Counterexamples on Uniform Convergence: Sequences, Series, by Andrei Bourchtein,Ludmila Bourchtein

By Andrei Bourchtein,Ludmila Bourchtein


A accomplished and thorough research of recommendations and effects on uniform convergence

Counterexamples on Uniform Convergence: Sequences, sequence, capabilities, and Integrals presents counterexamples to fake statements more often than not came across in the learn of mathematical research and calculus, all of that are regarding uniform convergence. The ebook comprises the convergence of sequences, sequence and households of capabilities, and correct and flawed integrals reckoning on a parameter. The exposition is specific to the most definitions and theorems that allows you to discover assorted models (wrong and proper) of the elemental ideas and results.

The aim of the ebook is threefold. First, the authors offer a quick survey and dialogue of central result of the speculation of uniform convergence in actual research. moment, the ebook goals to assist readers grasp the provided recommendations and theorems, that are typically hard and are resources of bewilderment and confusion. eventually, this publication illustrates how very important mathematical instruments resembling counterexamples can be utilized in numerous situations.

The positive factors of the ebook include:

• an outline of significant strategies and theorems on uniform convergence

• Well-organized assurance of nearly all of the subjects on uniform convergence studied in research courses

• An unique method of the research of vital effects on uniform convergence in line with counterexamples

• extra workouts at various degrees of complexity for every subject lined within the book

• A supplementary Instructor’s suggestions guide containing whole recommendations to all workouts, that is on hand through a spouse website

Counterexamples on Uniform Convergence: Sequences, sequence, capabilities, and Integrals is a suitable reference and/or supplementary examining for upper-undergraduate and graduate-level classes in mathematical research and complex calculus for college kids majoring in arithmetic, engineering, and different sciences. The e-book can be a important source for teachers educating mathematical research and calculus.

ANDREI BOURCHTEIN, PhD, is Professor within the division of arithmetic at Pelotas kingdom college in Brazil. the writer of greater than a hundred referred articles and 5 books, his study pursuits contain numerical research, computational fluid dynamics, numerical climate prediction, and genuine research. Dr. Andrei Bourchtein acquired his PhD in arithmetic and Physics from the Hydrometeorological heart of Russia.

LUDMILA BOURCHTEIN, PhD, is Senior learn Scientist on the Institute of Physics and arithmetic at Pelotas nation college in Brazil. the writer of greater than eighty referred articles and 3 books, her examine pursuits comprise genuine and intricate research, conformal mappings, and numerical research. Dr. Ludmila Bourchtein obtained her PhD in arithmetic from Saint Petersburg kingdom collage in Russia.

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