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Notes on Diffy Qs:
Introduction to Differential Equations
Jiří Lebl, Trefor Bazett
Contents
Index
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Contents
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Front Matter
Colophon
0
Introduction
Notes about these notes
Introduction to differential equations
Classification of differential equations
1
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
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
More on eigenvalue problems
Sturm–Liouville problems
Higher order eigenvalue problems
Steady periodic solutions
6
The Laplace transform
The Laplace transform
Transforms of derivatives and ODEs
Convolution
Dirac delta and impulse response
Solving PDEs with the Laplace transform
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
A
Linear algebra
Vectors, mappings, and matrices
Matrix algebra
Elimination
Subspaces, dimension, and the kernel
Inner product and projections
Determinant
B
Table of Laplace Transforms
Further Reading
Index
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Notes on Diffy Qs:
Introduction to Differential Equations
Jiří Lebl
Department of Mathematics
Oklahoma State University
jiri.lebl@gmail.com
Trefor Bazett
Department of Mathematics & Statistics
University of Victoria
tbazett@uvic.ca
July 23, 2021
Colophon
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