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This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, such us first order scalar equations, second order linear equations, and systems of linear equations. We use power series methods to solve variable coefficients second order linear equations. We introduce Laplace transform methods to find solutions to constant coefficients equations with generalized source functions. We provide a brief introduction to boundary value problems, eigenvalue-eigenfunction problems, and Fourier series expansions. We end these notes solving our first partial differential equation, the heat equation. We use the method of separation of variables, where solutions to the partial differential equation are obtained by solving infinitely many ordinary differential equations.
Preface.
First Order Equations.
Second Order Linear Equations.
Power Series Solutions.
The Laplace Transform Method.
Systems of Linear Differential Equations.
Autonomous Systems and Stability.
Boundary Value Problems.
Review of Linear Algebra.
Appendices.
Bibliography