# Calculus 1 - 2nd year

Involves a study of limits, continuity, derivatives and integrals; computations of derivativesâ€”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. Problemâ€“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.