Department of Mathematics
Course Outline for Mathematics 102
Differential Equations and Modeling
Spring 2018
Time MWF 9:00 AM - 9:50 AM
Place: Millikan Room 2131
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 - 9:50 am, or by appointment
Text: Differential Equations
by Paul Blanchard, Robert L. Devaney and Glen R. Hall.
Publisher: Brooks/Cole Cengage Learning.
Prerequisites: Linear Algebra and Multivariable
Calculus
Course
Description. This course is an introduction to the
modern qualitative theory of ordinary differential equations and its various
applications to modeling physical and biological phenomena. Emphasis will be placed in the modeling
aspects of differential equations. A
solid knowledge of Linear Algebra will be presupposed. The course topics are listed on the attached
tentative schedule of lectures and examinations.
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: Monday, May 7 9:00 am - 11:00 am.
Place: Millikan Room 2131
Math
102 Spring
2018
Tentative Schedule of Lectures and
Examinations
Date Topic
W Jan.
17 Introduction to
Modeling: The Chemostat System
F Jan.
19 The Chemostat System (continued)
M Jan. 22 Differential
equations
W Jan.
24 Linear systems of
differential equations
F Jan.
26 Solving linear systems
M Jan. 29 Solving
diagonal linear systems: Separation of variables
W Jan.
31 Solving non-diagonal
linear systems: Integrating factors.
F Feb.
2 Solving
diagonalizable systems
M Feb. 5 Solving non-diagonalizable systems
W Feb.
7 Existence
and uniqueness theory for linear systems
F Feb.
9 Existence and uniqueness theory (continued)
M Feb. 12 Review
W Feb.
14 Exam 1
F Feb.
16 General systems of
differential equations
M Feb. 19 Existence
and uniqueness
W Feb.
21 Existence and
uniqueness (continued)
F Feb.
23 Global existence
M Feb. 26 Analysis
of general systems of differential equations
W Feb.
28 Qualitative analysis: equilibrium solutions and stability
F Mar.
2 Qualitative analysi (continued)
M Mar. 5 Qualitative
analysis: Nullclines
W Mar.
7 Principle of linearized stability
F Mar.
9 Principle
of linearized stability (continued)
M Mar. 12 Spring Recess!
W Mar.
14 Spring Recess!
F Mar.
16 Spring Recess!
Date Topic
M Mar. 19 Review
W Mar.
21 Exam 2
F Mar.
23 Analysis of models
M Mar. 26 Analysis
of models: nondimensionalization
W Mar.
28 Nondimensionalization
(continued)
F Mar.
30 Cesar Chavez Day
M Apr. 2 Qualitative
analysis of first-order differential equations
W Apr.
4 Qualitative analysis of
second-order differential equations
F Apr.
6 Qualitative
analysis of second-order differential equations (continued)
M Apr. 9 Conservative systems
W Apr.
11 Conservative systems
(continued)
F Apr.
13 Dissipative systems
M Apr. 16 Dissipative
systems (continued)
W Apr.
18 Gradient systems
F Apr.
20 Gradient systems
(continued)
M Apr. 23 Review
W Apr.
25 Exam 3
F Apr, 27
Review
M Apr. 30 Review
W May
2 Review
M May
7 Final
Examination at 9 am