The Collected Works of Courant, Dunford, Henrici, and Kobayashi, Volume 2

This set features:Foundations of Differential Geometry, Volume 1  by Shoshichi Kobayashi and Katsumi Nomizu (978-0-471-15733-5)Foundations of Differential Geometry, Volume 2 by Shoshichi Kobayashi and Katsumi Nomizu  (978-0-471-15732-8)Differential and Integral Calculus, Volume 1 by Richard Courant (978-0-471-60842-4)Differential and Integral Calculus, Volume 2 by Richard Courant (978-0-471-60840-0)Linear Operators, Part 1: General Theory by Neilson Dunford and Jacob T. Schwartz (978-0-471-60848-6)Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert Space Theory by Neilson Dunford and Jacob T. Schwartz (978-0-471-60847-9)Linear Operators, Part 3: Spectral Operators by Neilson Dunford and Jacob T. Schwartz (978-0-471-60846-2)Applied and Computational Complex Analysis, Volume 1, Power Series Integration Conformal Mapping Location of Zero by Peter Henrici (978-0-471-60841-7)Applied and Computational Complex Analysis, Volume 2, Special Functions-Integral Transforms- Asymptotics-Continued Fractions by Peter Henrici (978-0-471-54289-6)Applied and Computational Complex Analysis, Volume 3, Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions by Peter Henrici (978-0-471-58986-0)

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.

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.