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Mathematical Analysis and the Mathem...
~
Römisch, Werner.
Mathematical Analysis and the Mathematics of Computation
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Mathematical Analysis and the Mathematics of Computation/ by Werner Römisch, Thomas Zeugmann.
作者:
Römisch, Werner.
其他作者:
Zeugmann, Thomas.
面頁冊數:
XXIII, 703 p. 52 illus., 32 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Computer science—Mathematics. -
電子資源:
https://doi.org/10.1007/978-3-319-42755-3
ISBN:
9783319427553
Mathematical Analysis and the Mathematics of Computation
Römisch, Werner.
Mathematical Analysis and the Mathematics of Computation
[electronic resource] /by Werner Römisch, Thomas Zeugmann. - 1st ed. 2016. - XXIII, 703 p. 52 illus., 32 illus. in color.online resource.
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:
1253519
Computer science—Mathematics.
LC Class. No.: QA76.9.M35
Dewey Class. No.: 004.0151
Mathematical Analysis and the Mathematics of Computation
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