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Course in Analysis, a - Volume I: Introductory Calculus, Analysis of Functions
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Course in Analysis, a - Volume I: Introductory Calculus, Analysis of Functions of One Real Variable Hardcover - 2015

by Niels Jacob; Kristian P. Evans


From the jacket flap

Volume 1 covers the content of two typical modules in undergraduate course for mathematics: Part 1: Introductory calculus Part 2: Analysis of functions of one variable These two parts are divided into 32 chapters. Part 1 begins with an overview of a set of real numbers: rational and irrational. This is accompanied by a discussion of arithmetic rules, inequalities, absolute values. Doing this, the authors, in a clever way, introduce elements of a set theory using Cantor's approach. This is followed by the definition of a function and discussion of operations on functions. From this they move to differential and integral calculus and their applications. Part 2 contains rigorous proofs of theorems from Part 1. In particular, they introduce the order structure on a real line using axioms of an ordered field. It is worth mentioning that Part 2 contains elements of topology obviously on real line and a good insight on convex functions. The convex functions relate Analysis to linear spaces equipped with norm. Finally, to close Part 2 the authors supply a number of Appendices, among them Appendices on logic, set theory and Peano axioms. Remarkably, Volume 1 contains 360 problems with complete solutions.

Details

  • Title Course in Analysis, a - Volume I: Introductory Calculus, Analysis of Functions of One Real Variable
  • Author Niels Jacob; Kristian P. Evans
  • Binding Hardcover
  • Pages 768
  • Volumes 1
  • Language ENG
  • Publisher World Scientific Publishing Company
  • Date 2015-11-22
  • ISBN 9789814689083 / 9814689084
  • Weight 2.8 lbs (1.27 kg)
  • Dimensions 9.8 x 6.6 x 1.8 in (24.89 x 16.76 x 4.57 cm)
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A Course in Analysis: Volume I: Introductory Calculus, Analysis of Functions of One Real Variable
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A Course in Analysis: Introductory Calculus, Analysis of Functions of One Real Variable: Vol 1
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A Course in Analysis: Introductory Calculus, Analysis of Functions of One Real Variable: Vol 1

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A Course in Analysis: Introductory Calculus, Analysis of Functions of One Real Variable: Vol 1
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A Course in Analysis: Introductory Calculus, Analysis of Functions of One Real Variable: Vol 1

by Jacob, Niels/ Evans, Kristian P.

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