Foundations, Methods, and Algorithms
von Oberguggenberger, Michael;Ostermann, Alexander
XII, 378 Seiten; 23.5 cm x 15.5 cm
2018 Springer International Publishing
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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.
Kurztext / Annotation
This textbook presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. It makes thorough use of examples and explanations using MATLAB, Maple and Java applets.
Mathematics and mathematical modelling are of central importance in computer science, and therefore it is vital that computer scientists are aware of the latest concepts and techniques.
This concise and easy-to-read textbook/reference presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations.
Topics and features: thoroughly describes the essential concepts of analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives and antiderivatives, definite integrals and double integrals, and curves; provides summaries and exercises in each chapter, as well as computer experiments; 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 definitions, propositions and examples throughout the text, together with a list of relevant textbooks and references for further reading; supplementary software can be downloaded from the book?s webpage at www.springer.com.
This textbook is essential for undergraduate students in Computer Science. Written to specifically address the needs of computer scientists and researchers, it will also serve professionals looking to bolster their knowledge in such fundamentals extremely well.
Sequences and Series
Limits and Continuity of Functions
The Derivative of a Function
Applications of the Derivative
Fractals and L-Systems
Scalar-Valued Functions of Two Variables
Vector-Valued Functions of Two Variables
Integration of Functions of Two Variables
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
Biografische Anmerkung zu den Verfassern
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.