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Texas A&M University

MATH 172 - Calculus

CATALOG DESCRIPTION: See catalog description here

Course Description

Math 172 is the second of a three semester beginning calculus sequence, which is taken, for the most part, by math, chemistry, and physics majors. The department expects that students passing Math 172 will be able to set up an appropriate definite integral to solve the applied problems (areas, volumes, arclength, work, and force) discussed in the course. Students must understand the relationship between definite integrals and Riemann sums, and be able to clearly state (write) this relationship. Regarding infinite series: students are expected to know what an infinite series is, how to use the convergence tests, be able to clearly state them, and explain (prove) why they work. Students are expected to know the alternating series test, including the error estimate for this test and the error estimate from the integral test for positive term series.

The instructor should not feel that he/she cannot test over topics which were covered in 171. For example, the Mean Value Theorem can be used to derive error estimates for some numerical integration techniques. Asking students to state this theorem, and perhaps apply it in a simple manner is entirely appropriate.

Students should become familiar with the standard notations of logic and set theory. Examples can be found at the end of this document.

Students should be required to demonstrate that they have learned the appropriate definitions and theorems. Keep these facts in mind when assigning homework, constructing quizzes or writing exams. (have link here to sample exam questions)

The priorities of this course are:

  1. Ability to correctly solve problems,and write the solutions in a coherent fashion.
  2. Conceptual understanding of material

The syllabus for this course does not leave much time for anything else. Instructors will have to take pains to stay on schedule. In order to ensure that conceptual ideas and computational techniques are covered and thoroughly discussed, the amount of time spent on Maple has to be carefully controlled. There are at least 13 class periods spent in a computer lab. It is suggested that only 2 or at most 3, of these days be used for Maple. This is not to say that Maple should not be used in the lecture. If the instructor feels that a Maple demo has pedagogical value, then he/she should feel free to present the demo. The question that needs to be addressed is what should a student learn about Maple. The answer, at least for Math 172 is,

• How to integrate.

The instructor needs to keep in mind that the department offers a sister sequence, which is taken by engineering majors. It is very common for students to start in one of these sequences and finish in the other. Because of this, it is imperative that ALL of the topics in the syllabus be covered.