Department of Mathematics & Statistics
SAC Room 305
800 Lancaster Avenue
Villanova, PA 19085
Coordinator: Maria Baranski (firstname.lastname@example.org, 610-519-6949)
Textbook: Calculus/Single Variable, Seventh Edition
Authors: Deborah Hughes-Hallett, Andrew M. Gleason, and William G. McCallum, et al.
* This book is available as a Wiley E-Text.
* Do not purchase an older edition. The sections are similar, but the exercises are very different.
* Do not purchase the version with “Multivariable” in the title.
Table of Contents
1. Foundation for Calculus: Functions and Limits
2. Key Concept: The Derivative
3. Short-Cuts to Differentiation
4. (Optional) Using the Derivative
5. Key Concept: The Definite Integral
1.1 Functions and Change
1.2 Exponential Functions
1.3 New Functions from Old
1.4 Logarithmic Functions
1.5 Trigonometric Functions
1.6 Powers, Polynomials, and Rational Functions
1.7 Introduction to Limits and Continuity
1.8 Extending the Idea of a Limit
1.9 Further Limit Calculations Using Algebra
2.1 How Do We Measure Speed?
2.2 The Derivative at a Point
2.3 The Derivative Function
2.4 Interpretations of the Derivative
2.5 The Second Derivative
3.1 Powers and Polynomials
3.2 The Exponential Function
3.3 The Product and Quotient Rules
3.4 The Chain Rule
3.5 The Trigonometric Functions
3.6 The Chain Rule and Inverse Functions (ln and a^x only)
5.1 How Do We Measure Distance Traveled?
5.2 The Definite Integral
5.3 The Fundamental Theorem and Interpretations
5.4 Theorems about Definite Integrals
The 1320-25 sequence is designed for liberal arts majors, not scientists or engineers. Among other things, that means they do not need a specific collection of techniques for future courses, so we do not have to cover every technique or topic that we assume from experience has always been important. If you are used to teaching 1500-1505-2500, please remember that those are 4 credit courses, while 1320 is a 3 credit course. We cannot cover as much material! That does not mean we should intellectually compromise or water down our presentations. The point of a course like this one counting as a core mathematics requirement is to give a true sense of what mathematics is about. Our task is to get across an appreciation of the basic concepts of both differential and integral calculus.