Differential and Integral Calculus, Volume 1

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.

• Partial table of contents: The Continuum of Numbers, The Concept of Function, The Concept ofthe 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 Integralsand the Mean Value Theorem of the Integral Calculus. Differentiation and Integration of the Elementary Functions: Maximaand Minima, The Logarithm and the Exponential Function, TheHyperbolic Functions. Further Development of the Integral Calculus: The Method ofSubstitution, Integration by Parts, Integration of RationalFunctions, Improper Integrals. Applications. Taylor's Theorem and the Approximate Expression of Functions byPolynomials. 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 ofVibration. Answers and Hints. Index.