• Learning Outcomes for 3450:335 Introduction to Ordinary Differential Equations 

    Students are expected to be able to

    • Communicate mathematical results through the proper use of mathematical notation and words
    • Recognize the proper technique and solve initial value problems for first order equations
    • Solve initial value problems for higher order linear homogeneous and inhomogeneous equations
    • Solve linear homogeneous systems using eigenvalues and eigenvectors
    • Use Laplace Transforms to solve first and second order linear equations and linear systems
    • Solve linear, variable coefficient equations using infinite series
  • Topical Outline
    • Definitions and Terminology
    • Initial-Value Problems
    • Separable Variables
    • Linear Equations
    • Exact Equations
    • Solutions by Substitutions
    • Differential Equations as Mathematical Models
    • Solution Curves Without a Solution
    • Linear Models
    • Nonlinear Models
    • Preliminary Theory – Linear Equations
    • Reduction of Order
    • Homogeneous Linear Equations with Constant Coefficients
    • Undetermined Coefficients-Superposition Approach
    • Variation of Parameters
    • Cauchy-Euler Equations
    • Linear Models:  Initial-Value Problems
    • Matrices
    • Preliminary Theory-Linear Systems
    • Homogenous Linear Systems
    • Definition of the Laplace Transform
    • Inverse Transforms and Transforms of Derivations
    • Operational Properties I
    • Operational Properties II
    • The Dirac Delta Function
    • Systems of Linear Differential Equations
    • Series Solutions About Ordinary Points
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