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Math 31A: General Course Outline

Catalog Description

31A. Differential and Integral Calculus. (4) Lecture, three hours; discussion, one hour. Preparation: at least three and one-half years of high school mathematics (including some coordinate geometry and trigonometry). Requisite: successful completion of Mathematics Diagnostic Test or course 1 with a grade of C- or better. Differential calculus and applications; introduction to integration. P/NP or letter grading.

Course Information:

The following schedule, with textbook sections and topics, is based on 26 lectures. The remaining classroom meetings are for leeway, reviews, and two midterm exams. These are scheduled by the individual instructor. Often there are reviews and midterm exams about the beginning of the 4th and 8th weeks of instruction, plus reviews for the final exam.

In certain cases (such as for coordinated classes), it may be possible to give midterm exams during additional class meetings scheduled in the evening. This has the advantage of saving class time. A decision on whether or not to do this must be made well in advance so that the extra exam sessions can be announced in the Schedule of Classes. Instructors wishing to consider this option should consult the mathematics undergraduate office for more information.

The goal of Math31AB is to provide a solid introduction to differential and integral calculus in one variable. The course is aimed at students in engineering, the physical sciences, mathematics, and economics. It is also recommended for students in the other social sciences and the life sciences who want a more thorough foundation in one-variable calculus than that provided by Math 3.

Students in 31AB are expected to have a strong background in precalculus mathematics, including polynomial functions, trigonometric functions, and exponential and logarithm functions. In order to enroll in 31A, students must either take and pass the Mathematics Diagnostic Test at the specified minimum performance level, or take and pass Math 1 at UCLA with a grade of C- or better.

Most students entering the 31-32-33 sequence at UCLA have taken a calculus course in high school and enter directly into Math 31B, for which there is no enforced prerequisite.

The course 31A covers the differential calculus and integration through the fundamental theorem of calculus. The first part of course 31B is concerned with integral calculus and its applications. The rest of the course is devoted to infinite sequences and series.

Single-variable calculus is traditionally treated at many universities as a three-quarter or two-semester course. Thus Math 31AB does not cover all of the topics included in the traditional single-variable course. The main topics that are omitted are parametric curves and polar coordinates, which are treated at the beginning of 32A.

Ample tutoring support is available for students in the course, including the walk-in tutoring service of the Student Mathematics Center.

Math 31A is not offered in the Spring Quarter. Students wishing to start calculus in the Spring may take 31A through University Extension in the Spring or in the Summer.

Please note: Students who are in the College of Letters and Science who will be enrolled at UCLA in Spring and wish to enroll in Extension simultaneously should meet with a College Counselor about whether they will be able to receive credit for the course because of concurrent enrollment restrictions: Concurrent Enrollment Information.

Textbook

J. Rogawski, Single Variable Calculus, (3rd Edition) , W.H. Freeman & CO

(a) Limits should be presented very informally with an emphasis on working with their properties: the "Limit Laws".

(b) Section 6.2 should be restricted to the topic of average value.

Outline update: 3/15 R. Brown

Schedule of Lectures

Lecture Section Topics

1

Introduction

2

2.3-4

Limit Laws, Limits and Continuity (a)

3

2.5

Evaluating Limits Algebraically

4

2.6-2.7

Trigonometric Limits, Limits at Infinity

5

2.8

Intermediate Value Theorem

6

3.1

Definition of the Derivative

7

3.2

The Derivative as a Function

8

3.3

Product and Quotient Rules

9

3.5-6

Higher Derivatives, Trig Functions

10

3.7

The Chain Rule

11

3.8

Implicit Differentiation

12

3.9

Related Rates

13

Midterm 1 (2.3-8, 3.1-3,3.5-7)

14

4.1-2

Linear Approximation, Extreme Values

15

4.2

Extreme Values continued

16

4.3

Mean Value Theorem

17

4.4

The Shape of a Graph

18

4.5

Graph Sketching

19

4.6

Applied Optimization

20

4.7, 5.1

Newton's Method, Area

21

5.2

The Definite Integral

22

Midterm 2 (3.8-9; 4.1-5)

23

5.3

The Indefinite Integral

24

5.4

Fundamental Theorem I

25

5.5

Fundamental Theorem II

26

5.7

The Substitution Method

27

6.1-2

Areas Between Curves, Average Value (b)

28

6.3

Volumes of Revolution

29

6.4

Method of Cylindrical Shells