Difference between revisions of "Math 334: Ordinary Differential Equations"
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Revision as of 15:03, 3 April 2013
Contents
Catalog Information
Title
Ordinary Differential Equations.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F, W, Sp, Su
Prerequisite
Description
Methods and theory of ordinary differential equations.
Desired Learning Outcomes
This course is aimed at students majoring in mathematical and physical sciences and mathematical education. The main purpose of the course is to introduce students to the theory and methods of ordinary differential equations. The course content contributes to all the expected learning outcomes of the Mathematics BS (see [1]).
Prerequisites
Students are expected to have completed Math 113, and Math 313 or be concurrently enrolled in Math 313.
Minimal learning outcomes
Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve nontrivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor.
 First order equations
 Linear, separable, and exact equations
 Existence and uniqueness of solutions
 Linear versus nonlinear equations
 Autonomous equations
 Models and Applications
 Higher order equations
 Theory of linear equations
 Linear independence and the Wronskian
 Homogeneous linear equations with constant coefficients
 Nonhomogeneous linear equations, method of undetermined coefficients and variation of parameters
 Mechanical and electrical vibrations
 Power series solutions
 The Laplace transform – definitions and applications
 Systems of equations
 General theory
 Eigenvalueeigenvector method for systems with constant coefficients
 Homogeneous linear systems with constant coefficients
 Fundamental matrices
 Nonhomogeneous linear systems, method of undetermined coefficients and variation of parameters
 Stability, instability, asymptotic stability, and phase plane analysis
 Models and applications
Textbooks
Possible textbooks for this course include (but are not limited to):
Additional topics
These are at the instructor's discretion as time allows; applications to physical problems are particularly helpful.
Courses for which this course is prerequisite
This course is required for Math 447, Math 480, Math 521, Math 534, Math 547, and Math 634.