This book has grown out of a set of lecture notes for a graduate course in numerical analysis which I gave at the Computation Laboratory of Harvard University during the years 1947 to 1949. Professor Howard Aiken of that laboratory foresaw the great need that would be felt throughout the country for men trained in the design and use of electronic digital computers and initiated at that early date a set of courses to meet this need. I was privileged during that time to devote full time to the preparation of the course on numerical methods. It was felt that such a course should cover those topics most directly needed for an understanding of the methods used in the numerical solution of differential equations, both ordinary and partial, and in the solution of integral equations. Thus in this book, as in the lectures, considerable time is devoted to finite-difference tables and notation, to numerical differentiation and integration, but peripheral subjects such as the smoothing of experimental data, least-squares approximation, and harmonic analysis are omitted. These omissions made it possible to include in one book all the background material needed for obtaining numerical solutions to advanced problems in applied mathematics. While the main reason for writing this book has been to acquaint the student with the best procedures available for obtaining numerical solutions to problems arising in applied mathematics, methods of doubtful practicality have often been included to broaden the student's understanding of the essential unity of all finite difference methods. Since the goal sought is largely a pragmatic one, only a modest attempt has been made to preserve mathematical rigor and free use has been made of symbolic methods and heuristic arguments.
Dr. Kaiser S. Kunz received his B.S. in Physics from the University of Indiana in 1936. The following year, he transferred to the University of Cincinnati where he received his M.S. (1937) and his Ph.D in Physics (1939). After graduation, he began his career in teaching and research in physics and mathematics, remaining in Cincinnati for three years as Mathematics Instructor at the University's Engineering College. As his career continued to progress, he became affiliated with several academic institutions including Harvard University (1942-49) where he worked as an Electronics Instructor, Research Associate, Research Fellow, and Lecturer. His other academic affiliations were with the Case Institute of Technology (1949-51) as an Associate Professor in Electrical Engineering and with New Mexico State University (beginning 1960 until retirement) as Research Professor in Physics and Electrical Engineering. Dr. Kunz has had several industrial affiliations as well including acting as a Consultant at White Sands Missile Range, Sandia Laboratory, the Physical Science Laboratory, and the Air Force-Cambridge Research Laboratory. He was Head of Applied Mathematics Group, Division Head-Electrical, Nuclear, and Sonic Logging, and Assistant Director of Research at Schlumberger Well Surveying Corporation (1951-60). His management and administration experience included the Chairmanship of the Computer Advisory Group for the New Mexico State University in Las Cruces, New Mexico, where he acted as advisor on matters such as computer acquisitions and operational policies for the University Computer Center. Among his many areas of specialization, Dr. Kunz focused on physics encompassing electromagnetic theory, lasers, optics, and nuclear research. He also worked on research projects in electrical engineering specializing in the theory and design of antennas, electro-optic crystals, circuit theory, and pulse propagation on multiconductor layered cable. In applied mathematics he researched numerical methods, probability and statistics, heat flow, mechanics of bodies and fluids, and data processing. Dr. Kunz has documented and published many works concerning his research and several are accessible through his website. http: //askdrkunz.co
