Lectures on Differential Equations by Craig A. Tracy2

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Lectures on Differential Equations written by Craig A. Tracy2 cover the following topics of complex number.

1. Introduction
What is a differential equation? Differential equation for the pendulum. Introduction to computer software. Exercises

2. First Order Equations & Conservative Systems
Linear first order equations. Conservative systems. Level curves of the energy. Exercises

3. Second Order Linear Equations
Theory of second order equations Reduction of order, Constant coefficients, Forced oscillations of the mass-spring system, Exercises

4. Difference Equations
Introduction, Constant coefficient difference equations, Inhomogeneous difference equations, Exercises

5. Matrix Differential Equations
The matrix exponential, Application of matrix exponential to DEs, Relation to earlier methods of solving constant coefficient DEs, Problem from Markov processes, Application of matrix DE to radioactive decays, Inhomogenous matrix equations, Exercises

6. Weighted String
Derivation of differential equations, Reduction to an eigenvalue problem, Computation of the eigenvalues, The eigenvectors, Determination of constants, Continuum limit: The wave equation, Inhomogeneous problem, Vibrating membrane, Exercises

7. Quantum Harmonic Oscillator
Schr¨odinger equation, Harmonic oscillator, Some properties of the harmonic oscillator, The Heisenberg Uncertainty Principle, Comparison of three problems, Exercises

8. Heat Equation
Introduction, Fourier transform, Solving the heat equation by the Fourier transform, Heat equation on the half-line, Heat equation on the circle, Exercises

9. Laplace Transform
Matrix version, Structure of (sIn − A)−1 , Exercises

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