Math 234

Differential Equations & Linear Algebra

Fall 2007

Professor Caristi

 

Office:             224 Gellersen

Phone:             5342

e-mail:             James.Caristi@.valpo.edu 

Webpage:       http://www.valpo.edu/home/faculty/jcaristi/m234

 

Text:  Differential Equations & Linear Algebra 2nd edition, by Farlow, Hall, McDill, and West

Text web page:  http://www.prenhall.com/farlow

 

Office Hours (tentative):          Mon., Wed., Thurs., Fri. 12:55     

and by appointment.  I’m usually here in the afternoons from 2-4:30

    

Grading:         3 exams @ 20% each               =  60

Final Exam                               =  25   **   Wednesday, Dec. 19  10:30-12:30

Homework, etc.                       =  15

 

Final Exam: Wednesday, Dec. 19  from10:30 to12:30. Note that this is Special Period #3.

Other exam dates:  Mon. Sept. 24;   Thurs. Oct. 25;   Mon. Dec. 3

 

Honor Code Regulations:

Homework: anything or anybody is authorized aid, but you may not take anything without permission.

Exams, quizzes, and the final:  an independently powered personal calculator/computer may be authorized for a particular exam (as well as the instructor).  If so, this will be announced prior to the exam.  Nothing else is authorized aid.

 

We will be covering most of the topics in chapters 1 through 4, section 5.3, most of 6, and some of 7.  The concepts in this course include elementary differential equations, both qualitative and quantitative aspects, matrices and systems of linear differential equations, eigenvalues and eigenvectors.  More detailed goals and objectives follow.

 

Course Goals and Objectives:

 

I. Goals:

A).  Develop  understanding of the conceptual foundations of  differential equations and linear algebra, and the interrelationship between differential equations and linear algebra.

B).  Develop  knowledge of, and ability to carry out, both exact and numerical procedures for finding solutions to problems of differential equations and linear algebra.

C).  Develop  ability to understand, interpret, and present graphical and qualitative representations of solutions to problems.

 

II. Measurable Objectives.

 

For Goal (A):

1.  define and identify systems of both linear equations and differential equations by order, linearity, and homogeneity.

2.  understand fundamental concepts of matrix algebra.

3.  have a basic understanding of the concept of a vector space, including the concepts of subspace, spanning, linear independence, basis, and dimension.

4.  understand the concepts eigenvalues and eigenvectors. 

5.  understand what it means to be a solution to a system of linear equations, a differential equation, a system of differential equations, or an initial value problem.

6.  understand the principle of superposition and its use in constructing solutions to systems of linear equations, differential equations, and systems of differential equations.

 

For Goal (B). 

1. solve systems of linear equations using matrix techniques.

2.  obtain solutions to a variety of differential equations and initial value problems through exact and numerical means:    

3.  understand how differential equations and systems of differential equations arise in mathematical models, including models of population growth, mixing, cooling, harmonic motion, and electric circuits.

 

For Goal (C): 

1.  determine and analyze the behavior of autonomous first-order differential equations using phase lines.

2.  construct and analyze direction fields of first-order differential equations.

3.  determine and analyze the behavior of linear systems of differential equations using phase plane diagrams.

4.  distinguish between stable and unstable equilibrium of linear systems using phase plane diagrams.

5.  use phase plane diagrams of non-linear autonomous systems of differential equations to analyze their solution near equilibrium points (time permitting).