MAT 1500 Syllabus

MAT 1500 Calculus I


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.

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

Dr. Douglas Norton

Christine Gadonas 610.519.4809