Ordinary differential equations : a practical guide /
Schroers, Bernd J.
Ordinary differential equations : a practical guide / Bernd J. Schroers. - Cambridge ; New York : Cambridge University Press, 2011. - 1 online resource (ix, 118 pages) : illustrations - African Institute of Mathematics library series . - AIMS library series. .
Includes bibliographical references (page 116) and index.
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 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 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 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
'Ordinary Differential Equations' introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, including mathematics, physics, computer science, statistics and biology.
English.
9781139191180 (electronic bk.) 1139191187 (electronic bk.) 9781139186285 1139186280 1283382644 9781283382649 1139235125 9781139235129 1107232473 9781107232471 1139057707 9781139057707 9786613382641 6613382647 1139189891 9781139189897 1139188585 9781139188586 1139183974 9781139183970
9786613382641
338264 MIL
Differential equations.
Équations différentielles.
MATHEMATICS--Differential Equations--Ordinary.
Differential equations.
Electronic books.
QA371 / .S37 2011eb
515.352
Ordinary differential equations : a practical guide / Bernd J. Schroers. - Cambridge ; New York : Cambridge University Press, 2011. - 1 online resource (ix, 118 pages) : illustrations - African Institute of Mathematics library series . - AIMS library series. .
Includes bibliographical references (page 116) and index.
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 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 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 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
'Ordinary Differential Equations' introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, including mathematics, physics, computer science, statistics and biology.
English.
9781139191180 (electronic bk.) 1139191187 (electronic bk.) 9781139186285 1139186280 1283382644 9781283382649 1139235125 9781139235129 1107232473 9781107232471 1139057707 9781139057707 9786613382641 6613382647 1139189891 9781139189897 1139188585 9781139188586 1139183974 9781139183970
9786613382641
338264 MIL
Differential equations.
Équations différentielles.
MATHEMATICS--Differential Equations--Ordinary.
Differential equations.
Electronic books.
QA371 / .S37 2011eb
515.352