Department of Mathematics
Course Outline for Mathematics 32S
Calculus III with Applications to the
Sciences
Spring 2019
Time MWF 10:00 am - 10:50 am
Place: Millikan 2393
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew 2287
Phone/e-mail: ext. 18713 /
Courses
Website: http://pages.pomona.edu/~ajr04747/
Office
Hours: TR
9:00 am – 10:00 am, or by appointment
Text: Online lecture notes at http://pages.pomona.edu/~ajr04747/
Prerequisites: Calculus II
Course
Description. This course presents the core topics of Multivariable
Calculus (Math 32), Linear Algebra and Probability in the context of problems from
the sciences. Topics include: vector fields, limits and continuity,
differentiability, linearization, probability distributions, multiple
integrals, line integrals, and Green's Theorem. Applications include models of
species interaction in ecosystems, the spread of disease and mutations.
Assigned Readings and Problems.
Grading
Policy. Grades will be based on the homework, three
50-minute examinations, plus a comprehensive final examination. The overall score will be computed as
follows:
homework 20%
three 50-minute exams 50%
final examination 30%
Final
Examination.
Time: Thursday, May 16 9:00 am - 12:00 pm.
Place: Millikan 2393
Math 32S Spring
2019
Tentative Schedule of Lectures and
Examinations
Date Topic
W Jan.
23 Introduction: An
Example from Epidemiology
F Jan.
25 A simple SIR Model
M Jan. 28 Paths
in the plane and in space
W Jan.
30 Continuous paths
F Feb.
1 Differentiable
paths
M Feb. 4 Tangent
lines to paths
W Feb.
6 Applications:
Modeling the interactions of species in an ecosystem
F Feb.
8 Predator-prey
systems
M Feb. 11 Phase plane analysis
W Feb.
13 Phase plane analysis
(Continued)
F Feb.
15 Equilibrium points and
stability
M Feb. 18 Review
W Feb.
20 Exam 1
F Feb.
22 Vector fields
M Feb. 25 Differentiable
vector fields
W Feb.
27 Derivative of a vector
field
F Mar.
1 Linearization
M Mar. 4 Linearization (continued)
W Mar.
6 The
derivative map
F Mar.
8 The derivative map (continued)
M Mar. 11 Real
valued functions of a several variables
W Mar.
13 Differentiability and
the gradient
F Mar.
15 Problems
M Mar. 18 Spring Recess!
W Mar.
20 Spring Recess!
F Mar.
22 Spring Recess!
Date Topic
M Mar. 25 The
predator-prey system (revisited)
W Mar.
27 Integral curves
F Mar.
29 Cesar Chavez Day
M Apr. 1 Review
W Apr.
3 Exam 2
F Apr.
5 Application: Probability distributions
M Apr. 8 Integration
in the plane and in space
W Apr.
10 Double and triple
integrals
F Apr.
12 Double and triple
integrals (continued)
M Apr. 15 Integration
on paths
W Apr.
17 Integration on paths
(continued)
F Apr.
19 Application: Periodic
solutions
M Apr. 22 Applications:
Modeling mutation rates
W Apr.
24 Probability
distributions
F Apr.
26 The Binomial and
Poisson distributions
M Apr. 29 Review
W May
1 Exam 3
F May
3 Review
M May 6 Review
W May
8 Review
Th May
16 Final Examination at
9 am