This course focuses on the concepts related to and applications of ordinary differential equations. Students examine and solve first order, linear, and non-linear differential equations and higher order linear differential equations. Existence and uniqueness theorems are discussed. Students also explore and apply numerical methods and series solutions of differential equations.
Review of Ordinary Differential Equations Concepts
Solve concrete and applied problems relating to ordinary differential equations.
Differential Equations and Matrices
Identify numerical methods for solving differential equations.
Solve real-world initial value problems using various methods.
Series Solutions of Second Order Linear Equations
Apply the Euler equation to series solutions.
Calculate series solutions near ordinary points and regular singular points.
Higher Order Linear Equations
Solve real-world problems involving mechanical, electrical, and forced vibrations.
Use various methods to solve homogenous equations.
Describe solution methods for higher order differential equations.
Introduction and First Order Differential Equations
Prove existence and uniqueness theorems.
Use differential equations in real-world examples.
Solve first order differential equations using various methods.
Explain slope fields and their connection to differential equations.
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