Math 333
Differential Equations with Matrix Theory
Catalog Description
M 333 DIFFERENTIAL EQUATIONS WITH MATRIX THEORY (4-0-4) Use of differential equations to model phenomena in sciences and engineering. Solution of differential equations via analytic, qualitative and numerical techniques. Linear and nonlinear systems of differential equations. Introduction to matrix algebra, determinants, eigenvalues, and solutions of linear systems. Laplace transforms. PREREQ: M 175.
Prerequisites
M 175 Calculus and Analytic Geometry, or equivalent calculus elsewhere, or permission of the instructor. The rationale for the prerequisite is that students should have enough experience with the concept of the derivative and the integral that the idea of a differential equation makes sense, and that the computations involved in some of the solution techniques are possible for them.
Jurisdiction
This course is not currently controlled by a departmental committee and individual instructors may choose different textbooks. Exams, homework, and grading system are left to the instructor.
Learning Objectives
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:
Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:
Topics and Approximate Timeline
The following table is based on a typical semester schedule-60 class meetingsof 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.
Text
The current text is Differential Equations, Paul Blanchard, Bob Devaney, and Glen Hall, PWS Publishing Company. Other textbooks that have been used in recent years include Differential Equations, A Modeling Approach, Frank R. Giordano and Maurice D. Weir, Addison-Wesley, Ordinary Differential Equations and Their Applications, Short Version, Martin Braun, Springer-Verlag, Introduction to Differential Equations with Boundary Value Problems, Larry C. Andrews, Harper Collins, and A First Course in Differential Equations, 5e, Dennis G. Zill, PWS-Kent.
Format, Student Activities, and Grades
Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity; the instructor chooses the appropriate mix. The computer algebra system, Maple, is used for laboratory activities and homework. Homework is an important part of the course; many exercises involve extensions of ideas in the text to new situations, rather than just routine applications. Some exams may be partially take-home. The instructor chooses the exact grading scheme, but a typical distribution might be:
Letter grades are based on a scale in which 90% of the total possible points guarantees an A, 80% a B, 70% a C, and 60% a D, with the instructor having the discretion to lower these cut-offs if warranted.
Differential Equations with Matrix Theory
Catalog Description
M 333 DIFFERENTIAL EQUATIONS WITH MATRIX THEORY (4-0-4) Use of differential equations to model phenomena in sciences and engineering. Solution of differential equations via analytic, qualitative and numerical techniques. Linear and nonlinear systems of differential equations. Introduction to matrix algebra, determinants, eigenvalues, and solutions of linear systems. Laplace transforms. PREREQ: M 175.
Prerequisites
M 175 Calculus and Analytic Geometry, or equivalent calculus elsewhere, or permission of the instructor. The rationale for the prerequisite is that students should have enough experience with the concept of the derivative and the integral that the idea of a differential equation makes sense, and that the computations involved in some of the solution techniques are possible for them.
Jurisdiction
This course is not currently controlled by a departmental committee and individual instructors may choose different textbooks. Exams, homework, and grading system are left to the instructor.
Learning Objectives
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.
Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:
- Periodic problem sets for homework serve both as learning
and as assessment tools. Classroom activities may vary depending on
students' outcomes on homework assignments.
- Problems given on take-home exams are designed to evaluate a
student's ability to solve more complicated and time consuming
problems. Moreover, take-home problems give students the
opportunity to demonstrate their ability to use technology to solve
problems involving real data or otherwise not amenable to simple
analytic techniques.
- Problems given on in-class exams are designed to give students the opportunity to demonstrate their ability to work simpler and less time consuming problems which probably do not involve real data.
Topics and Approximate Timeline
The following table is based on a typical semester schedule-60 class meetingsof 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.
| Topic | Number of Lectures |
| Introduction and General Modeling Considerations | 3 |
| Modeling with First Order Equations | 2 |
| Qualitative Theory of First Order Equations | 4 |
| Solution Techniques for First Order Equations | 3 |
| Numerical Methods for First Order Equations | 2 |
| Modeling with First Order Systems | 3 |
| Qualitative and numerical analysis of first order systems | 3 |
| Second Order Equations | 2 |
| Matrices and Gaussian elimination | 2 |
| Elementary matrix algebra | 3 |
| Matrix inverses | 2 |
| Determinants | 3 |
| Eigenvalues and Eigenvectors | 4 |
| Systems of linear differential equations | 9 |
| Systems of nonlinear differential equations | 3 |
| Forcing and resonance | 3 |
| The Laplace Transform | 4 |
| Exams | 3 |
| Total | 58 |
Text
The current text is Differential Equations, Paul Blanchard, Bob Devaney, and Glen Hall, PWS Publishing Company. Other textbooks that have been used in recent years include Differential Equations, A Modeling Approach, Frank R. Giordano and Maurice D. Weir, Addison-Wesley, Ordinary Differential Equations and Their Applications, Short Version, Martin Braun, Springer-Verlag, Introduction to Differential Equations with Boundary Value Problems, Larry C. Andrews, Harper Collins, and A First Course in Differential Equations, 5e, Dennis G. Zill, PWS-Kent.
Format, Student Activities, and Grades
Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity; the instructor chooses the appropriate mix. The computer algebra system, Maple, is used for laboratory activities and homework. Homework is an important part of the course; many exercises involve extensions of ideas in the text to new situations, rather than just routine applications. Some exams may be partially take-home. The instructor chooses the exact grading scheme, but a typical distribution might be:
| Homework (including a writing assignment and project) | 33⅓% |
| 3 Exams | 33⅓% |
| Final Exam | 33⅓% |
| Total | 100% |
Letter grades are based on a scale in which 90% of the total possible points guarantees an A, 80% a B, 70% a C, and 60% a D, with the instructor having the discretion to lower these cut-offs if warranted.
Updated Fall 1998
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