The second edition of a bestseller, this book elucidates integral methods, field equation derivations, and operations applicable to modern science systems. Written for readers who already have some knowledge of differential and integral calculus and an introductory level of ordinary differential equations, each chapter contains many solved examples and many problems with answers. Those chapters which cover boundary value problems and partial differential equations also include derivation of the governing differential equations in many fields of applied physics and engineering such as wave mechanics, acoustics, heat flow in solids, diffusion of liquids and gasses and fluid flow.