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Other titles in the Undergraduate Topics in Computer Science series:
Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science)by Michael Oberguggenberger
Synopses & ReviewsPublisher Comments: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 easytoread 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 curvesProvides summaries and exercises in each chapter, as well as computer experimentsDiscusses important applications and advanced topics, such as fractals and Lsystems, numerical integration, linear regression, and differential equationsPresents tools from vector and matrix algebra in the appendices, together with further information on continuityIncludes definitions, propositions and examples throughout the text, together with a list of relevant textbooks and references for further readingSupplementary software can be downloaded from the book's webpage at www.springer.comThis 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. Dr. Michael Oberguggenberger is a professor in the Department of Civil Engineering Sciences at the University of Innsbruck, Austria. Dr. Alexander Ostermann is a professor in the Department of Mathematics at the University of Innsbruck, Austria.
Synopsis: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.
Synopsis:This textbook 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. Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book's webpage.
About the AuthorDr. Michael Oberguggenberger is a professor in the Department of Civil Engineering Sciences 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 ContentsNumbers RealValued Functions Trigonometry Complex Numbers Sequences and Series Limits and Continuity of Functions The Derivative of a Function Applications of the Derivative Fractals and LSystems Antiderivatives Definite Integrals Taylor Series Numerical Integration Curves ScalarValued Functions of Two Variables VectorValued Functions of Two Variables Integration of Functions of Two Variables Linear Regression Differential Equations Systems of Differential Equations Numerical Solution of Differential Equations
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