Complex Variable Theory and Transform Calculus (2^nd Ed., Revised edition) With Technical Applications

The purpose of this book, first published in 1939, updated in 1953, is to give a treatment of the so-called operational method and to illustrate its application to problems in various branches of technology. It is written primarily for technologists who use mathematics in solving technical problems in industrial and applied research work, and the treatment is sufficiently rigorous for their needs. The theory of the complex variable and of transform calculus occupy the first half of the book. A further third of the book describes the application of this theory to problems arising in electrical circuits; vibrational systems; aeroplane dynamics; the deflexion of beams; radio and television receivers; the solution of partial differential equations; electrical transmission limes; electrical wave filters; solenoids with metal cores; condenser microphones; loud speaker horns and the absorption of moisture. The final part contains over 100 problems - many with hints for their solution - appendices and references.

Preface to the second edition; Preface to the first edition; Part I. Theory of Complex Variable: 1. Functions of a complex variable; 2. Integration: Cauchy's theorem: Taylor's and Laurent's theorems; 3. Calculus of residues; 4. The Bromwich contour: equivalent contours: evaluation of integrals; 5. Gamma, error and Bessel functions; 6. Evaluation of 1/2∏i∫Br1 eztø(z)dz/z when ø(z) has branch points; 7. Differentiation and integration under the integral sign; Part II. Theory of Transform Calculus: 8. Mellin inversion theorem: transform theory; 9. Solution of ordinary linear differential equations; 10. Discontinuous functions: impulses: frequency spectra; Part III. Technical Applications of Parts I and II: 11. Electrical circuits: vibrational systems: aeroplane dynamics: deflexion of beams; 12. Radio and television receivers; 13. Partial linear differential equations: electrical transmission lines: electrical wave filters; 14. Solenoid with metal core: condenser microphone: loud speaker horn; 15. Diffusion of heat: absorption of moisture problems to be worked out by the reader; Part IV. Appendices and List of References; Index.