Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science 2nd ed. 2018)

Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science 2nd ed. 2018)

By: Michael Oberguggenberger (author), Alexander Ostermann (author)Paperback

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Description

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.

About Author

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.

Contents

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

Product Details

  • ISBN13: 9783319911540
  • Format: Paperback
  • Number Of Pages: 378
  • ID: 9783319911540
  • weight: 599
  • ISBN10: 3319911546
  • edition: 2nd ed. 2018

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