Perturbation Techniques in Mathematics, Engineering and Physics,9780486432588

Perturbation Techniques in Mathematics, Engineering and Physics

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Edition: Reprint
ISBN13: 9780486432588
ISBN10: 0486432580
Format: Paperback
Pub. Date: 2003-06-27
Publisher(s): Dover Publications
List Price: $13.64

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Summary

This three-part graduate-level treatment begins with classical perturbation techniques, discussing the Lagrange expansion theorem, matrix exponential, invariant imbedding, and dynamic programming. The second part concentrates on equations, presenting renormalization techniques of Lindstedt and Shohat and averaging techniques by Bellman and Richardson. The concluding chapter focuses on second-order linear differential equations, illustrating applications of the WKB-Liouville method and asymptotic series. Exercises, comments, and an annotated bibliography follow each demonstration of technique. A course in intermediate calculus and a basic understanding of ordinary differential equations are prerequisites. 1966 ed. 7 figures.

Table of Contents

Preface v
Part 1. Classical Perturbation Techniques 1(53)
1. Introduction
1(1)
2. The Fundamental Technique
2(2)
3. Discussion
4(1)
4. Lagrange Expansion
5(3)
5. Multidimensional Lagrange Expansion
8(1)
6. Linear Differential Equations
9(2)
7. Linear Equations with Almost Constant Coefficients
11(1)
8. Inhomogeneous Linear Equations
12(3)
9. Linear Perturbation Series-I
15(1)
10. Linear Perturbation Series-II
16(3)
11. Two-point Boundary-value Problems
19(4)
12. Perturbation Techniques-I
23(2)
13. Perturbation Techniques-II
25(3)
14. Perturbation in General
28(1)
15. Invariant Imbedding
28(4)
16. Multidimensional Considerations
32(1)
17. The Matrix Exponential
33(2)
18. eA+€B
35(2)
19. Variable Coefficients
37(1)
20. Baker-Campbell-Hausdorff Series
38(1)
21. Nonlinear Perturbation
39(2)
22. Poincaré-Lyapunov Theorem
41(1)
23. Asymptotic Behavior
42(1)
24. Functional Equations
43(2)
25. Relative Invariants
45(2)
26. Iteration and Recurrence Relations
47(1)
27. The Abel-Schroder Functional Equation
48(2)
28. Irregular Perturbation
50(2)
29. Equations with Small Time Lags
52(2)
Part 2. Periodic Solutions of Nonlinear Differential Equations and Renormalization Techniques 54(26)
1. Introduction
54(1)
2. Secular Terms
55(2)
3. Renormalization à la Lindstedt
57(2)
4. The Van der Pol Equation
59(2)
5. The Shohat Expansion
61(3)
6. Perturbation Series for the Period
64(3)
7. Self-consistent Techniques
67(2)
8. Carleman Linearization
69(1)
9. Finite Closure
70(1)
10. Closure
71(1)
11. Self-consistent Techniques-II
72(2)
12. Dynamic Programming and Perturbation Series
74(2)
13. Temple's Regularization Technique
76(2)
14. Elliptic Functions and Mathieu Functions
78(2)
Part 3. The Liouville-WKB Approximation and Asymptotic Series 80(35)
1. Introduction
80(1)
2. The Liouville Transformation
80(1)
3. Elimination of Middle Term
81(2)
4. Transform of u" + a2(t)u=0
83(1)
5. The Equation u" +(1 + b(t))u=0
83(3)
6. Asymptotic Behavior
86(1)
7. Statement of Results
87(2)
8. Asymptotic Form
89(3)
9. u" -(1 + ~sigmaRk=1zke-2kt)u=0
92(2)
10. WKB Approximation
94(2)
11. Riccati Equation
96(2)
12. Langer Approximation
98(1)
13. Wave Propagation and the WKB Approximation
99(4)
14. u" -(1 + t-2)u=0
103(1)
15. Discussion
104(1)
16. Determination of Coefficients
105(1)
17. The Second Solution-I
106(1)
18. The Second Solution-II
106(1)
19. Asymptotic Series
107(3)
20. The Exponential Integral
110(1)
21. The Laplace Transform
111(4)
Subject Index 115(2)
Author Index 117

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