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Advanced Calculus: An Introduction to Linear Analysis
Advanced Calculus: An Introduction to Linear Analysis
Leonard F. Richardson, Department of Mathematics, Louisiana State University, Baton Rouge, LA
ISBN: 978-0-470-23288-0
©2008
388 pages
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Description
Advanced Calculus highlights the connections between calculus and linear algebra in an effort to prepare readers for more advanced mathematical topics.  This approach highlights that the concepts of analysis are the foundations of undergraduate calculus, and it also provides a mathematically sophisticated introduction to functional analytic concepts.  The central theorems and examples of advanced calculus are treated as instances and motivations for the concepts of functional analysis.  This book was written from the point of view that readers should learn the importance of rigorous proof in order to develop skills in coherent written exposition to counter the universal temptation to engage in wishful thinking. Unlike the competition, this book approaches the rigorous foundations of calculus in a manner the reorients thinking in the directions taken by modern analysis.  The classic theorems are couched in a manner that reflects the perspectives of modern analysis.

Related Website https://www.math.lsu.edu/dept/personal/rich/ACLA  

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