Mathematics applied to deterministic problems in the natural sciences

C. C. Lin, L. A. Segel9780898712292, 0898712297

Addresses the construction, analysis, and interpretation of mathematical models that shed light on significant problems in the physical sciences.
The authors’ case studies approach leads to excitement in teaching realistic problems. The exercises reinforce, test and extend the reader’s understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.

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Table of contents :
Mathematics Applied to Deterministic Problems in the Natural Sciences……Page 1
Foreword……Page 8
Preface……Page 10
Contents……Page 16
Conventions……Page 24
PART A An Overview of the Interaction of Mathematics and Natural Science……Page 26
CHAPTER 1 What Is Applied Mathematics?……Page 28
CHAPTER 2 Deterministic Systems and Ordinary Differential Equations……Page 61
CHAPTER 3 Random Processes and Partial Differential Equations……Page 96
CHAPTER 4 Superposition, Heat Flow, and Fourier Analysis……Page 139
CHAPTER 5 Further Developments in Fourier Analysis……Page 175
PART B Some Fundamental Procedures Illustrated on Ordinary Differential Equations……Page 208
CHAPTER 6 Simplification, Dimensional Analysis, and Scaling……Page 210
CHAPTER 7 Regular Perturbation Theory……Page 250
CHAPTER 8 Illustration of Techniques on a Physiological Flow Problem……Page 269
CHAPTER 9 Introduction to Singular Perturbation Theory……Page 302
CHAPTER 10 Singular Perturbation Theory Applied to a Problem in Biochemical Kinetics……Page 327
CHAPTER 11 Three Techniques Applied to the Simple Pendulum……Page 346
PART C Introduction to Theories of Continuous Fields……Page 372
CHAPTER 12 Longitudinal Motion of a Bar……Page 374
CHAPTER 13 The Continuous Medium……Page 437
CHAPTER 14 Field Equations of Continuum Mechanics……Page 465
CHAPTER 15 Inviscid Fluid Flow……Page 530
CHAPTER 16 Potential Theory……Page 591
Bibliography……Page 614
Supplementary Bibliography (1994)……Page 620
Updated Material……Page 623
Hints and Answers (for exercises marked with :)……Page 625
Authors Cited……Page 629
Subject Index……Page 630