Barry McQuarrie

Math 2401 Differential Equations

Topic	Lecture Resources	Resources/Practice Problems
Course Introduction and Review DE as seen in Calculus II	Review DE as seen in Calc II	Review Mathematica Basics Review Mathematica Intermediate
Terminology	Wikipedia introduction to DE MMA used in Lecture	Practice Problems
1st Order: Linear Equations (integrating factor method)		Practice Problems MMA for Practice Problems
1st Order: Separable Equations and Modeling	MMA mixing problems	Practice Problems MMA for Practice Problems
1st Order: Differences Between Linear & Nonlinear Equations	MMA used in Lecture	Practice Problems MMA for Practice Problems
1st Order: Autonomous Equations and Population Dynamics	Lecture Notes MMA used in Lecture	Practice Problems
1st Order: Exact Equations		Practice Problems MMA for Practice Problems
1st Order: Taylor's Method of Order n: Numerical Solutions to IVP	MMA used in Lecture
1st Order: The Existence & Uniqueness Theorem	MMA Picard's Iteration Method	Practice Problems MMA for Practice Problems
2nd Order Linear: Homogeneous Equations with Constant Coefficients	MMA used in Lecture	Practice Problems MMA for Practice Problems
2nd Order Linear: Solutions of Linear Homogeneous Equations & Wronskian	Handout used in Lecture	Practice Problems MMA for Practice Problems
2nd Order Linear: Repeated Roots & Reduction of Order	MMA Examples of repeated, complex, and distinct roots	Practice Problems MMA for Practice Problems
2nd Order Linear: Nonhomogeneous Equations: Method of Undetermined Coefficients	Handout used in Lecture MMA used in Lecture	Practice Problems MMA for Practice Problems
2nd Order Linear: Nonhomogeneous Equations: Variation of Parameters		Practice Problems MMA for Practice Problems
2nd Order Linear: Application: Vibrations	MMA The Three Types of Damping	Practice Problems MMA for Practice Problems
2nd Order Linear: Application: Forced Vibrations	MMA Exploration of Forced Vibrations
Higher Order Linear: General Theory of Homogeneous Equations Constant Coefficients	MMA Higher Order Repeated Roots Roots of Unity	Practice Problems MMA for Practice Problems
Higher Order Linear: Undetermined Coefficients and Variation of Parameters	Lecture Notes MMA used in Lecture	Practice Problems MMA for Practice Problems
Power Series Review	MMA Power Series Review	Practice Problems MMA for Practice Problems
Series Solution about Ordinary Point	Concept Map for Series Solution MMA used in Lecture MMA used in Lecture	Practice Problems MMA for Practice Problems
Euler Equations & Regular Singular Points	MMA Taylor Series Fail with Singular Points	Practice Problems
Series Solutions about Regular Singular Point		Practice Problems
Series Solutions in General (not looking for patterns)	Lecture Notes from 1986 Lecture Notes MMA used in Lecture
Bessel's Equation	Lecture Notes MMA used in Lecture
Laplace Transforms: Definition of Laplace Transform and Solution of Initial Value Problems	MMA Basics for Laplace Transform	Practice Problems MMA for Practice Problems
Laplace Transforms: Step Functions	MMA Basics for Step Functions	Practice Problems MMA for Practice Problems
Laplace Transforms: Equations with Discontinuous Forcing Functions		Practice Problems MMA for Practice Problems
Laplace Transforms: Impulse Functions	MMA Basics for Impulse Functions	Practice Problems MMA for Practice Problems
Linear Systems: Introduction to Systems of First Order Linear Equations		Practice Problems MMA for Practice Problems
Linear Systems: Systems of Algebraic Equations	MMA Eigensystem Basics	Practice Problems MMA for Practice Problems
Linear Systems: Basic Theory of Systems of First Order Linear Equations	Pronunciation of Greek Alphabet	Practice Problems
Linear Systems: Homogeneous Linear Systems with Constant Coefficients	MMA for Homogeneous Linear Systems	Practice Problems
Linear Systems: Complex and Repeated Eigenvalues		Practice Problem Practice Problem
Linear Systems: Nonhomogeneous Linear Systems
Linear Systems: The Phase Plane	MMA The Phase Plane	Practice Problems MMA for Practice Problems
Nonlinear Systems: Autonomous Systems and Stability	MMA Taylor's Method of Order n for Systems
Nonlinear Systems: Locally Linear Systems	MMA Locally Linear Systems	Practice Problems
Nonlinear Systems: Competing Species	MMA Competing Species

Barry McQuarrie's Math 2401 Archive

Math 2401 Differential Equations