A course in single-variable calculus. This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series.
There are two main things we hope to accomplish (that many high-school calculus courses do not):
- Students will gain a fundamental understanding of single-variable calculus, beyond the level of rote calculation.
- Students will learn how to apply calculus techniques to solve difficult problems.
The course also covers techniques of integration, applications of integration, infinite sequences and series,Taylor polynomials, and power series. Although everyone is welcome in the course, it is aimed primarily to students who have taken a precalculus course and will continue taking more advanced quantitative classes which require a strong calculus background.
Course Outline:
- Sets and Functions
- Trig Functions, Logarithms, and Exponentials
- Limits and Continuity
- Definition of the Derivative
- Chain Rule and Implicit Differentiation
- Interpretation of the Derivative
- Optimization
- More Derivative Applications
- Related Rates
- The Fundamental Theorem of Calculus
- Integration (Riemann)
- Integration (Infinite)
- Integration (Improper)
- Applications of the Integral
- Sequence
- Infinite and Power Series
- Taylor Series
Textbook: Single Variable Calculus: Concepts and Contexts, 4th edition, by James Stewart. We will cover most of the materials from this book. Most homework exercises and reading assignments are taken from the book.
| Attachment | Size |
|---|---|
| chapter_1.pdf | 765.82 KB |
| chapter_2.pdf | 834.98 KB |