search for books and compare prices
Tables of Contents for Differential Equations
Chapter/Section Title
Page #
Page Count
Preface
v
Introduction
1
32
Examples of Dynamical Systems
1
13
Vector Fields and Dynamical Systems
14
9
Nonautonomous Systems
23
3
Fixed Points
26
1
Reduction to 1st-Order, Autonomous
27
5
Summary
32
1
Techniques, Concepts, and Examples
33
42
Euler's Numerical Method
34
5
The Geometric View
34
2
The Analytical View
36
3
Gradient Vector Fields
39
6
Fixed Points and Stability
45
6
Limit Cycles
51
4
The Two-Body Problem
55
17
Jacobi Coordinates
57
2
The Central Force Problem
59
13
Summary
72
3
Existence and Uniqueness: The Flow Map
75
40
Picard Iteration
78
4
Existence and Uniqueness Theorems
82
10
Maximum Interval of Existence
92
3
The Flow Generated by a Time-Dependent Vector Field
95
9
The Flow for Autonomous Systems
104
8
Summary
112
3
One-Dimensional Systems
115
42
Autonomous, One-Dimensional Systems
116
12
Construction of the Flow for 1-D, Autonomous Systems
123
5
Separable Differential Equations
128
7
Integrable Differential Equations
135
12
Homogeneous Differential Equations
147
4
Linear and Bernoulli Differential Equations
151
4
Summary
155
2
Linear Systems
157
74
Existence and Uniqueness for Linear Systems
162
3
The Fundamental Matrix and the Flow
165
9
Homogeneous, Constant Coefficient Systems
174
6
The Geometry of the Integral Curves
180
31
Real Eigenvalues
182
10
Complex Eigenvalues
192
19
Canonical Systems
211
16
Diagonalizable Matrices
214
3
Complex Diagonalizable Matrices
217
2
The Nondiagonalizable Case: Jordan Forms
219
8
Summary
227
4
Linearization and Transformation
231
44
Linearization
231
16
Transforming Systems of DEs
247
19
The Spherical Coordinate Transformation
253
4
Some Results on Differentiable Equivalence
257
9
The Linearization and Flow Box Theorems
266
9
Stability Theory
275
48
Stability of Fixed Points
276
3
Linear Stability of Fixed Points
279
11
Computation of the Matrix Exponential for Jordan Forms
280
10
Nonlinear Stability
290
2
Liapunov Functions
292
11
Stability of Periodic Solutions
303
20
Integrable Systems
323
38
First Integrals (Constants of the Motion)
324
5
Integrable Systems in the Plane
329
5
Integrable Systems in 3-D
334
14
Integrable Systems in Higher Dimensions
348
13
Newtonian Mechanics
361
102
The N-Body Problem
362
22
Fixed Points
365
1
Initial Conditions
366
1
Conservation Laws
366
8
Stability of Conservative Systems
374
10
Euler's Method and the N-body Problem
384
17
Discrete Conservation Laws
392
9
The Central Force Problem Revisited
401
23
Effective Potentials
404
1
Qualitative Analysis
405
4
Linearization and Stability
409
1
Circular Orbits
410
2
Analytical Solution
412
12
Rigid-Body Motions
424
39
The Rigid-Body Differential Equations
432
6
Kinetic Energy and Moments of Inertia
438
8
The Degenerate Case
446
1
Euler's Equation
447
4
The General Solution of Euler's Equation
451
12
Motion on a Submanifold
463
78
Motion on a Stationary Submanifold
464
20
Motion Constrained to a Curve
471
5
Motion Constrained to a Surface
476
8
Geometry of Submanifolds
484
9
Conservation of Energy
493
2
Fixed Points and Stability
495
7
Motion on a Given Curve
502
11
Motion on a Given Surface
513
18
Surfaces of Revolution
520
6
Visualization of Motion on a Given Surface
526
5
Motion Constrained to a Moving Submanifold
531
10
Hamiltonian Systems
541
48
1-Dimensional Hamiltonian Systems
544
7
Conservation of Energy
547
4
Conservation Laws and Poisson Brackets
551
14
Lie Brackets and Arnold's Theorem
565
17
Arnold's Theorem
567
15
Liouville's Theorem
582
7
A Elementary Analysis
589
18
Multivariable Calculus
589
6
The Chain Rule
595
1
The Inverse and Implicit Function Theorems
596
6
Taylor's Theorem and The Hessian
602
4
The Change of Variables Formula
606
1
B Lipschitz Maps and Linearization
607
26
Norms
608
1
Lipschitz Functions
609
4
The Contraction Mapping Principle
613
6
The Linearization Theorem
619
14
C Linear Algebra
633
32
Vector Spaces and Direct Sums
633
3
Bilinear Forms
636
2
Inner Product Spaces
638
4
The Principal Axes Theorem
642
3
Generalized Eigenspaces
645
11
Matrix Analysis
656
9
Power Series with Matrix Coefficients
662
3
D CD-ROM Contents
665
4
Bibliography
669
Index
675