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Analysis for Computer Scientists (2nd Edition)

Foundations, Methods, and Algorithms

Author(s):
Publisher:

Springer

Pages: 378
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AVAILABLE FORMATS

Paperback - 9783319911540

06 November 2018

$54.99

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Ebook - 9783319911557

24 October 2018

$39.99

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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....

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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.

Topics and features: 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.

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Presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis  

Makes thorough use of examples and explanations using MATLAB, Maple, and Java applets 

Describes mathematical theory alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises  

Numbers
Real-Valued Functions
Trigonometry
Complex Numbers
Sequences and Series
Limits and Continuity of Functions
The Derivative of a Function
Applications of the Derivative
Fractals and L-Systems
Antiderivatives
Definite Integrals
Taylor Series
Numerical Integration
Curves
Scalar-Valued Functions of Two Variables
Vector-Valued Functions of Two Variables
Integration of Functions of Two Variables
Linear Regression
Differential Equations
Systems of Differential Equations
Numerical Solution of Differential Equations
Appendix A: Vector Algebra
Appendix B: Matrices
Appendix C: Further Results on Continuity
Appendix D: Description of the Supplementary Software.

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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.

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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.

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