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Advanced Calculus
Posted by Arun on 11:05 AM
Advanced Calculus, Revised Edition
Author : Lynn H. Loomis and Shlomo Sternberg, Department of Mathematics, Hardvard University
Publication Date : 1990
Publisher : Jones and Bartlett Publishers
Free License : Creative Commons license
download link (58 mb) : http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf
Book Excerpts:
This book is based on an honors course in Advanced Calculus given at Department of Mathematics, Hardvard University. 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.
These 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. As possible introductory texts, reader should read Differential and Integral Calculus by R. Courant, Calculus by T. Apostol, Calculus by M. Spivak, and Pure Mathematics by G. Hardy. The reader should also have some experience with partial derivatives.
In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author : Lynn H. Loomis and Shlomo Sternberg, Department of Mathematics, Hardvard University
Publication Date : 1990
Publisher : Jones and Bartlett Publishers
Free License : Creative Commons license
download link (58 mb) : http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf
Book Excerpts:
This book is based on an honors course in Advanced Calculus given at Department of Mathematics, Hardvard University. 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.
These 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. As possible introductory texts, reader should read Differential and Integral Calculus by R. Courant, Calculus by T. Apostol, Calculus by M. Spivak, and Pure Mathematics by G. Hardy. The reader should also have some experience with partial derivatives.
In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Labels: Mathematics
