Math 334: Ordinary Differential Equations

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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]).


Students are expected to have completed Math 113, and Math 343 or be concurrently enrolled in Math 343.

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 non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor.

  1. First order equations
    • Linear, separable, and exact equations
    • Existence and uniqueness of solutions
    • Linear versus nonlinear equations
    • Autonomous equations
    • Models and Applications
  2. 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
  3. Systems of equations
    • General theory
    • Eigenvalue-eigenvector 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

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 347, Math 480, Math 521, Math 534, and Math 547.