Introduction to Calculus and Analysis Volume II/1: Chapters 1 - 4 / Edition 1

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Overview

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." —Acta Scientiarum Mathematicarum, 1991

"..this book intends to lead students directly to the heart of calculus & prepare them for active application of their knowledge, revealing the interconnections & purposes of the whole."

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Editorial Reviews

From the Publisher
From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991
Booknews
Reprint of the 1965 textbook (John Wiley and Sons) originally written by Courant in 1927 and translated into English in 1934. This first volume is concerned primarily with functions of a single variable. Problems and examples. No bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9783540665694
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/14/1999
  • Series: Classics in Mathematics Series
  • Edition description: Reprint of the 1st ed. New York 1989
  • Edition number: 1
  • Pages: 556
  • Product dimensions: 1.21 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Functions of Several Variables and Their Derivatives: Points and Points Sets in the Plane and in Space; Functions of Several Independent Variables; Continuity; The Partial Derivatives of a Function; The Differential of a Function and Its Geometrical Meaning; Functions of Functions (Compound Functions) and the Introduction of New Independent Variables; The mean Value Theorem and Taylor's Theorem for Functions of Several Variables; Integrals of a Function Depending on a Parameter; Differentials and Line Integrals; The Fundamental Theorem on Integrability of Linear Differential Forms; Appendix.-
Vectors, Matrices, Linear Transformations: Operatios with Vectors; Matrices and Linear Transformations; Determinants; Geometrical Interpretation of Determinants; Vector Notions in Analysis.-
Developments and Applications of the Differential Calculus: Implicit Functions; Curves and Surfaces in Implicit Form; Systems of Functions, Transformations, and Mappings; Applications; Families of Curves, Families of Surfaces, and Their Envelopes; Alternating Differential Forms; Maxima and Minima; Appendix.-
Multiple Integrals: Areas in the Plane; Double Integrals; Integrals over Regions in three and more Dimensions; Space Differentiation. Mass and Density; Reduction of the Multiple Integral to Repeated Single Integrals; Transformation of Multiple Integrals; Improper Multiple Integrals; Geometrical Applications; Physical Applications; Multiple Integrals in Curvilinear Coordinates; Volumes and Surface Areas in Any Number of Dimensions; Improper Single Integrals as Functions of a Parameter; The Fourier Integral; The Eulerian Integrals (Gamma Function); Appendix

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