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Notes on Diffy Qs
Differential Equations for Engineers
Jiří Lebl
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Front Matter
Colophon
0
Introduction
Notes about these notes
Introduction to differential equations
Classification of differential equations
1
First order ODEs
Integrals as solutions
Slope fields
Separable equations
Linear equations and the integrating factor
Substitution
Autonomous equations
Numerical methods: Euler's method
Exact equations
2
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
3
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
4
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
5
Eigenvalue problems
Sturm-Liouville problems
Application of eigenfunction series
Steady periodic solutions
6
The Laplace transform
The Laplace transform
Transforms of derivatives and ODEs
Convolution
Dirac delta and impulse response
7
Power series methods
Power series
Series solutions of linear second order ODEs
Singular points and the method of Frobenius
8
Nonlinear systems
Linearization, critical points, and equilibria
Stability and classification of isolated critical points
Applications of nonlinear systems
Limit cycles
Chaos
Back Matter
Further Reading
Index
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Notes on Diffy Qs
Differential Equations for Engineers
Jiří Lebl
Department of Mathematics
Oklahoma State University
jiri.lebl@gmail.com
October 11, 2018
Colophon
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