Ordinary Differential Equations : a Practical Guide.

A compact treatment that takes the reader from simple examples to current research involving ordinary differential equations.

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Bibliographic Details
Main Author: Schroers, Bernd J.
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2011.
Series:AIMS Library of Mathematical Sciences.
Subjects:
Online Access:Click for online access

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100 1 |a Schroers, Bernd J. 
245 1 0 |a Ordinary Differential Equations :  |b a Practical Guide. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2011. 
300 |a 1 online resource (130 pages) 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a AIMS Library of Mathematical Sciences 
505 0 |a Cover; ORDINARY DIFFERENTIAL EQUATIONS; African Institute of Mathematics Library Series; Title; Copyright; Contents; Preface; 1 First order differential equations; 1.1 General remarks about differential equations; 1.1.1 Terminology; 1.1.2 Approaches to problems involving differential equations; 1.2 Exactly solvable first order ODEs; 1.2.1 Terminology; 1.2.2 Solution by integration; 1.2.3 Separable equations; 1.2.4 Linear first order differential equations; 1.2.5 Exact equations; 1.2.6 Changing variables; 1.3 Existence and uniqueness of solutions; 1.4 Geometric methods: direction fields. 
505 8 |a 1.5 Remarks on numerical methods2 Systems and higher order equations; 2.1 General remarks; 2.2 Existence and uniqueness of solutions for systems; 2.3 Linear systems; 2.3.1 General remarks; 2.3.2 Linear algebra revisited; 2.4 Homogeneous linear systems; 2.4.1 The vector space of solutions; 2.4.2 The eigenvector method; 2.5 Inhomogeneous linear systems; 3 Second order equations and oscillations; 3.1 Second order differential equations; 3.1.1 Linear, homogeneous ODEs with constant coefficients; 3.1.2 Inhomogeneous linear equations; 3.1.3 Euler equations; 3.1.4 Reduction of order. 
505 8 |a 3.2 The oscillating spring3.2.1 Deriving the equation of motion; 3.2.2 Unforced motion with damping; 3.2.3 Forced motion with damping; 3.2.4 Forced motion without damping; 4 Geometric methods; 4.1 Phase diagrams; 4.1.1 Motivation; 4.1.2 Definitions and examples; 4.1.3 Phase diagrams for linear systems; 4.2 Nonlinear systems; 4.2.1 The Linearisation Theorem; 4.2.2 Lyapunov functions; 5 Projects; 5.1 Ants on polygons; 5.2 A boundary value problem in mathematical physics; 5.3 What was the trouble with the Millennium Bridge?; 5.4 A system of ODEs arising in differential geometry. 
505 8 |a 5.5 Proving the Picard-Lindelöf Theorem5.5.1 The Contraction Mapping Theorem; 5.5.2 Strategy of the proof; 5.5.3 Completing the proof; References; Index. 
520 |a A compact treatment that takes the reader from simple examples to current research involving ordinary differential equations. 
588 0 |a Print version record. 
504 |a Includes bibliographical references and index. 
650 0 |a Differential equations. 
650 7 |a Differential equations  |2 fast 
776 0 8 |i Print version:  |a Schroers, Bernd J.  |t Ordinary Differential Equations : A Practical Guide.  |d Cambridge : Cambridge University Press, ©2011  |z 9781107697492 
830 0 |a AIMS Library of Mathematical Sciences. 
856 4 0 |u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=807364  |y Click for online access 
903 |a EBC-AC 
994 |a 92  |b HCD