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This section contains free e-books and guides on Differential Equations, some of the resources in this section can be viewed online and some of them can be downloaded.

Differential Equations Books
Online Books
Elementary Differential Equations With Boundary Value Problems

PDF | 806 Pages | English
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.

 
Introduction to Differential Equations

PDF | 128 Pages | English
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.

 
Numerical Solution of Differential Equations

Online | NA Pages | English
This note gives an understanding of numerical methods for the solution of ordinary and partial differential equations, their derivation, analysis and applicability.

 
Ordinary and Partial Differential Equations

Online | NA Pages | English
This note explains the following topics: Existence and Uniqueness, Systems, Stability, Sturm-Liouville Theory, First Order, Quasi-Linear, Classification, Hyperbolic Problems, Elliptic Problems, Parabolic Problems.

 
Notes on Partial Differential Equations

PDF | 224 Pages | English
This book covers the following topics: Laplace's equations, Sobolev spaces, Functions of one variable, Elliptic PDEs, Heat flow, The heat equation, The Fourier transform, Parabolic equations, Vector-valued functions and Hyperbolic equations.

 
Differential equations by Harry Bateman

Online | 320 Pages | English
Harry Bateman was a famous English mathematician. In writing this book he had endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions. The chapters on partial differential equations have consequently been devoted almost entirely to the discussion of linear equations.

 
Mathematical Methods For Partial Differential Equations

Online | NA Pages | English
These 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.

 
Ordinary differential equations an elementary text book with an introduction to Lie's theory of the group of one parameter

Online | 264 Pages | English
This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure Mathematics. On account of the elementary character of the book, only the simpler portions of the subject have been touched upon at all ; and much care has been taken to make all the developments as clear as possible every important step being illustrated by easy examples.

 
Harmonic Analysis and Partial Differential Equations
Integral And Differential Equations

Online | NA Pages | English
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.

 
Linear Partial Differential Equations and Fourier Theory

PDF | 619 Pages | English
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.

 
Difference Equations to Differential Equations

Online | NA Pages | English
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.

 
Ordinary Differential Equations and Dynamical Systems

PDF | 364 Pages | English
The aim of this book is to give a self contained introduction to the field of ordinary differential equations with emphasis on the dynamical systems point of view while still keeping an eye on classical tools as pointed out before. Covered topics are: Newton’s equations, Classification of differential equations, First order autonomous equations, Qualitative analysis of first order equations, Initial value problems, Linear equations, Differential equations in the complex domain, Boundary value problems, Dynamical systems, Planar dynamical systems, Higher dimensional dynamical systems, Local behavior near fixed points, Chaos, Discrete dynamical systems, Discrete dynamical systems in one dimension, Periodic solutions, Chaos in higher dimensional systems.

 
Integral And Differential Equations

Online | NA Pages | English
This note covers the following topics: Integral Equations, Ordinary Differential Equations, Partial Differential Equations.

 
Notes on Differential Equations by Bob Terrell

PDF | 100 Pages | English
This Notes on Differential Equations are an introduction and invitation. The focus is on important models and calculus in applied contexts.

 
Partial Differential Equations ebook

PDF | 25 Pages | English
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 Coordinates.

 
Ordinary Differential Equations

PDF | 33 Pages | English
This note covers the following topics related to Ordinary Differential Equations: Linear Constant-Coefficient, Damped Oscillator, Forced Oscillations, Series Solutions, Trigonometry via ODE's, Green's Functions, Separation of Variables, Circuits, Simultaneous Equations, Simultaneous ODE's, Legendre's Equation, Asymptotic Behavior.

 
Partial Differential Equations

PDF | 21 Pages | English
This note covers the following topics: Model Problems, finite Difference Methods, Matrix Representation, Numerical Stability, The L-Shaped Membrane.

 
Partial Differential Equations pdf

PDF | 21 Pages | English
This note covers the following topics: Model Problems, finite Difference Methods, Matrix Representation, Numerical Stability, The L-Shaped Membrane.

 
Linear Differential Equations

PDF | 26 Pages | English
This note covers the following topics: Derivatives, differential equations, partial differential equations, distributions, Cauchy-Kowalewsky theorem, heat equation, Laplace equation, Schrodinger equation, wave equation, Cauchy-Riemann equations.

 
Second Order Linear Differential Equations

PDF | 10 Pages | English
This note contains problems and their solutions related to Second-Order Linear Differential Equations.

 
LINEAR DIFFERENTIAL EQUATIONS
Entropy and Partial Differential Equations
Monograph on quasilinear partial differential equations (EJDE)
Hilbert Space Methods for Partial Differential Equations
An Introduction to Stochastic Differential Equations
Differential Equations (Dawkins P)
Lectures Notes on Ordinary Differential Equations (Veeh J.A pdf)
PDE From a Probability Point of View(Bass R.F pdf)
Analysis Tools with Applications and PDE Notes
Entropy and Partial Differential Equations(Evans L.C pdf)
A PDE Primer (Showalter R.E)
Partial Differential Equations of Mathematical Physics(Symes W.W pdf)
Linear Algebra and Differential Equations
Ordinary Differential Equations Sheldon
Partial Differential Equations of Mathematical Physics
Analytic differential equations
Exterior Differential Systems and Euler Lagrange Partial Differential Equations
Monograph on quasilinear partial differential equations
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