Notes on Differential Equations

Description

2014. — 186 p.Introduction to Ordinary Differential Equations. A Gallery of Differential Equations. Introduction to Partial Differential Equations. The Logistic Population Model. Separable Equations. Separable Partial Differential Equations. Existence and Uniqueness and Software. Linear First Order Equations. Euler’s Numerical Method. Second Order Linear Equations. The Heat Equation. Complex Numbers and the Characteristic Equation. Forced Second Order. Systems of ODE’s, part 1. Systems of ODE’s, part 2. Linear Algebra, part 1. Linear Algebra, part 2. Linear Algebra, part 3. Linear Algebra, part 4. More on the Determinant. Linear Differential Equation Systems. Systems with Complex Eigenvalues. Classification Theorem for Linear Plane Systems. Nonlinear Systems in the Plane. Examples of Nonlinear Systems in 3 Dimensions. Boundary Value Problems. The Conduction of Heat. Solving the Heat Equation. More Heat Solutions. The Wave Equation. Beams and Columns. Power Series. More on Power Series. Power Series used: A Drum Model. The Euler equation for Fluid Flow, and Acoustic Waves. Exact equations for Air and Steam. The Laplace Equation. Laplace leads to Fourier. Fourier answered by Orthogonality. Uniqueness. Three masses oscillate. Selected answers and hints.