## MAT 1500 Calculus I

## Syllabus

Textbook: Stewart: *Calculus: Early Trancendentals,* 8th Edition, Brooks/Cole(Cengage), 2015 [click link for format options]

Coordinators: Kathleen Acker

**Chapter 1: Functions and Models**

1.1 Four ways to Represent a Function

1.2 Mathematical Models

1.4 Exponential Functions

1.6 Inverse Functions and Logarithms

**Chapter 2. Limits and Derivatives**

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change

2.8 The Derivative as a Function

**Chapter 3. Differentiation Rules**

3.1 Derivatives of Polynomials and Exponential Functions

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Natural Sciences

3.8 Exponential Growth and Decay

3.9 Related Rates

**4. Applications of Differentiation**

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 Derivatives and the Shapes Of Curves

4.4 Indeterminate Forms and L'Hopital's Rule

4.5 Summary of Curve Sketching

4.6 Graphing with Calculus and Calculators

4.7 Optimization Problems

4.9 Antiderivatives

**Chapter 5: Integrals**

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

This material is covered over a 14 week (56 class hours) semester.

**WebAssign Remarks.**

**Maple or other computer software**

Maple or other computer software discussions should be determined by each instructor. Each student should master the following topics at the very minimum:

(1) assigning variables, expressions, and functions, (2) evaluating expressions and functions, (3) distinctions between exact and approximate arithmetic, (4) graphing, (5) using graphs to solve equations exactly and approximately, (6) finding limits (numerical and exact) and derivatives, and (7) knowing how to use the "help" command.