Singular perturbation theory: techniques with applications to engineering

Cover......Page 1
CONTENTS......Page 8
FOREWORD......Page 12
PREFACE......Page 14
1. MATHEMATICAL PRELIMINARIES......Page 18
1.1 SOME INTRODUCTORY EXAMPLES......Page 19
1.2 NOTATION......Page 27
1.3 ASYMPTOTIC SEQUENCES AND ASYMPTOTIC EXPANSIONS......Page 30
1.4 CONVERGENT SERIES VERSUS DIVERGENT SERIES......Page 33
1.5 ASYMPTOTIC EXPANSIONS WITH A PARAMETER......Page 37
1.6 UNIFORMITY OR BREAKDOWN......Page 39
1.7 INTERMEDIATE VARIABLES AND THE OVERLAP REGION......Page 43
1.8 THE MATCHING PRINCIPLE......Page 45
1.9 MATCHING WITH LOGARITHMIC TERMS......Page 49
1.10 COMPOSITE EXPANSIONS......Page 52
2.1 ROOTS OF EQUATIONS......Page 64
2.2 INTEGRATION OF FUNCTIONS REPRESENTED......Page 72
2.3 ORDINARY DIFFERENTIAL EQUATIONS: REGULAR PROBLEMS......Page 76
2.4 ORDINARY DIFFERENTIAL EQUATIONS: SIMPLE SINGULAR PROBLEMS......Page 83
2.5 SCALING OF DIFFERENTIAL EQUATIONS......Page 92
2.6 EQUATIONS WHICH EXHIBIT A BOUNDARY-LAYER BEHAVIOUR......Page 97
2.7 WHERE IS THE BOUNDARY LAYER?......Page 103
2.8 BOUNDARY LAYERS AND TRANSITION LAYERS......Page 107
3. FURTHER APPLICATIONS......Page 132
3.1 A REGULAR PROBLEM......Page 133
3.2 SINGULAR PROBLEMS I......Page 135
3.3 SINGULAR PROBLEMS II......Page 145
3.4 FURTHER APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS......Page 156
4.1 NEARLY LINEAR OSCILLATIONS......Page 174
4.2 NONLINEAR OSCILLATORS......Page 182
4.3 APPLICATIONS TO CLASSICAL ORDINARY DIFFERENTIAL EQUATIONS......Page 185
4.4 APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS......Page 193
4.5 A LIMITATION ON THE USE OF THE METHOD OF MULTIPLE SCALES......Page 200
4.6 BOUNDARY-LAYER PROBLEMS......Page 201
5. SOME WORKED EXAMPLES ARISING FROM PHYSICAL PROBLEMS......Page 214
5.1 MECHANICAL & ELECTRICAL SYSTEMS......Page 215
5.2 CELESTIAL MECHANICS......Page 236
5.3 PHYSICS OF PARTICLES AND OF LIGHT......Page 243
5.4 SEMI- AND SUPERCONDUCTORS......Page 252
5.5 FLUID MECHANICS......Page 259
5.6 EXTREME THERMAL PROCESSES......Page 272
5.7 CHEMICAL AND BIOCHEMICAL REACTIONS......Page 279
APPENDIX: THE JACOBIAN ELLIPTIC FUNCTIONS......Page 286
ANSWERS AND HINTS......Page 288
REFERENCES......Page 300
SUBJECT INDEX......Page 304