Functions, Limits, continuity and derivatives. Applications. Extreme values, the Mean Value Theorem and its applications. Graphing. The definite integral. Area and volume as integrals. The indefinite integral. Transcendental functions and their derivatives. L'Hopital's rule. Techniques of integration. Improper integrals. Applications. Parametric curves. Polar coordinates.
The objective of this course is to provide a good background on single variable calculus, including limits, derivatives, applications of derivatives, and integration.
| Week | Topic |
|---|---|
| 1 | Functions and models.Overview of the essential functions.The domain and range.Odd and even functions. |
| 2 | New functions from old ones. One-to-one and onto functions. Bijections. Inverse functions. |
| 3 | The concept of the limit, precise definition. One-sided limits. Infinite limits, vertical asymptotes. |
| 4 | Limits at infinity, horizontal asymptotes. Indeterminate forms. The sandwich theorem. Continuity. |
| 5 | The concept of the derivative.The formal definition of the derivative.Constructing the table of der. |
| 6 | Techniques of differentiation. The sum, product, ratio and chain rule. Higher order derivatives. |
| 7 | Application of derivatives: Monotony and local extreme values. Concavity and inflection points. Sketching graphs of functions. |
| 8 | Midterm exam. |
| 9 | Applications of derivatives: mean value theorem, L'Hospital's rule. |
| 10 | Applications of derivatives: optimization problems. |
| 11 | Related rate problems. Implicit differentiation. |
| 12 | Introduction to integrals.The fundamental theorem of calculus. |
| 13 | Techniques of integration. The substitution rule, integration by parts, integration of rational functions. |
| 14 | Improper integrals. |
| Method | % Each | Quantity |
|---|---|---|
| Homework | 10 | 1 |
| Midterm Exam(s) | 35 | 1 |
| Final Exam | 45 | 1 |
| Other | 10 | 1 |
"STEWART CALCULUS Early Transcendentals", James Stewart (8th edition)