Course Syllabus

Course Description

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.

Course Objectives

The objective of this course is to provide a good background on single variable calculus, including limits, derivatives, applications of derivatives, and integration.

Key Concepts

1. Overview of the essential functions.The domain and range.Odd and even functions.
2. Bijections. Inverse functions.
3. One-sided limits. Infinite limits, vertical asymptotes.
4. Limits at infinity, horizontal asymptotes
5. The concept of the derivative
6. Techniques of differentiation
7. Monotony and local extreme values
8. L'Hospital's rule.
9. Implicit differentiation.
10. Techniques of integration

Learning Outcomes

1. Ability to follow a chain of logical arguments.
2. Knowledge of the fundamentals of differential and integral calculus for functions of one variable
3. Gaining an adequate ability in computation.

Recommended Textbooks

"STEWART CALCULUS Early Transcendentals", James Stewart (8th edition)