• 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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