This book covers the following topics: Introduction to odes,
First-order odes, Second-order odes, constant coefficients, The Laplace
transform, Series solutions, Systems of equations, Nonlinear differential
equations, Partial differential equations.
explains the following topics: The translation equation, The wave equation,
The diffusion equation, The Laplace equation, The Schrodinger equation,
Diffusion and equilibrium, Fourier series, Fourier transforms, Gradient and
divergence, Spherical harmonics.
covers the following topics: Classification of Differential Equations, First
Order Differential Equations, Second Order Linear Equations, Higher Order Linear
Equations, The Laplace Transform, Systems of Two Linear Differential Equations,
Fourier Series, Partial Differential Equations.
This note describes the
following topics: First Order Ordinary Differential Equations, Applications and
Examples of First Order ode’s, Linear Differential Equations, Second Order
Linear Equations, Applications of Second Order Differential Equations, Higher
Order Linear Differential Equations, Power Series Solutions to Linear
Differential Equations, Linear Systems, Existence and Uniqueness Theorems,
This book explains the following topics: First Order Equations, Numerical
Methods, Applications of First Order Equations1em, Linear Second Order
Equations, Applcations of Linear Second Order Equations, Series Solutions of
Linear Second Order Equations, Laplace Transforms, Linear Higher Order
Equations, Linear Systems of Differential Equations, Boundary Value Problems and
Fourier Expansions, Fourier Solutions of Partial Differential Equations,
Boundary Value Problems for Second Order Linear Equations.
This note explains the following topics: Existence
and Uniqueness, Systems, Stability, Sturm-Liouville Theory, First Order,
Quasi-Linear, Classification, Hyperbolic Problems, Elliptic Problems, Parabolic
This is a textbook for an introductory course on linear partial
differential equations (PDEs) and initial/boundary value problems (I/BVPs). It
also provides a mathematically rigorous introduction to Fourier analysis
which is the main tool used to solve linear PDEs in Cartesian coordinates.
This book covers the following
topics: Sequences, limits, and difference equations, Functions and their properties,
Best affine approximations, Integration, Polynomial approximations and Taylor
series, transcendental functions, The complex plane and Differential equations.
This note covers the following topics
related to Partial Differential Equations: The Heat Equation, Separation
of Variables, Oscillating Temperatures, Spatial Temperature Distributions, The
Heat Flow into the Box, Specified Heat Flow, Electrostatics, Cylindrical
These lecture notes are intended as a straightforward introduction to
partial differential equations which can serve as a textbook for undergraduate
and beginning graduate students. Topics covered includes: Equations of first
order, Classification, Hyperbolic equations, Fourier transform, Parabolic
equations and Elliptic equations of second order.