MAT 1320 Syllabus

Math 1320 Calculus I for Liberal Arts

Coordinator: Paul Pasles (paul.pasles@villanova.edu, 610-519-7345)

Text: Calculus: Single Variable, 6th Edition, by Deborah Hughes-Hallett, Andre Gleason, William McCallum, et al. (Wiley & Sons, 2013), ISBN: 978-0-470-88864-3. This text is also used for the continuation, MAT 1325.


Table of Contents (first semester):

1. A Library of Functions
2. Key Concept: The Derivative
3. Short-Cuts to Differentiation
4. Using the Derivative (optional)
5. Key Concept: The Definite Integral

Required Sections:

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 continuity
1.8: Limits
   
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
2.6: Differentiability
   
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
   
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

Schedule of Topics:

Below you wil find a rough schedule based on a 14 week, 3 hours/week semester. The sections listed here shuld be covered by all instructors. Additional sections may be chosen at your discretion.

Week Sections
1 1.1, 1.2
2 1.3, 1.4, 1.5
3 1.6,1.7, review for exam
4 1st exam, 1.8
5 2.1, 2.2, 2.3
6 2.4, 2.5, 2.6
7 3.1, 3.2, review for exam
8 2nd exam, 3.3, start 3.4
9 finish 3.4, 3.5, 5.1
10 5.2, 5.3, 5.4
11 to 14 instructor's selected topics from the rest of chapter 3 and 4, with a 3rd exam some time during this period

Please consider the timing suggestions as very rough; use your own judgment to set the pace. The number of exams is up to you, obviously. Do try to keep in occasional contact with me during the semester, so that we can reach a common starting place for 1325 if it runs in the spring.

The 1320-25 sequence is designed for liberal arts majors, not scientists or engineers. Among other things, that means they don't need a specific collection of techniques for future courses, so we don't 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 very basic concepts of both differential and integral calculus. A slower pace and fewer topics can coexists with honest mathematical insight and presentation.

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