Ordinary Differential Equations: Brief Revision
First-Order Equations
Homogeneous Linear Equations with Constant Coefficients
Nonhomogeneous Linear Equations with Constant Coefficients
Cauchy–Euler Equations
Functions and Operators
Fourier Series
The Full Fourier Series
Fourier Sine Series
Fourier Cosine Series
Convergence and Differentiation
Sturm–Liouville Problems
Regular Sturm–Liouville Problems
Other Problems
Bessel Functions
Legendre Polynomials
Spherical Harmonics
Some Fundamental Equations of Mathematical Physics
The Heat Equation
The Laplace Equation
The Wave Equation
Other Equations
The Method of Separation of Variables
The Heat Equation
The Wave Equation
The Laplace Equation
Other Equations
Equations with More than Two Variables
Linear Nonhomogeneous Problems
Equilibrium Solutions
Nonhomogeneous Problems
The Method of Eigenfunction Expansion
The Heat Equation
The Wave Equation
The Laplace Equation
Other Equations
The Fourier Transformations
The Full Fourier Transformation
The Fourier Sine and Cosine Transformations
Other Applications
The Laplace Transformation
Definition and Properties
Applications
The Method of Green’s Functions
The Heat Equation
The Laplace Equation
The Wave Equation
General Second-Order Linear Partial Differential Equations with Two Independent Variables
The Canonical Form
Hyperbolic Equations
Parabolic Equations
Elliptic Equations
The Method of Characteristics
First-Order Linear Equations
First-Order Quasilinear Equations
The One-Dimensional Wave Equation
Other Hyperbolic Equations
Perturbation and Asymptotic Methods
Asymptotic Series
Regular Perturbation Problems
Singular Perturbation Problems
Complex Variable Methods
Elliptic Equations
Systems of Equations
Answers to Odd-Numbered Exercises
Appendix
Bibliography
Index