Department of Mathematics
Course Outline for Mathematics 102
Differential Equations and Modeling
Spring 2017
Time MWF 11:00 AM - 11:50
AM
Place: Millikan Room 1249
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew 2287.
Phone/e-mail: ext. 18713 /
Courses
Website: http://pages.pomona.edu/~ajr04747/
Office
Hours: MWF 10:00 am - 10:50 am, or by appointment
Text: Differential Equations
by Paul Blanchard, Robert L. Devaney and Glen
R.Hall. Publisher: 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 8 9:00 am - 11:00 am.
Place: Millikan Room 1249
Math
102 Spring 2017
Tentative Schedule of Lectures and
Examinations
Date Topic
W Jan. 18 Introduction to Modeling: The Chemostat System
F Jan. 20 The Chemostat
System (continued)
M Jan. 23 Differential
equations
W Jan. 25 Linear systems of differential
equations
F Jan. 27 Solving linear systems
M Jan. 30 Solving
diagonal linear systems: Separation of variables
W Feb. 1 Solving
non-diagonal linear systems: Integrating factors.
F Feb. 3 Solving
diagonalizable systems
M Feb. 6 Solving non-diagonalizable systems
W Feb. 8 Existence
and uniqueness theory for linear systems
F Feb. 10 Existence and uniqueness theory
(continued)
M Feb. 13 Review
W Feb. 15 Exam 1
F Feb. 17 General systems of differential
equations
M Feb. 20 Existence
and uniqueness
W Feb. 22 Existence and uniqueness (continued)
F Feb. 24 Global existence
M Feb. 27 Analysis
of general systems of differential equations
W Mar. 1 Qualitative
analysis: equilibrium solutions and stability
F Mar.
3 Qualitative analysi (continued)
M Mar. 6 Qualitative
analysis: Nullclines
W Mar. 8 Principle
of linearized stability
F Mar.
10 Principle of
linearized stability (continued)
M Mar. 13 Spring Recess!
W Mar. 15 Spring
Recess!
F Mar.
17 Spring Recess!
Date Topic
M Mar. 20 Review
W Mar. 22 Exam 2
F Mar.
24 Analysis of models
M Mar. 27 Analysis
of models: nondimensionalization
W Mar. 29 Nondimensionalization
(continued)
F Mar.
31 Cesar Chavez Day
M Apr. 3 Qualitative
analysis of first-order differential equations
W Apr. 5 Qualitative analysis of second-order
differential equations
F Apr. 7 Qualitative
analysis of second-order differential equations (continued)
M Apr. 10 Conservative
systems
W Apr. 12 Conservative systems (continued)
F Apr. 14 Dissipative systems
M Apr. 17 Dissipative
systems (continued)
W Apr. 19 Gradient systems
F Apr. 21 Gradient systems (continued)
M Apr. 24 Review
W Apr. 26 Exam 3
F Apr,
28 Review
M May 1 Review
W May
3 Review
M May
8 Final
Examination at 9 am