MATH 264 - Differential Equations

1. Classify differential equations by order, type, and linearity.
2. Identify bifurcation values for first- and second-order 1-parameter differential equations.
3. Solve first-order differential equations using:
   1. Separation of variables
   2. Method of integrating factor
   3. Exact equations
4. Implement elementary numerical methods including Euler’s and an introduction to Runge-Kutta.
5. Model with first and second-order differential equations.
6. Solve homogeneous differential equations with constant coefficients.
7. Solve nonhomogeneous differential equations with constant coefficients using:
   1. Method of undetermined coefficients - Superposition Approach
   2. Variation of parameters
8. Solve differential equations using the method of Laplace transform.
9. Solve linear systems of first-order differential equations.
10. Perform stability analysis for linear systems.

• Initial-Value Problems
• Solution Curves for first-order differential equations
• First order Separable Equations
• First order and Higher order Linear Equations
• First order Exact Equations
• Runge-Kutta numerical method
• First order Linear Models
• First order Non-linear models
• Higher order Homogeneous Linear Equations with Constant Coefficients
• Higher order Undetermined Coefficients - Superposition and Annihilator Approaches
• Higher order Variation of Parameters
• Higher order Linear Models - Initial-Value Problems
• Laplace Transform, Inverse Transforms and Transforms of Derivatives
• Operational Properties
• Systems of Linear First-Order Differential Equations (Homogeneous and Nonhomogeneous Linear)
• Autonomous Systems of Nonlinear First-Order Differential Equations
• Stability of Linear Systems of Nonlinear First-Order Differential Equations
• Bifurcation analysis for first- and second-order 1-parameter linear differential equations with constant coefficients.

 
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Course Addendum - Syllabus (Click to expand)