# Math 3B: General Course Outline

## Catalog Description

3B. Calculus for Life Sciences Students. (4) Lecture, three hours; discussion, one hour. Requisite: course 3A with grade of C- or better. Not open for credit to students with credit for course 31B. Applications of differentiation, integration, differential equations, linear models in biology, phase lines and classifying equilibrium values, bifurcations. P/NP or letter grading.

## Course Information:

The following schedule, with textbook sections and topics. 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

4.1

Graphing Using Calculus

2

4.2

Extreme Values

3

4.3

Optimization in Biology

4

4.4

Decision and Optimization

5

4.5

Linearization and Difference Equations

6

Catch-Up, Review

7

5.1

Antiderivatives

8

5.2

Accumulated Change and Area under a Curve

9

5.3

The Definite Integral

10

5.4

The Fundamental Theorem

11

5.5

Substitution

12

5.6

Integration by Parts and Partial Fractions

13

5.8

Application of Integration

14

Catch-Up, Review

15

6.1

Introduction to Differential Equations

16

6.2

Solutions and Separable Equations

17

6.3

Linear Models in Biology

18

6.4

Slope Fields and Euler's Method

19

6.5

Phase Lines and Classifying Equilibria

20

6.6

Bifurcation Preview of Modeling and Calculus

21

Catch-Up

22

Review