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.
explains the following topics: First Order Equations, Second Order Linear
Equations, Reduction of Order Methods, Homogenous Constant Coefficients
Equations ,Power Series Solutions, The Laplace Transform Method, Systems of
Linear Differential Equations, Autonomous Systems and Stability, Boundary
This note covers the following topics: First Order Equations,
Numerical Methods, Applications of First Order Equations, Linear Second
Order Equations, Applcations of Linear Second Order Equations, Series
Solutions of Linear Second Order Equations, Laplace Transforms, Linear
Higher Order Equations.
describes the main ideas to solve certain differential equations, such us
first order scalar equations, second order linear equations, and systems of
linear equations. It uses power series methods to solve variable
coefficients second order linear equations. Also introduces Laplace
transform methods to find solutions to constant coefficients equations with
generalized source functions.
This note describes
the following topics: First Order Differential Equations, N-th Order
Differential Equations, Linear Differential Equations, Laplace Transforms,
Inverse Laplace Transform, Systems Of Linear Differential Equations, Series
Solution Of Linear Differential Equations.
note covers the following topics: Qualitative Analysis, Existence and
Uniqueness of Solutions to First Order Linear IVP, Solving First Order Linear
Homogeneous DE, Solving First Order Linear Non Homogeneous DE: The Method of
Integrating Factor, Modeling with First Order Linear Differential Equations,
Additional Applications: Mixing Problems and Cooling Problems, Separable
Differential Equations, Exact Differential Equations, Substitution Techniques:
Bernoulli and Ricatti Equations, Applications of First Order Nonlinear
Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations,
The General Solution of Homogeneous Equations, Existence of Many Fundamental
Sets, Second Order Linear Homogeneous Equations with Constant, Coefficients,
Characteristic Equations with Repeated Roots, The Method of Undetermined
Coefficients, Applications of Nonhomogeneous Second Order Linear Differential
This note introduces students to differential equations. Topics covered
includes: Boundary value problems for heat and wave equations, eigenfunctionexpansions, Surm-Liouville theory and Fourier series, D'Alembert's
solution to wave equation, characteristic, Laplace's equation, maximum principle
and Bessel's functions.
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.
are the sample pages from the textbook. Topics Covered: Partial differential equations, Orthogonal functions, Fourier Series, Fourier
Integrals, Separation of Variables, Boundary Value Problems, Laplace Transform,
Fourier Transforms, Finite Transforms, Green's Functions and Special Functions.
This book covers the following topics: Geometry and a Linear Function,
Fredholm Alternative Theorems, Separable Kernels, The Kernel is Small, Ordinary
Differential Equations, Differential Operators and Their Adjoints, G(x,t) in the
First and Second Alternative and Partial Differential Equations.
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.
These notes are a concise understanding-based presentation of the
basic linear-operator aspects of solving linear differential equations.
Topics covered includes: Operators and Linear Combinations, Homogeneous
linear equations, Complex Exponentials and Real Homogeneous Linear
Equations, Non-homogeneous linear equations and Systems of Linear