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Mathematical Methods for Physicists, 3rd edition: George Arfken

Mathematical Methods for Physicists is based upon two courses in mathematics for physicists given by the author over the past fourteen years, one at the junior level and one at the beginning graduate level. This book is intended to provide the student with the mathematics he needs for advanced undergraduate and beginning graduate study in physical science and to develop a strong background for those who will continue into the mathematics of advanced theoretical physics. A mastery of calculus and a willingness to build on this mathematical foundation are assumed.

This text has been organized with two basic principles in view. First, it has been written in a form that it is hoped will encourage independent study. There are frequent cross references but no fixed, rigid page-by-page or chapter-by-chapter sequence is demanded.

The reader will see that mathematics as a language is beautiful and elegant. Unfortunately, elegance all too often means elegance for the expert and obscurity for the beginner. While still attempting to point out the intrinsic beauty of mathematics, elegance has occasionally been reluctantly but deliberately sacrificed in the hope of achieving greater flexibility and greater clarity for the student. Mathematical rigor has been treated in a similar spirit. It is not stressed to the point of becoming a mental block to the use of mathematics. Limitations are explained, however, and warnings given against blind, uncomprehending application of mathematical relations.

The second basic principle has been to emphasize and re-emphasize physical examples in the text and in the exercises to help motivate the student, to illustrate the relevance of mathematics to his science and engineering.

This principle has also played a decisive role in the selection and development of material. The subject of differential equations, for example, is no longer a series of trick solutions of abstract, relatively meaningless puzzles but the solutions and general properties of the differential equations the student will most frequently encounter in a description of our real physical world.

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