Math 3C: General Course Outline

Catalog Description

3C. Ordinary Differential Equations with Linear Algebra for Life Sciences Students. (4) Lecture, three hours; discussion, one hour. Requisite: course 3B with grade of C- or better. Multivariable modeling, matrices and vectors, eigenvalues and eigenvectors, linear and nonlinear systems of differential equations, probabilistic applications of integration. P/NP or letter grading.

Course Information:

The following schedule, with textbook sections and topics, is based on 25 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, 3/16

Schedule of Lectures

Lecture Section Topics

1-3

7.1, 7.2

Histograms, PDFs and CDFs
Improper integrals

4-6

7.3,7.4

Mean and Variance
Bell shaped distributions

7-9

7.5

Life tables

10-12

Catch-Up, Review

13-15

8.1

Multivariate Modeling

16-18

8.2

Matrices and Vectors

19-21

8.3

Eigenvalues and Eigenvectors
Catch-Up, Review

22-24

8.4

Systems of Linear Differential Equations

25-27

8.5

Non-linear systems

28-30

Catch up, Review