## e-books in Ordinary Differential Equations (ODE) category

**Ordinary Differential Equations**

by

**Stephen Wiggins**-

**University of Bristol**,

**2017**

This book consists of ten weeks of material given as a course on ordinary differential equations for second year mathematics majors. Rather than seeking to find specific solutions, we seek to understand how all solutions are related in phase space.

(

**1947**views)

**Differential Equations and Linear Algebra**

by

**Simon J.A. Malham**-

**Heriot-Watt University**,

**2010**

From the table of contents: Linear second order ODEs; Homogeneous linear ODEs; Non-homogeneous linear ODEs; Laplace transforms; Linear algebraic equations; Matrix Equations; Linear algebraic eigenvalue problems; Systems of differential equations.

(

**3271**views)

**Differential Equations with YouTube Examples**

by

**Jeffrey R. Chasnov**-

**BookBoon**,

**2014**

This book, together with the linked YouTube videos, reviews a first course on differential equations. The purpose is to help students prepare for their exams. Theory is summarized, and the solutions of questions are demonstrated in YouTube videos.

(

**2350**views)

**Examples of differential equations, with rules for their solution**

by

**George A. Osborne**-

**Boston, Ginn & Company**,

**1899**

This work has been prepared to meet a want in a course on the subject, arranged for advanced students in Physics. It could be used in connection with lectures on the theory of Differential Equations and the derivation of the methods of solution.

(

**3260**views)

**A First Course in Ordinary Differential Equations**

by

**Norbert Euler**-

**Bookboon**,

**2015**

The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, general vector spaces and integral calculus.

(

**2228**views)

**A Friendly Introduction to Differential Equations**

by

**Mohammed K A Kaabar**,

**2015**

The book covers: The Laplace Transform, Systems of Homogeneous Linear Differential Equations, First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, Applications of Differential Equations.

(

**5950**views)

**Ordinary Differential Equations: A Systems Approach**

by

**Bruce P. Conrad**,

**2010**

This is a revision of a text that was on the market for a while. It focuses on systems of differential equations. Some popular topics, which were present in the original text, have been left out to concentrate on the initial value problem.

(

**5590**views)

**Elementary Differential Equations**

by

**William F. Trench**-

**Brooks Cole**,

**2001**

This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner.

(

**3063**views)

**Ordinary Differential Equations**

by

**Wong Yan Loi**-

**National University of Singapore**,

**2013**

From the table of contents: First Order Differential Equations; Linear Differential Equations; Second Order Linear Differential Equations; Linear Differential Systems; Power Series Solutions; Fundamental Theory of Ordinary Differential Equations.

(

**6103**views)

**Second-order Ordinary Differential Equations**

by

**R.S. Johnson**-

**Bookboon**,

**2012**

This text provides an introduction to all the relevant material normally encountered at university level: series solution, special functions, Sturm-Liouville theory and the definition, properties and use of various integral transforms.

(

**5029**views)

**Integration and Differential Equations**

by

**R.S. Johnson**-

**BookBoon**,

**2012**

Part I introduces the standard techniques of elementary integration and, in some cases, takes the ideas a little further. In Part II, ordinary differential equation are explored, and the solution methods for some standard types are explained.

(

**5341**views)

**Linearization via the Lie Derivative**

by

**Carmen Chicone, Richard Swanson**-

**American Mathematical Society**,

**2000**

The proof of the Grobman-Hartman linearization theorem for a flow at a hyperbolic rest point proceeds by establishing the analogous result for hyperbolic fixed points of local diffeomorphisms. We present a proof that avoids the discrete case.

(

**4781**views)

**Periodic Solutions for Evolution Equations**

by

**Mihai Bostan**-

**American Mathematical Society**,

**2002**

We study the existence and uniqueness of periodic solutions for evolution equations. We analyze the one-dimensional case, then for arbitrary dimensions. We consider linear symmetric operators. We prove the same results for non-linear operators.

(

**4946**views)

**The Contraction Mapping Principle and Some Applications**

by

**Robert M. Brooks, Klaus Schmitt**-

**American Mathematical Society**,

**2009**

These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric.

(

**5473**views)

**Lectures on Differential Equations**

by

**Craig A. Tracy**-

**University of California**,

**2011**

From the table of contents: Pendulum and MatLab; First Order Equations; Second Order Linear Equations; Difference Equations; Matrix Differential Equations; Weighted String; Quantum Harmonic Oscillator; Laplace Transform, etc.

(

**6748**views)

**A Second Course in Elementary Ordinary Differential Equations**

by

**Marcel B. Finan**-

**Arkansas Tech University**,

**2006**

Calculus of Matrix-Valued Functions of a Real Variable; nth Order Linear Differential Equations; General Solution of nth Order Linear Homogeneous Equations; Fundamental Sets and Linear Independence; Higher Order Homogeneous Linear Equations; etc.

(

**7992**views)

**A First Course in Elementary Differential Equations**

by

**Marcel B. Finan**-

**Arkansas Tech University**,

**2006**

Contents: Basic Terminology; Qualitative Analysis: Direction Field of y'=f(t,y); Existence and Uniqueness of Solutions to First Order Linear IVP; Solving First Order Linear Homogeneous DE; Solving First Order Linear Non Homogeneous DE; etc.

(

**7112**views)

**Introduction to the Galois Theory of Linear Differential Equations**

by

**Michael F. Singer**-

**arXiv**,

**2008**

The author's goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on examples.

(

**6278**views)

**Differential Equations**

by

**H. B. Phillips**-

**John Wiley & Sons**,

**1922**

With the formal exercise in solving the usual types of ordinary differential equations it is the object of this text to combine a thorough drill in the solution of problems in which the student sets up and integrates his own differential equation.

(

**8839**views)

**Real Functions in One Variable: Simple Differential Equations I**

by

**Leif Mejlbro**-

**BookBoon**,

**2007**

Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations.

(

**7882**views)

**Ordinary Differential Equations and Dynamical Systems**

by

**Gerald Teschl**-

**Universitaet Wien**,

**2009**

This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.

(

**11270**views)

**Nonlinear Analysis and Differential Equations**

by

**Klaus Schmitt, Russell C. Thompson**-

**University of Utah**,

**2004**

The intent of this set of notes is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions of solutions.

(

**8394**views)

**Lectures on Analytic Differential Equations**

by

**Yulij Ilyashenko, Sergei Yakovenko**-

**American Mathematical Society**,

**2007**

A graduate-level textbook and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. The book includes self-contained demonstrations of several fundamental results.

(

**9912**views)