Analysis For Computer Scientists (Foundations, Methods, and Algorithms)

Introduction

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises.

Describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves

Discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations

Presents tools from vector and matrix algebra in the appendices, together with further information on continuity

Includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW)

Contains experiments, exercises, definitions, and propositions throughout the text

Supplies programming examples in Python, in addition to MATLAB (NEW)

Provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material

Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.

Dr. Michael Oberguggenberger is a professor in the Unit of Engineering Mathematics at the University of Innsbruck, Austria. Dr. Alexander Ostermann is a professor in the Department of Mathematics at the University of Innsbruck, Austria.

TABLE OF CONTENTS (21 Chapters)

Front Matter

Pages i-xii

Numbers

Pages 1-12

Real-Valued Functions

Pages 13-25

Trigonometry

Pages 27-37

Complex Numbers

Pages 39-47

Sequences and Series

Pages 49-67

Limits and Continuity of Functions

Pages 69-79

The Derivative of a Function

Pages 81-103

Applications of the Derivative

Pages 105-121

Fractals and L-systems

Pages 123-138

Antiderivatives

Pages 139-147

Definite Integrals

Pages 149-163

Taylor Series

Pages 165-174

Numerical Integration

Pages 175-184

Curves

Pages 185-207

Scalar-Valued Functions of Two Variables

Pages 209-230

Vector-Valued Functions of Two Variables

Pages 231-239

Integration of Functions of Two Variables

Pages 241-254

Linear Regression

Pages 255-273

Differential Equations

Pages 275-295

Systems of Differential Equations

Pages 297-319

Numerical Solution of Differential Equations

Pages 321-329

Back Matter

Pages 331-378

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Bibliographic information

DOI: https://doi.org/10.1007/978-3-319-91155-7

Copyright Information: Springer Nature Switzerland AG 2018

Publisher Name: Springer, Cham

eBook Packages: Computer Science

Print ISBN: 978-3-319-91154-0

Online ISBN: 978-3-319-91155-7

Series Print ISSN: 1863-7310

Series Online ISSN: 2197-1781