Dealing with analytical and semi-analytical methods in engineering and sciences, this book is an attempt to lay the foundation for developing efficient computational methods. It draws upon the results and methods of mathematical physics and systematically develops the solution methods for ordinary and partial differential equations encountered in different engineering disciplines and sciences. The treatment is confined to linear equations for the most part, except for some nonlinear problems considered in the chapters on approximate methods. The book offers a large amount of supplemental material, including solved examples and exercises to convey the applications of analytical methods.