Advanced Calculus - download pdf or read online

By Lynn Harold Loomis,Shlomo Sternberg

ISBN-10: 9814583928

ISBN-13: 9789814583923

ISBN-10: 9814583936

ISBN-13: 9789814583930

An accepted reissue of the lengthy out of print vintage textbook, Advanced Calculus via the overdue Dr Lynn Loomis and Dr Shlomo Sternberg either one of Harvard collage has been a respected yet difficult to discover textbook for the complex calculus path for decades.

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

The must haves are a great grounding within the calculus of 1 variable from a mathematically rigorous standpoint, including a few acquaintance with linear algebra. The reader will be accustomed to restrict and continuity style arguments and feature a specific amount of mathematical sophistication. As attainable introductory texts, we point out Differential and indispensable Calculus through R Courant, Calculus by way of T Apostol, Calculus by way of M Spivak, and Pure Mathematics through G Hardy. The reader also needs to have a few event with partial derivatives.

In total plan the ebook 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 imperative Calculus on Manifolds
  • Exterior Calculus
  • Potential conception in En
  • Classical Mechanics

Readership: Undergraduates in mathematics.

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg


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