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Math 3A: General Course Outline

Catalog Description

3A. Calculus for Life Sciences Students. (4) Lecture, three hours; discussion, one hour. Preparation: three and one-half years of high school mathematics (including trigonometry). Requisite: successful completion of Mathematics Diagnostic Test (score of 35 or better) or course 1 at UCLA with a grade of C- or better. Not open for credit to students with credit in another calculus sequence. Modeling with functions, limits and derivatives, decisions and optimization in biology, derivative rules and tools. P/NP or letter grading.

Course Information:

The following schedule, with textbook sections and topics, is based on 24 lectures. The remaining classroom meetings are for leeway, reviews, and two midterm exams. These are scheduled by the individual instructor.

Math 3ABC is the "fast" calculus sequence at UCLA. It aims to provide students in three terms with the fundamental ideas and tools of calculus that will put them in a good position for understanding more technical work in their own areas. The course sequence covers basic topics in single-variable and multi-variable calculus. This includes some material on ordinary differential equations such as those governing population-growth models. The course also covers some material on calculus-based probability theory, including continuous probability distributions, the normal distribution, and the idea of hypothesis testing.

The course sequence 3ABC is suitable for students who want to be introduced to the powerful tools that the calculus provides without going through some of the more technical material required of the students in engineering and the physical sciences. While examples and illustrations are drawn from the life sciences when possible, the course sequence is also suitable for students in the social sciences and humanities who do not require a heavy mathematical background.

Students in 3ABC are expected to have a good background in precalculus mathematics, including polynomial functions, trigonometric functions, and exponential and logarithm functions. In order to enroll in 3A, 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.

Many of the students in Math 3ABC take Physics 6, either concurrently or later. The topics covered in 3ABC are selected so as to provide students with the prerequisite foundations for Physics 6.

Ample tutoring support is available for students in the course, including the walk-in tutoring service of the Student Mathematics Center at MS 3974.

Textbook

S. J. Schreiber, Calculus for the Life Sciences, Wiley.

Outline update: P. Greene, 11/15

Schedule of Lectures

Lecture Section Topics

1

Intro

Preview of Modeling and Calculus

2

1.1

Real Numbers and Functions

3

1.2

Data Fitting with Linear and Periodic Functions

4

1.3

Power Functions and Scaling Laws

5

1.4

Exponential Growth

6

1.5

Function Building

7

1.6

Inverse Functions and Logarithms

8

1.7

Sequences and Difference Equations

9

Catch-Up, Review

10

2.1

Rates of Change and Tangent Lines

11

2.2

Limits (no formal definition)

12

2.3

Limit Laws and Continuity

13

2.4

Asymptotes and Infinity

14

2.5

Sequential Limits

15

2.6

Derivatives at a Point

16

2.7

The Derivative as a Function

17

Catch-Up, Review

18

3.1

Derivative of Polynomial and Exponential Functions

19

3.2

Product And Quotient Rule (no proof required)

20

3.3

Chain Rule and Implicit Differentiation

21

3.4

Derivatives of Trigonometric Functions

22

3.5

Linear Approximation

23

3.6

Higher Derivatives

24

3.7

L'Hopital's Rule
Catch-Up, Review