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Advanced calculus / Lynn Harold Loomis and Shlomo Sternberg.

By: Contributor(s): Material type: TextTextPublication details: Singapore : World Scientific, 2016.Edition: Revised editionDescription: 9 unnumbered, 580 pages : illustrations ; 26 cmISBN:
  • 9789814583930
Subject(s): DDC classification:
  • 515 23 L863
Summary: This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515 L863 (Browse shelf(Opens below)) Checked out 30/01/2025 137354
Total holds: 0

Includes bibliographical references and index.

0. Introduction --
1. Vector spaces --
2. Finite-dimensional vector spaces --
3. The differential calculus --
4. Compactness and completeness --
5. Scalar product spaces --
6. Differential equations --
7. Multilinear functionals --
8. Integration --
9. Differentiable manifolds --
10. The integral calculus on manifolds --
11. Exterior calculus --
12. Potential theory in E[superscript]n --
13. Classical mechanics.

This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication.

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