ข้อมูลทรัพยากร

เนื้อหาย่อ : The subject commonly called "Advanced Calculus" means different things to different people. To some it essentially represents elementary calculus from an advanced viewpoint, i.e. with rigorous statements and proofs of theorems. To others it represents a variety of special advanced topics which are considered important but which cannot be covered in an elementary course. In this book an effort has been made to adopt a reasonable compromise between these extreme approaches which, it is believed, will serve a variety of individuals. The early chapters of the book serve in general to review and extend fundamental concepts already presented in elementary calculus. This should be valuable to those who have forgotten some of the calculus studied previously and who need "a bit of refreshing". It may also serve to provide a common background for students who have been given different types of courses in elementary calculus. Later chapters serve to present special advanced topics which are fundamental to the scientist, engineer and mathematician if he is to become proficient in his intended field. This book has been designed for use either as a supplement to all current standard text- books or as a textbook for a formal course in advanced calculus. It should also prove useful to students taking courses in physics, engineering or any of the numerous other fields in which advanced mathematical methods are employed. Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principles so vital to effective learning. Numerous proofs of theorems and derivations of basic results are included among the solved problems. The large number of supplementary problems with answers serve as a complete review of the material of each chapter. Topics covered include the differential and integral calculus of functions of one or more variables and their applications. Vector methods, which lend themselves so readily to concise notation and to geometric and physical interpretations, are introduced early and used whenever they can contribute to motivation and understanding. Special topics include line and surface integrals and integral theorems, infinite series, improper integrals, gamma and beta functions, and Fourier series. Added features are the chapters on Fourier integrals, elliptic integrals and functions of a complex variable which should prove extremely useful in the study of advanced engineering, physics and mathematics. Considerably more material has been included here than can be covered in most courses. This has been done to make the book more flexible, to provide a more useful book of reference and to stimulate further interest in the topics. I wish to take this opportunity to thank the staff of the Schaum Publishing Company for their splendid cooperation in meeting the seemingly endless attempts at perfection by the author.