By Lynn Harold Loomis,Shlomo Sternberg

ISBN-10: 9814583928

ISBN-13: 9789814583923

ISBN-10: 9814583936

ISBN-13: 9789814583930

An approved reissue of the lengthy out of print vintage textbook, Advanced Calculus by means of the overdue Dr Lynn Loomis and Dr Shlomo Sternberg either one of Harvard college has been a respected yet challenging to discover textbook for the complicated calculus direction for decades.

This e-book is predicated on an honors path in complex calculus that the authors gave within the 1960's. The foundational fabric, awarded within the unstarred sections of Chapters 1 via eleven, was once in general coated, yet varied functions of this simple fabric have been under pressure from 12 months to yr, and the ebook for that reason comprises extra fabric than used to be lined in anyone yr. it could possibly therefore be used (with omissions) as a textual content for a year's direction in complicated calculus, or as a textual content for a three-semester creation to analysis.

The necessities are an exceptional grounding within the calculus of 1 variable from a mathematically rigorous viewpoint, including a few acquaintance with linear algebra. The reader could be acquainted with restrict and continuity variety arguments and feature a certain quantity of mathematical sophistication. As attainable introductory texts, we point out Differential and fundamental Calculus by means of R Courant, Calculus via T Apostol, Calculus via M Spivak, and Pure Mathematics through G Hardy. The reader also needs to have a few adventure with partial derivatives.

In total plan the booklet divides approximately right into a first part which develops the calculus (principally the differential calculus) within the surroundings of normed vector areas, and a moment part which offers with the calculus of differentiable manifolds.

Contents:

  • Introduction
  • Vector Spaces
  • Finite-Dimensional Vector Spaces
  • The Differential Calculus
  • Compactness and Completeness
  • Scalar Product Spaces
  • Differential Equations
  • Multilinear Functionals
  • Integration
  • Differentiable Manifolds
  • The fundamental Calculus on Manifolds
  • Exterior Calculus
  • Potential concept in En
  • Classical Mechanics

Readership: Undergraduates in mathematics.

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg


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