Titlebook: Real Analysis via Sequences and Series; Charles H.C. Little,Kee L. Teo,Bruce van Brunt Textbook 2015 Springer Science+Business Media New Y

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Continuity,ogarithm function is introduced as an example of a continuous function and is then used to establish Gauss’s test for convergence of a series of positive terms. The chapter concludes with a study of uniform continuity.

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LIKEN

Sequences of Functions,ion processes, is raised. The concept of uniform convergence of a sequence of functions is introduced as a justification of such interchanges. The idea of uniform convergence is extended to series of functions, and the book concludes with a number of tests for uniform convergence of series.

畸形

0172-6056 amples and counterexamples to help the reader understand and.This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but studen

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Series, are developed and their influence on the permissibility of reordering the terms of a series is explored. After a discussion of products of series, power series are introduced. The exponential, sine and cosine functions are defined as special cases of power series, and their fundamental properties a

Anticoagulants

Continuity,ogarithm function is introduced as an example of a continuous function and is then used to establish Gauss’s test for convergence of a series of positive terms. The chapter concludes with a study of uniform continuity.

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Differentiability,ctions. The mean value theorem for derivatives is then proved and some applications explored. The ideas of a local maximum and a local minimum of a function are introduced and derivatives used to locate them. Derivatives are then applied to study further properties of the sine and cosine functions a

終端

The Riemann Integral,n is uncovered in the fundamental theorem of calculus. The techniques of integration by substitution and by parts are established, and the latter is used to develop Stirling’s formula for the approximation of the factorial of a positive integer. It is also used to prove the irrationality of the cons