Mathematical Analysis
Functions of One Variable
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Beschreibung
This self-contained work introduces the main ideas and fundamental
methods of analysis at the advanced undergraduate/graduate level. It
provides the historical context out of which these concepts emerged,
and aims to develop connections between analysis and other
mathematical disciplines (e.g., topology and geometry) as well as
physics and engineering. A rigorous exposition, numerous examples,
beautiful illustrations, good problems, comprehensive bibliography,
and index are some of the key features of the book. Excellent for self
-study or the classroom.
Interesting and valuable historical account of ideas and methods in analysis with beautiful illustrations Rigorous exposition with full proofs motivated by numerous examples Exercises, comprehensive bibliography and index
Autor*in
Mariano Giaquinta
Themen in »Mathematical Analysis«
Complex analysis Derivative Fundamental theorem of calculus Minimum applications of mathematics calculus differential equation logarithm one variable optimization ordinary differential equations real functions
Stimmen zu »Mathematical Analysis«
From the reviews:
"Many teachers and students could benefit from thinking about its unique perspectives."
---SIAM Review
"Giaquinta . . . and Modica . . . present the differential and integral calculus for real functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source of unique perspectives on the logical development of calculus ideas and their physical applications . . . [so that] it will better serve the experienced calculus instructor seeking new approaches to familiar material, or the student who has already mastered the basic ideas and techniques of calculus but wishes to see it all again, 'done right,' . . . Highly recommended."
---CHOICE
"This self-contained book introduces the main ideas and fundamental methods of mathematical analysis without loosing sight of the context in which it was developed and the role played in science, particularly in physics…. Each chapter has a short summary where the most important facts discussed are collected. There is also a large number of exercises inserted at various points into the text…. The book is meant principally for students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics."
---ZENTRALBLATT MATH
"The presentation of the theory is clearly arranged, all theorems have rigorous proofs and every chapter closes with a summing up of the results and exericeses with different requirements. The aim of the authors was very successful[ly] realized, and this book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties." ---Journal of Analysis and its Applications
"This is the first of several volumes on analysis by theseauthors. … It is essentially a calculus book at the advanced undergraduate level, or an analysis textbook for someone who has never seen calculus before. … I like this book … ." (Warren Johnson, The Mathematical Association of America, October, 2009)
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