MATH246 Exercise Environment
First-Order Systems of Ordinary Differential Equations
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Course Introduction and Overview
Introduction to First-Order Equations
Linear Equations
Separable Equations
General Theory
Graphical Methods
Applications
Numerical Methods
Exact Differential Forms and Integrating Factors
Special Equations and Substitution
Introduction to Higher-Order Linear Equations
Homogeneous Equations: General Methods and Theory
Supplement: Linear Algebraic Systems and Determinants
Homogeneous Equations with Constant Coefficients
Nonhomogeneous Equations: General Methods and Theory
Nonhomogeneous Equations with Constant Coefficients
Nonhomogeneous Equations with Variable Coefficients
Application: Mechanical Vibrations
Laplace Transform Method
Introduction to First-Order Systems
Linear Systems: General Methods and Theory
Supplement: Matrices and Vectors
Linear Systems: Matrix Exponentials
Linear Systems: Eigen Methods
Linear Systems: Laplace Transform Methods
Linear Planar Systems
Autonomous Planar Systems: Integral Methods
Autonomous Planar Systems: Nonintegral Methods
Application: Population Dynamics