How to Solve Applied Mathematics Problems

by B. L. Moiseiwitsch

Overview

The ability to solve problems in applied mathematics depends upon understanding concepts rather than memorizing formulas or rote learning. This volume bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields.
The two-part treatment begins with chapters on vector algebra, kinematics, dynamics of a particle, vector field theory, Newtonian gravitation, electricity and magnetism, fluid dynamics, and classical dynamics. The second part examines Fourier series and Fourier and Laplace transforms, integral equations, wave motion, heat conduction, tensor analysis, special and general relativity, quantum theory, and variational principles. The final chapter contains problems associated with many of the preceding chapters and expresses them in terms of the calculus of variations.

Product Details

ISBN-13:	9780486479279
Publisher:	Dover Publications
Publication date:	07/19/2011
Series:	Dover Books on Mathematics Series
Pages:	334
Product dimensions:	6.40(w) x 9.20(h) x 0.80(d)

Table of Contents

Preface 3

Introduction 5

1 Vector algebra 21

2 Kinematics 27

2-1 Radial and transverse resolutes of velocity and acceleration 28

2-2 Tangential and normal resolutes of velocity and acceleration 30

3 Dynamics of a particle 33

3-1 One-dimensional motion 33

3-2 Projectile motion 36

3-3 Vibrational motion 40

3-4 Orbital motion 43

3-5 Motion of a charged particle in electric and magnetic fields 48

3-6 Rotating frames of reference 52

4 Vector field theory 55

5 Newtonian gravitation 63

6 Electricity and magnetism 69

6-1 Electrostatics 69

6-2 Magnetism 91

6-3 Electric current flow 95

6-4 Electromagnetism 104

7 Fluid dynamics 109

8 Classical dynamics 123

8-1 Lagrange's equations 123

8-2 Tops 131

8-3 Hamilton's equations 134

8-4 Contact transformations 137

8-5 Hamilton-Jacobi equation 138

8-6 Vibrational motion 141

9 Fourier series, Fourier and Laplace transforms 145

9-1 Fourier series 145

9-2 Fourier transforms 150

9-3 Laplace transforms 155

10 Integral equations 163

11 Wave motion 181

11-1 Vibrations of strings 181

11-2 Sound waves 190

11-3 Water waves 195

12 Heat conduction 203

13 Tensor analysis 213

13-1 Cartesian tensors 213

13-2 Contravariant and covariant tensors 216

14 Theory of relativity 229

14-1 Special theory of relativity 229

14-2 General theory of relativity 244

15 Quantum theory 253

15-1 Exactly soluble problems 254

15-2 Variational methods 266

15-3 Time-independent perturbation theory 271

15-4 Semi-classical approximation 274

15-5 Spin and orbital angular momenta 276

15-6 Scattering theory 280

15-7 Time-dependent problems 287

16 Variational principles 293

16-1 Geodesies 293

16-2 Mechanics 296

16-3 Light rays 301

16-4 Field equations 303

16-5 Eigenvalue problems 308

Bibliography 315

Index 316