# MAT 1500 Syllabus

## Syllabus

Textbook: Stewart: Calculus: Early Trancendentals, 8th Edition, Brooks/Cole(Cengage), 2015 [click link for format options]
Coordinators: Marilyn Belkin and Joyce Longman

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

Chapter 5:  Integrals

5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus

A suggested schedule based on a 14 week (56 class hours) semester, is given below. It may be modified at the instructor's discretion. [needs updating for new syllabus ending at 5.3]

Algebra & Trig Review            2 class hours                  Use Appendix  A, B, D
1.1, 1.5                                3 class hours
2.1-2.8                                 9 class hours
3.1-3.9                                 12 class hours
4.1-4.9                                 13 class hours

5.1-5.3                                 6 Class hours

Chapter Reviews                    4 class hours               Reviews appear at                                                                                                             end of each Chapter.

Exam Reviews                       4 class hours                 Includes Final Exam
Review

Exams                                  3 class hours

Maple or other computer software

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

(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.

### Contact Information

Department of Mathematics & Statistics
SAC Room 305
Villanova University
800 Lancaster Avenue
Villanova, PA 19085
Tel: 610.519.4850
Fax: 610.519.6928
Email: math@villanova.edu

Chair:
Dr. Douglas Norton

Staff:
Marie O'Brien, 610.519.4809