Blackboard at UCD MATH 3200 - 001

College of Liberal Arts and Sciences
Fall 2008

Instructor Information

Name:
Andrew Knyazev

Email:
Andrew.Knyazev[at]ucdenver.edu

Office:
1250 14th St. UC Denver Room 644

Office Hours:
Tue.,Th. 2:30-4PM

Official Course Description

ELEMENTARY DIFFERENTIAL EQUATIONS

MATH 3200-3. Elementary Differential Equations. First and second order differential equations, Laplace transforms, systems of equations, with an emphasis on modeling and applications.

Section Details - MATH 3200 - 001
NO JOINT CREDIT WITH MATH 3195.
Prereq: MATH 2411; coreq is MATH 3191.

Meetings
T R - 01:00PM to 02:15PM at WC 159

Textbooks

Required

A Course in Ordinary Differential Equations (typos and comments)

by Randall J. Swift and Stephen A. Wirkus
Chapman & Hall/CRC; 1 edition (October 23, 2006)

ISBN: 1584884762

Book is required

http://books.google.com/books?id=quW5ULE7RIIC

Ordinary Differential Equations

by Morris Tenenbaum and Harry Pollard
Dover Publications (October 1, 1985)

ISBN: 0486649407

Book is required

http://books.google.com/books?id=29utVed7QMIC

GRADING

Grading will be based on 7 take-home quizzes: one quiz for every chapter, 10% each (70% total), the final in-class test 30%, and a MATLAB computer project 20%. A linear scale for grades will be used with no curving.
Grading scale for UCD and Metro
% 0-20%21-40%41-60%61-80%81-100%
Metro F D C B A
% 0-20%21-27%28-34%35-40%41-47%48-54%55-60%61-67%68-74%75-80%81-90%91-100%
UCD F D- D D+ C- C C+ B- B B+ A- A

TENTATIVE CONTENTS

The class is planned to follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

From the textbook by Morris Tenenbaum and Harry Pollard

Chapter 1. BASIC CONCEPTS.

From the textbook by Swift and Wirkus

TRADITIONAL FIRST ORDER DIFFERENTIAL EQUATIONS
Some Basic Terminology
Separable Differential Equations
Some Physical Problems arising as Separable Equations
Exact Equations
Linear Equations

GEOMETRICAL & NUMERICAL METHODS FOR FIRST ORDER EQUATIONS
Direction Fields - the Geometry of Differential Equations
Existence and Uniqueness for First Order Equations
First Order Autonomous Equations - Geometrical Insight
Population Modeling: An Application of Autonomous Equations (independent reading)
Numerical Approximation with the Euler Method

ELEMENTS OF HIGHER ORDER LINEAR EQUATIONS
Some Terminology
Essential Topics from Linear Algebra
Reduction of Order - The Case n=2
Operator Notation
Numerical Considerations for nth Order Equations

TECHNIQUES OF HIGHER ORDER LINEAR EQUATIONS
Homogeneous Equations with Constant Coefficients
A Mass on a Spring (independent reading)
Nonhomogeneous Equations
The Method of Undetermined Coefficients via Tables

FUNDAMENTALS OF SYSTEMS OF DIFFERENTIAL EQUATIONS
Systems of Two Equations - Motivational Examples (independent reading)
Useful Terminology
Linear Transformations and the Fundamental Subspaces
Eigenvalues and Eigenvectors

TECHNIQUES OF SYSTEMS OF DIFFERENTIAL EQUATIONS
A General Method, Part I: Solving Systems with Real, Distinct Eigenvalues
A General Method, Part II: Solving Systems with Repeated Real or Complex Eigenvalues
Solving Linear Homogeneous and Nonhomogeneous Systems of Equations