دانلود کتاب Ordinary differential equations. A brief eclectic tour

فهرست مطالب :

Title......Page 1
Preface......Page 3
Contents......Page 9
1 Polynomials......Page 11
3 Implicit Equations......Page 12
4 Ordinary Differential Equations......Page 13
5 Existence and Uniqueness-Preliminaries......Page 15
6 Continuation......Page 16
1 The Separable Equation?Expanded......Page 19
2 Equilibria-A First Look at Stability......Page 23
3 Multiple Equilibria......Page 26
4 The Linear Equation......Page 30
5 The Riccati Equation......Page 36
6 Comparison Sometimes Helps......Page 41
7 Periodic Solutions......Page 42
8 Differentiation in Search of a Solution......Page 46
9 Dependence on Initial Conditions......Page 48
10 Continuing Continuatioa......Page 49
2 Two Simple Schemes......Page 53
3 Key Stuff......Page 54
4 RKF Methods......Page 57
5 A Few Examples......Page 58
1 What Is The Initial Value Problem......Page 63
2 The Linear Equation......Page 65
3 Approach 1-Dealing Directly......Page 67
4 Approach 2-The Linear System......Page 70
6 Constant Coefficient Equations-The Homogeneous Case......Page 74
7 What To Do With Solutions......Page 77
8 The Nonhomogeneous Equation or the Variation of Parameters Formula Untangled......Page 81
9 Cosines and Convolutions......Page 86
10 Second Thoughts......Page 91
1 Constant Coefficient Linear Systems......Page 99
2 The Phase Plane......Page 102
3 The Linear System and the Phase Plane......Page 104
4 Competition and Predator-Prey Systems......Page 109
5 Harvesting......Page 113
6 A Conservative Detour......Page 114
7 Stability and Gronwall-ing......Page 125
References......Page 137
Index......Page 141