Basic Analysis I
CRC Press (Verlag)
978-1-138-05502-5 (ISBN)
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
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.
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.
| Erscheinungsdatum | 15.05.2020 |
|---|---|
| Zusatzinfo | 58 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1229 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Technik ► Umwelttechnik / Biotechnologie | |
| ISBN-10 | 1-138-05502-6 / 1138055026 |
| ISBN-13 | 978-1-138-05502-5 / 9781138055025 |
| Zustand | Neuware |
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