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Mathematical analysis and the mathem...

Romisch, Werner.

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Mathematical analysis and the mathematics of computation

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical analysis and the mathematics of computation/ by Werner Romisch, Thomas Zeugmann.
Author:	Romisch, Werner.
other author:	Zeugmann, Thomas.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xxiii, 703 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Sets, Structures, Numbers -- Metric Spaces -- Continuous Functions in Metric Spaces -- Linear Normed Spaces, Linear Operators -- The Differential Calculus -- Applications of the Differential Calculus -- The Integral Calculus -- Linear Integral Operators -- Inner Product Spaces -- Approximative Representation of Functions -- Ordinary Differential Equations -- Discretization of Operator Equations -- Numerical Solution of Ordinary Differential Equations.
Contained By:	Springer eBooks
Subject:	Mathematical analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-42755-3
ISBN:	9783319427553

Mathematical analysis and the mathematics of computation
Romisch, Werner.

Mathematical analysis and the mathematics of computation[electronic resource] /by Werner Romisch, Thomas Zeugmann. - Cham :Springer International Publishing :2016. - xxiii, 703 p. :ill. (some col.), digital ;24 cm.

Sets, Structures, Numbers -- Metric Spaces -- Continuous Functions in Metric Spaces -- Linear Normed Spaces, Linear Operators -- The Differential Calculus -- Applications of the Differential Calculus -- The Integral Calculus -- Linear Integral Operators -- Inner Product Spaces -- Approximative Representation of Functions -- Ordinary Differential Equations -- Discretization of Operator Equations -- Numerical Solution of Ordinary Differential Equations.

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

ISBN: 9783319427553

Standard No.: 10.1007/978-3-319-42755-3doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Mathematical analysis and the mathematics of computation
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100 1 $a Romisch, Werner. $3 3166402
245 1 0 $a Mathematical analysis and the mathematics of computation $h [electronic resource] / $c by Werner Romisch, Thomas Zeugmann.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xxiii, 703 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Sets, Structures, Numbers -- Metric Spaces -- Continuous Functions in Metric Spaces -- Linear Normed Spaces, Linear Operators -- The Differential Calculus -- Applications of the Differential Calculus -- The Integral Calculus -- Linear Integral Operators -- Inner Product Spaces -- Approximative Representation of Functions -- Ordinary Differential Equations -- Discretization of Operator Equations -- Numerical Solution of Ordinary Differential Equations.
520 $a This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.
650 0 $a Mathematical analysis. $3 516833
650 0 $a Computer science $x Mathematics. $3 532725
650 1 4 $a Computer Science. $3 626642
650 2 4 $a Mathematics of Computing. $3 891213
650 2 4 $a Analysis. $3 891106
700 1 $a Zeugmann, Thomas. $3 1071937
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-42755-3
950 $a Computer Science (Springer-11645)