Bøger af Richard Courant

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47 brauchen nur den Nennern so gro zu wahlen, da das Intervall [0, 1/n] kleiner wird als das fragliche Intervall [A, B], dann mu mindestens einer der Bruche mfn innerhalb des Intervalls liegen. Also kann es kein noch so kleines Intervall auf der Achse geben, das von rationalen Punkten frei ware. Es folgt weiterhin, da es in jedem Intervall unendlich viele rationale Punkte geben mu; denn wenn es nur eine endliche Anzahl gabe, so konnte das Intervall zwischen zwei beliebigen benachbarten Punkten keine rationalen Punkte enthalten, was, wie wir eben sahen, unmoglich ist. 2. Inkommensurable Strecken, irrationale Zahlen und der Grenzwertbegriff 1. Einleitung Vergleicht man zwei Strecken a und b hinsichtlich ihrer Groe, so kann es vor- kommen, da a in b genau r-mal enthalten ist, wobei r eine ganze Zahl darstellt. In diesem Fall konnen wir das Ma der Strecke b durch das von a ausdrucken, indem wir sagen, da die Lange von b das r-fache der Lange von a ist. Oder es kann sich zeigen, da man, wenn auch kein ganzes Vielfaches von a genau gleich b ist, doch a in, sagen wir, n gleiche Strecken von der Lange afn teilen kann, so da ein ganzes Vielfaches m der Strecke afn gleich b wird: b=!!!..a.

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)

The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

Volume 2 of the classic advanced calculus text Richard Courant's Differential and Integral Calculus is considered an essential text for those working toward a career in physics or other applied math. Volume 2 covers the more advanced concepts of analytical geometry and vector analysis, including multivariable functions, multiple integrals, integration over regions, and much more, with extensive appendices featuring additional instruction and author annotations. The included supplement contains formula and theorem lists, examples, and answers to in-text problems for quick reference.

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

This introduction to the ideas and elements of mathematics should be of interest to students with a desire to develop mathematical skills, and general readers with an interest in mathematics.

First published in 1924, Courant and Hilbert's treatment of the subject restored the historical connections between physical intuition and mathematical development, providing readers with a unified approach. This volume represents Courant's second and final revision of 1953.