An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Notes on Diffy Qs for free.
- Title
- Notes on Diffy Qs
- Subtitle
- Differential Equations for Engineers
- Publisher
- Independently published
- Author(s)
- Jiri Lebl
- Published
- 2024-05-15
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 466
- Language
- English
- ISBN-10
- 1706230230
- ISBN-13
- 9781706230236
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Title Page Introduction Notes about these notes Introduction to differential equations Classification of differential equations First order equations Integrals as solutions Slope fields Separable equations Linear equations and the integrating factor Substitution Autonomous equations Numerical methods: Euler's method Exact equations First order linear PDE Higher order linear ODEs Second order linear ODEs Constant coefficient second order linear ODEs Higher order linear ODEs Mechanical vibrations Nonhomogeneous equations Forced oscillations and resonance Systems of ODEs Introduction to systems of ODEs Matrices and linear systems Linear systems of ODEs Eigenvalue method Two-dimensional systems and their vector fields Second order systems and applications Multiple eigenvalues Matrix exponentials Nonhomogeneous systems Fourier series and PDEs Boundary value problems The trigonometric series More on the Fourier series Sine and cosine series Applications of Fourier series PDEs, separation of variables, and the heat equation One-dimensional wave equation D'Alembert solution of the wave equation Steady state temperature and the Laplacian Dirichlet problem in the circle and the Poisson kernel More on eigenvalue problems Sturm–Liouville problems Higher order eigenvalue problems Steady periodic solutions The Laplace transform The Laplace transform Transforms of derivatives and ODEs Convolution Dirac delta and impulse response Solving PDEs with the Laplace transform Power series methods Power series Series solutions of linear second order ODEs Singular points and the method of Frobenius Nonlinear systems Linearization, critical points, and equilibria Stability and classification of isolated critical points Applications of nonlinear systems Limit cycles Chaos Linear algebra Vectors, mappings, and matrices Matrix algebra Elimination Subspaces, dimension, and the kernel Inner product and projections Determinant Table of Laplace Transforms Further Reading Solutions to Selected Exercises Index
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