MATH 333 - Differential Equations with Matrix Theory

Instructor: Barbara Zubik-Kowal

Office: MG 220 A, Phone: 426-2802

Office Hours: M,T,W 8:40-9:30 am

Textbooks: Differential Equations with Boundary Value Problems, J. Polking/A. Boggess/D. Arnold, Pearson Education, Inc. 2002
 

• Introduction and General Modeling Considerations
• Modeling with First Order Equations
• Qualitative Theory of First Order Equations
• Solution Techniques for First Order Equations
• Numerical Methods for First Order Equations
• Modeling with First Order Systems
• Qualitative and numerical analysis of first order systems
• Second Order Equations
• Matrices and Gaussian elimination
• Elementary matrix algebra
• Matrix inverses
• Determinants
• Eigenvalues and Eigenvectors
• Systems of linear differential equations
• Systems of nonlinear differential equations
• Forcing and resonance
• The Laplace Transform

 

As an applied mathematics course, the objectives of M 333 reflect three of the Department's teaching goals: that  students be able to give examples of nontrivial applications of mathematics to various (non-mathematical) fields, that students be able to use suitable mathematical tools, and that students use mathematics as a language. As a service course taken primarily by non-majors, M 333 does not stress the aesthetic side of mathematics or the idea  of mathematics as the study of patterns.

Upon completion of this course, students should:

• Be able to explain the meaning of an ordinary differential equation, both geometrically and analytically.
• Use calculus to obtain qualitative information about solutions of a differential equation even if no analytic form of the solution is available.
• Be able to formulate a differential equation describing a situation in the sciences or engineering, given a clear  statement of the scientific or engineering principles involved.
• Be able to use a number of elementary techniques for the analytic solution of differential equations.
• Be able to use simple numerical algorithms for the approximate solution of differential equations and be able to explain the difference between a solution obtained analytically and one obtained numerically.
• Be able to solve problems using computer software implementing advanced numerical algorithms.
• Be able to solve problems involving basic matrix theory including matrix algebra, determinants, and eigenvalues.
• Be able to use matrix theory to solve systems of linear differential equations.

 

Tests, Quizes, Homework, Final Exam
Test 1 : 02/13/2006	comprehensive problems
Test 2 : 03/13/2006	comprehensive problems
Test 3 : 04/10/2006	comprehensive problems
Unexpected quizes	short and quick problems
Link to Homework Assignments	full solutions collected each Monday
Final Exam	comprehensive problems

Grading Policy
Three tests and unexpected quizes	100/3 %
Homework	100/3 %
Final Exam	100/3 %
Total	100 %
A: 90% and above; B: 80%-90%; C: 70%-80%; D: 60%-70%; E: below 60%.

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