Methods of Mathematical Physics

Volume 1
1. Auflage 2024
ISBN: 978-3-527-41447-5
Verlag: Wiley-VCH GmbH

Buch, Englisch, 575 Seiten, Format (B × H): 172 mm x 246 mm, Gewicht: 1100 g

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

Autoren/Hrsg.

Courant, R.

Courant, Richard

Hilbert

Hilbert, David

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

I. THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS 1

II. SERIES EXPANSION OF ARBITRARY FUNCTIONS 48

III. LINEAR INTEGRAL EQUATIONS 112

IV. THE CALCULUS OF VARIATIONS 164

V. VIBRATION AND EIGENVALUE PROBLEMS 275

VI. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS 397

VII. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS 466

Additional Bibliography 546

Index 551

Über Autor(innen)

David Hilbert (1862 - 1943) received his PhD from the University of Königsberg, Prussia (now Kaliningrad, Russia) in 1884. He remained there until 1895, after which he was appointed Professor of Mathematics at the University of Göttingen. He held this professorship for most of his life. Hilbert is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. His own discoveries alone would have given him that honour, yet it was his leadership in the field of mathematics throughout his later life that distinguishes him. Hilbert's name is given to Infinite-Dimensional space, called Hilbert space, used as a conception for the mathematical analysis of the kinetic gas theory and the theory of radiations.

Richard Courant (1888 - 1972) obtained his doctorate at the University of Göttingen in 1910. Here, he became Hilbert's assistant. He returned to Göttingen to continue his research after World War I, and founded and headed the university's Mathematical Institute. In 1933, Courant left Germany for England, from whence he went on to the United States after a year. In 1936, he became a professor at the New York University. Here, he headed the Department of Mathematics and was Director of the Institute of Mathematical Sciences - which was subsequently renamed the Courant Institute of Mathematical Sciences. Among other things, Courant is well remembered for his achievement regarding the finite element method, which he set on a solid mathematical basis and which is nowadays the most important way to solve partial differential equations numerically.