E-Book, Englisch, 326 Seiten
Reihe: Universitext
Agarwal / O'Regan An Introduction to Ordinary Differential Equations
1. Auflage 2008
ISBN: 978-0-387-71276-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 326 Seiten
Reihe: Universitext
ISBN: 978-0-387-71276-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
"Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an ""answers and hints"" section, are included. The book further provides a background and history of the subject."
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
2;Contents;9
3;Introduction;11
4;Historical Notes;17
5;Exact Equations;23
6;Elementary First-Order Equations;31
7;First-Order Linear Equations;38
8;Second-Order Linear Equations;45
9;Preliminaries to Existence and Uniqueness of Solutions;55
10;Picard’s Method of Successive Approximations;63
11;Existence Theorems;71
12;Uniqueness Theorems;78
13;Differential Inequalities;87
14;Continuous Dependence on Initial Conditions;94
15;Preliminary Results from Algebra and Analysis;101
16;Preliminary Results from Algebra and Analysis ( Contd.);107
17;Existence and Uniqueness of Solutions of Systems;113
18;Existence and Uniqueness of Solutions of Systems ( Contd.);119
19;General Properties of Linear Systems;126
20;Fundamental Matrix Solution;134
21;Systems with Constant Coefficients;143
22;Periodic Linear Systems;154
23;Asymptotic Behavior of Solutions of Linear Systems;162
24;Asymptotic Behavior of Solutions of Linear Systems ( Contd.);169
25;Preliminaries to Stability of Solutions;178
26;Stability of Quasi- Linear Systems;185
27;Two-Dimensional Autonomous Systems;191
28;Two-Dimensional Autonomous Systems ( Contd.);197
29;Limit Cycles and Periodic Solutions;206
30;Lyapunov’s Direct Method for Autonomous Systems;214
31;Lyapunov’s Direct Method for Nonautonomous Systems;221
32;Higher-Order Exact and Adjoint Equations;227
33;Oscillatory Equations;235
34;Linear Boundary Value Problems;243
35;Green’s Functions;250
36;Degenerate Linear Boundary Value Problems;260
37;Maximum Principles;268
38;Sturm–Liouville Problems;275
39;Sturm–Liouville Problems ( Contd.);281
40;Eigenfunction Expansions;289
41;Eigenfunction Expansions ( Contd.);296
42;Nonlinear Boundary Value Problems;305
43;Nonlinear Boundary Value Problems ( Contd.);310
44;Topics for Further Studies;318
45;References;324
46;Index;327
