Basic Analysis I
Functions of a Real Variable
1st Edition
Published on 14. May 2020
Book
Hardback
594 pages
978-1-138-05502-5 (ISBN)
Description
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists.
This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth.
Features
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction
Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth.
Features
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction
Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Reviews / Votes
"Mathematics is fortunate to be populated by bright practitioners. Nonetheless, amongst these we are fortunate to have rare individuals who are wise. Professor Peterson is a member of this distinguished group. His works clearly demonstrate the importance of a long career of research and teaching where he combines the two perspectives of: (1) clearly understanding the needs of diverse readers for clear exposition that scaffolds their exposure to complex material with a transparency about both where they are going and what the utility is of what they are currently reading; and, (2) the benefits of having used the mathematics under consideration in so many diverse applications. The masterly synthesis of so much complex material by a single individual is a superb achievement which will reward serious readers with insight, surprise, and breadth as well as depth."-Professor John R. Jungck, University of Delaware
"Analysis is the bedrock of rigorous mathematical thinking and abstraction. Prof. Peterson's book does a fascinating job by taking a critical approach - highly recommended."
-Professor Nithin Nagaraj, National Institute of Advanced Studies "Mathematics is fortunate to be populated by bright practitioners. Nonetheless, amongst these we are fortunate to have rare individuals who are wise. Professor Peterson is a member of this distinguished group. His works clearly demonstrate the importance of a long career of research and teaching where he combines the two perspectives of: (1) clearly understanding the needs of diverse readers for clear exposition that scaffolds their exposure to complex material with a transparency about both where they are going and what the utility is of what they are currently reading; and, (2) the benefits of having used the mathematics under consideration in so many diverse applications. The masterly synthesis of so much complex material by a single individual is a superb achievement which will reward serious readers with insight, surprise, and breadth as well as depth."
- Professor John R. Jungck, University of Delaware
"Analysis is the bedrock of rigorous mathematical thinking and abstraction. Prof. Peterson's book does a fascinating job by taking a critical approach - highly recommended."
- Professor Nithin Nagaraj, National Institute of Advanced Studies
"Dr. Peterson's thoughtful and detailed explanations reflect his insights to a very fundamental but complex subject in Mathematics. The treatment in the book does justice to recent trends in Mathematical Analysis while staying true to the classical spirit of the subject. A thoroughly enjoyable read."
- Professor Snehanshu Saha, BITS PIlani (K K Birla Goa Campus)
More details
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
58 s/w Abbildungen
58 Illustrations, black and white
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 36 mm
Weight
1300 gr
ISBN-13
978-1-138-05502-5 (9781138055025)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
05/2020
1st Edition
Chapman & Hall/CRC
€125.99
Available for download
E-Book
05/2020
1st Edition
Chapman & Hall/CRC
€125.99
Available for download
Person
James Peterson has been an associate professor in the School of Mathematical and Statistical Sciences
since 1990. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2016.
He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages and from first principles analysis of natural phenomena was absolutely essential to make progress.
In both mathematical and applied areas, students often need to use advanced mathematics tools they have not
learned properly. So recently, he has written a series of books on analysis to help researchers with the problem
of learning new things after their degrees are done and they are practicing scientists. Along the way, he has also written papers in immunology, cognitive science and neural network technology in addition to having grants from NSF, NASA and the Army.
He also likes to paint, build furniture and write stories.
since 1990. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2016.
He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages and from first principles analysis of natural phenomena was absolutely essential to make progress.
In both mathematical and applied areas, students often need to use advanced mathematics tools they have not
learned properly. So recently, he has written a series of books on analysis to help researchers with the problem
of learning new things after their degrees are done and they are practicing scientists. Along the way, he has also written papers in immunology, cognitive science and neural network technology in addition to having grants from NSF, NASA and the Army.
He also likes to paint, build furniture and write stories.
Content
I.Introduction. II. Understanding Smoothness. 2.Proving Propositions. 3. Sequences of Real Numbers. 4. BolzanoWeierstrass Results. 5. Topological Compactness. 6. Function Limits. 7. Continuity. 8. Consequences of continuity of intervals. 9. Lower Semicontinuous and Convex Functions. 10. Basic Differentiability. 11. The Properties of Derivatives. 12. Consequences of Derivatives. 13. Exponential and Logarithm Functions. 14. Extremal Theory for One Variable. 15. Differentiation in R2 and R3.16. Multivariable Extremal Theory. III. Integration and Sequences of Functions. 17. Uniform Continuity. 18. Cauchy Sequences of Real Numbers. 19. Series of Real Numbers. 20. Series in Gerenal. 21. Integration Theiry. 22. Existence of Reimann Integral Theories. 23. The Fundamental Theorem of Calculus (FTOC). 24. Convergence of sequences of functions. 25. Series of Functions and Power Series. 26. Riemann Integration: Discontinuities and Compositions. 27. Fourier Series. 28. Application. IV. Summing it All Up . 29. Summary. V. References. VI. Detailed References.