## Course Notes

Here is an interactive text to accompany the course. We invite you to take advantage of the many demonstrations to explore Calculus more deeply.

- Definite Integrals and the Fundamental Theorem of Calculus

- Introduction
- Overview of calculus from a historical perspective
- Some special sums
- How Archimedes found the area of a circle
- The area under a curve
- The average value
- The definite integral
- The Fundamental Theorem of Calculus
- How to use the Fundamental Theorem

- Applications of the Definite Integral

- Acceleration, Velocity, and Position
- Average value of a function
- Calculating Simple Volumes
- Arc Length and Surface Area
- Work

- Techniques for Antidifferentiation

- More Applications

- Differential Equations
- Weighted Averages

- More Techniques for Integration

- Taylor polynomials and series
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