Differential and Integral Calculus, 2 Volume Set (Volume I Paper Edition; Volume II Cloth Edition)

by Courant, Richard; Hilbert, David

• ISBN13: 9780471588818
• ISBN10: 0471588814
• Edition: 1st
• Format: Paperback
• Copyright: 1992-08-04
• Publisher: Wiley-Interscience

Summary

This Set Contains: Differential and Integral Calculus, Volume 1 by R. Courant; Differential and Integral Calculus, Volume 2 by R. Courant.

Author Biography

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.

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.

Table of Contents

Partial table of contents

The Continuum of Numbers

The Concept of Function

The Concept of the Limit of a Sequence

The Concept of Continuity

The Fundamental Ideas of the Integral and Differential Calculus: The Definite Integral

The Derivative

The Estimation of Integrals and the Mean Value Theorem of the Integral Calculus

Differentiation and Integration of the Elementary Functions: Maxima and Minima

The Logarithm and the Exponential Function

The Hyperbolic Functions

Further Development of the Integral Calculus: The Method of Substitution

Integration by Parts

Integration of Rational Functions

Improper Integrals

Applications

Taylor's Theorem and the Approximate Expression of Functions by Polynomials

Numerical Methods

Infinite Series and Other Limiting Processes

Fourier Series

A Sketch of the Theory of Functions of Several Variables

The Differential Equations for the Simplest Types of Vibration

Answers and Hints

Index

Table of Contents provided by Publisher. All Rights Reserved.