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This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.

Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. Indeed, the earth's gravitational field imposes a stratification on its atmosphere, oceans and lakes. It is well known that their stratification has a profound effect on the propagation of sound in these fluids. The most striking effect is probably the occurrence of acoustic ducts, due to minima of the sound s...

The scattering of acoustic and electromagnetic waves by periodic sur­ faces plays a role in many areas of applied physics and engineering. Opti­ cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering o...

Solutions of the d'Alembert equation in ?n.- Solutions of the d'Alembert equation in arbitrary domains.- Steady-state scattering theory in exterior domains and the limiting absorption principle.- Time-dependent scattering theory in exterior domains.- Steady-state scattering theory and eigenfunction expansions for A.- Wave operators and asymptotic solutions of the d'Alembert equation in exterior domains.- Asymptotic wave functions and energy di...