A Course in Analysis

Author: Niels Jacob
Publisher: World Scientific Publishing Company
ISBN: 9814689106
Format: PDF, ePub
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Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis. Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions. Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.

Introduction to Calculus and Analysis Volume II 2

Author: Richard Courant
Publisher: Springer Science & Business Media
ISBN: 9783540665700
Format: PDF, Kindle
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From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

The Best in the literature of science technology and medicine

Author: Paul T. Durbin
Publisher: Rr Bowker Llc
ISBN: 9780835221498
Format: PDF, ePub, Mobi
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Includes coverage of General Science; History of Science, Technology, & Medicine; Philosophy of Science & Pseudoscience; Mathematics; Statistics & Probability; Information & Communication Science; Earth & Space Sciences; Physics; Chemistry; Biology; Ecology & Environmental Science; Genetics; Medicine; Clinical Psychology & Psychiatry; Engineering & Technology; Energy; Ethics of Science, Technology, & Medicine. See main listing under Bibliography for more information.

Differential and Integral Calculus

Author: Richard Courant
Publisher: John Wiley & Sons
ISBN: 1118031490
Format: PDF, Docs
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The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

Vector Calculus

Author: Bill Cox
Publisher: Butterworth-Heinemann
ISBN: 0340677414
Format: PDF, ePub
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Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation and multiple integration. Undergraduates who already have a basic understanding of calculus and vectors, will find this text provides tools with which to progress onto further studies; scientists who need an overview of higher order differential equations will find it a useful introduction and basic reference.

The Reader s Adviser

Author: Barbara Ann Chernow
Publisher: Rr Bowker Llc
ISBN: 9780835221498
Format: PDF, ePub, Docs
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Includes coverage of General Science; History of Science, Technology, & Medicine; Philosophy of Science & Pseudoscience; Mathematics; Statistics & Probability; Information & Communication Science; Earth & Space Sciences; Physics; Chemistry; Biology; Ecology & Environmental Science; Genetics; Medicine; Clinical Psychology & Psychiatry; Engineering & Technology; Energy; Ethics of Science, Technology, & Medicine. See main listing under Bibliography for more information.

Introduction to Calculus and Analysis II 1

Author: Richard Courant
Publisher: Springer Science & Business Media
ISBN: 9783540665694
Format: PDF, ePub
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From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991