Lectures on Differential Equations by Craig A. Tracy2

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Lectures on Differential Equations written by Craig A. Tracy2
. This is an other great mathematics book 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

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