Mat 1325: Calculus II for Liberal Arts

 

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

Textbook:

Calculus: Single Variable, 6th edition, by Deborah Hughes-Hallett, Andrew Gleason, William McCallum, et al., John Wiley & Sons, 2013. ISBN: 978-0-470-88864-3.

The course:

The MAT 1320-25 sequence provides an opportunity for arts majors to encounter calculus without committing to the 4 credit hours required by MAT 1500 or 1505. In the first semester, students will cover sections 1.1-3.5 amd 5.1-5.4. In addition to those required sections, they will also cover selected optional material from sections 3.6-4.8, depending on the instructor's preferences.

In the second semester, the instructor will select material from Chapters 6-11.

Because MAT 1325 is a terminal course, and in fact is not a prerequisite for any other course, we have traditionally allowed this total freedom of choice on the part of the instructor. (It is a tradition that dates back to the "Stewart" era of the course.) One sample syllabus is shown below. You are under no obligation to follow this particular choice of sections:

6.1: Antiderivatives Graphically and Numerically

6.2: Constructing Antiderivatives Analytically

6.3: Differential Equations and Motion

6.4: Second Fundamental Theorem of Calculus

7.1: Integration by Substitution

7.2: Integration by Parts

7.3: Tables of Integrals

7.4: Algebraic Identities and Trigonometric Substitutions

7.5: Numerical Methods for Definite Integrals

7.6: Improper Integrals

7.7: Comparison of Improper Integrals

8.1: Areas and Volumes

8.2: Applications to Geometry

8.6: Applications to Economics

11.1: What is a Differential Equation?

11.4: Separation of Variables

11.5: Growth and Decay

11.6: Applications and Modeling

11.7: The Logistic Model

Instructors should be aware that the chain rule is touched on lightly in 1320, so you will need to review sections 3.4/3.6 if you intend to teach substitution (section 7.1).

The audience:

Most students who take MAT 1320 do not go on to take 1325.  Those who do usually have high interest in the course.  The result is that the students in 1325 are, on average, a little more capable than the "average" 1320 student, and this is good news for you as an instructor.

Important note:

Remember that 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 courses total 12 credits, while 1320-25 totals only 6 credits.  We cannot cover as much as the engineers!  That doesn't 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 coexist with honest mathematical insight and presentation.

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