Worked Problems in Applied Mathematics

An unparalleled collection, this volume features 566 problems plus answers. They cover a wide range of topics in an accessible manner, including steady-state harmonic oscillations, the Fourier method, and the eigenfunction method for solving inhomogeneous problems. More advanced problems deal with integral transforms, curvilinear coordinates, and integral equations. 1965 edition.

Part 1 PROBLEMS
1 DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS
  1. Mechanics
  2. Heat Conduction
  3. Electricity and Magnetism
2 SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS
  1. Hyperbolic Functions
  2. Elliptic Equations: The Green's Function Method
  3. Elliptic Equations: The Method of Conformal Mapping
3 STEADY-STATE HARMONIC OSCILLATIONS
  1. Elastic Bodies: Free Oscillations
  2. Elastic Bodies: Forced Oscillations
  3. Electromagnetic Oscillations
4 THE FOURIER METHOD
  1. "Mechanics: Vibrating Systems, Acoustics"
  2. "Mechanics: Statics of Deformable Media, Fluid Dynamics"
  3. Heat Conduction: Nonstationary Problems
  4. Heat Conduction: Stationary Problems
  5. Electricity and Magnetism
5 THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS
  1. Mechanics: Vibrating Systems
  2. Mechanics: Statics of Deformable Media
  3. Heat Conduction: Nonstationary Problems
  4. Heat Conduction: Stationary Problems
  5. Electricity and Magnetism
6. INTEGRAL TRANSFORMS
  1. The Fourier Transform
  2. The Hankel Transform
  3. The Laplace Transform
  4. The Mellin Transform
  5. Integral Transforms Involving Cylinder Functions of Imaginary Order
7. CURVILINEAR COORDINATES
  1. Elliptic Coordinates
  2. Parabolic Coordinates
  3. Two-Dimensional Bipolar Coordinates
  4. Spheroidal Coordinates
  5. Paraboloidal Coordinates
  6. Toroidal Coordinates
  7. Three-Dimensional Bipolar Coordinates
  8. Some General Problems on Separation of Variables
8. INTEGRAL EQUATIONS
  1. Diffraction Theory
  2. Electrostatics
PART 2 SOLUTIONS
MATHEMATICAL APPENDIX
1. Special Functions Appearing in the Text
2. Expansions in Series of Orthogonal Functions
3. Some Definite Integrals Frequently Encountered in the Applications
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates
Supplement. VARIATIONAL AND RELATED METHODS
1. Variational Methods
  1.1 Formulation of Variational Problems
  1.2 The Ritz Method
  1.3 Kantorovich's Method
2. Related Methods
  2.1 Galerkin's Method
  2.2 Collocation
  2.3 Least Squares
3. References
BIBLIOGRAPHY
NAME INDEX
SUBJECT INDEX