of the Limit
6. Section 1.8-Intermediate Value Theorem
7. Section 1.8-Bisection Method-Related to Intermediate Val Thm
8. Section 1.8-Secant Method-Related to Intermediate Value Thm
9. Section 4.2-Antipodal Points Theorem
10. Section 6.1-Differentiability
11. Section 2.2-Sketching Graph of Derivative
12. Section 3.2-Mean Value Theorem
13. Section 6.6-Blancmange Function
14. Section 5.1-Limit of Compositions
15. Section 5.3-Epsilon Delta Definition of Limits
16. Section 1.2-Precise definition of the limit
17. Section 7.1-Riemann Integral
18. Random Polynomials
From Calculus
1. Appendix A-Really an overview of ideas for the entire course
2. Graphing Functions-Section 1.1
3. Section 11.8-Power Series
4. Section 11.10-More Complicated Taylor Series
5. Section 11.10-Taylor Series
6. Section 11.10-More Complicated Taylor Series
Fractals
1. Sierpinski Triangle
2. Foldable Fractal
3. Foldable Fractal 2
4. Menger Sponge: Stage 1
5. Mandelbrot Visualization
6. Koch Snowflake 1

1.

For Advanced Calculus specifically

1. Section 2.1-Sequences-Approximating Pi
2. Section 2.3-Epsilon X Game
3. Section 2.4-Subsequences
4. Section 2.5-Monotone Convergence Theorem
5. Section 1.7-Formal Definition of the Limit
6. Section 1.8-Intermediate Value Theorem
7. Section 1.8-Bisection Method-Related to Intermediate Val Thm
8. Section 1.8-Secant Method-Related to Intermediate Value Thm
9. Section 4.2-Antipodal Points Theorem
10. Section 6.1-Differentiability
11. Section 2.2-Sketching Graph of Derivative
12. Section 3.2-Mean Value Theorem
13. Section 6.6-Blancmange Function
14. Section 5.1-Limit of Compositions
15. Section 5.3-Epsilon Delta Definition of Limits
16. Section 1.2-Precise definition of the limit
17. Section 7.1-Riemann Integral
18. Random Polynomials

1.1.

Section 2.1-Sequences-Approximating Pi

Approximating Pi

1.2.

1.3.

1.4.

1.5.

1.6.

1.7.

1.8.

1.9.

1.10.

1.11.

1.12.

1.13.

1.14.

1.15.

1.16.

1.17.

1.18.

2.

From Calculus

1. Appendix A-Really an overview of ideas for the entire course
2. Graphing Functions-Section 1.1
3. Section 11.8-Power Series
4. Section 11.10-More Complicated Taylor Series
5. Section 11.10-Taylor Series
6. Section 11.10-More Complicated Taylor Series

2.1.

Appendix A-Really an overview of ideas for the entire course

Ideas related to solving a problem.

2.2.

2.3.

2.4.

2.5.

2.6.

3.

Fractals

3.1.

Sierpinski Triangle

A student asked if the Blancmange Function was related to the Cantor Set. A google search of these topics showed a relationship to fractals in general. So, we looked at a few fractal images (produced by a sequence of steps to see what develops). I developed a worksheets related to Sierpinski Triangle. Not only does one of the standard processes for generating, but allows for skewing the probability toward one or more vertices and allows for placing the new point at some fraction of the distance between the two points other than 1/2 the distance. It also allows the option of using more sides (where the probability needs to be less than .5 to move the points closer to the vertices) to see any kind of pattern.

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