This book constructs the kernels of integral transforms by solving the generalized Sturm-Liouville problems associated with the partial differential equations at hand.<BR>In the first part of the book, the authors construct the kernels and use them to solve elementary problems of mathematical physics. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy-current testing.<BR>The first part of the book is accessible to undergraduates, while the second part is aimed at graduate students and researchers. Because of the applications, the book will interest engineers (especially petroleum engineers) and physicists.