Department of Mathematics

Pomona College

 

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 / arumbos@pomona.edu

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.   Readings and problem sets will be assigned at every lecture.  Homework assignments will be collected on an alternate basis.  Students are strongly encouraged to work on every assigned problem.  Late homework assignments will not be graded.

 

 

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