EQUATIONS OF MATHEMATICAL PHYSICS (Mathematics for Future Engineers)

This book, the sixth volume of the series, is addressed to all those who wish a practical initiation in the domain of partial differential equations and their applications to various practical domains. While inspired from a course, we provide here several novelties. We established a pattern structured in stages, to be followed by the reader to the end of establishing the mathematical model corresponding to a physical phenomenon. We introduced the formal computation by differential polynomials, to simplify, both in writing and thinking, the reduction to the canonical form of second-order PDEs. The formal computation is structured in stages and fully exemplified throughout the book, in applications and exercises.At the introduction of supplementary conditions associated to the PDEs, we gave mathematical examples of ill and well posed problems. We illustrated this concept by practical examples, involving e.g. the particle accelerator or the electrostatic gun, thus emphasizing the tight connection existing between the mathematical model and the corresponding physical problem.We provided for the chapters 1, 2 and 4, along with examples, also summaries containing a series of applications and solved problems, structured in stages. Moreover, each chapter ends by a section containing exercises and problems, accompanied by hints and answers, and even by complete resolution.The mathematical concepts presented here require only elementary notions, usually learnt in the first year of study at a technical university, fully presented in the first five volumes of this series. Read more