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