Calculus 1 - 2nd year
Involves a study of limits, continuity, derivatives and integrals; computations of derivatives—sum, product, and quotient formulas, chain rule, implicit differentiation, applications of derivatives to optimization problems and related rate problems; mean-value theorem; definite integrals and fundamental theorem of calculus; application of definite integrals to computations of areas (length, surface) and volumes.
Objectives:
By the end of this course, students will be able to:
1. Demonstrate knowledge of basic precalculus concepts and skills;
2. Evaluate limits;
3. Recognize continuity and use the properties of continuous functions;
4. Find derivatives of algebraic and trigonometric functions using the definition or basic rules of differentiation;
5. Find rates of change;
6. Solve related rate problems;
7. Analyze and sketch the graphs of curves;
8. Find extreme values in optimization problems.
Topics:
Course topics will include the following:
1. Pre-calculus preliminaries
2. Limits
3. Continuity
4. Differentiation
5. Applications of differentiation
Method of Instruction:
1. Classroom lecture
2. Problem–solving activities
Types of Assignments:
1. Reading assignments
2. Problem-solving
Sample Text:
1. Calculus of a Single Variable, 7th ed., Larson, Hostetler, Edwards, 2002.
