# Analysis for Computer Scientists: Foundations, Methods, and Algorithms

Springer Science & Business Media, Mar 19, 2011 - Computers - 342 pages

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.

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### Contents

 Numbers 1 RealValued Functions 13 Trigonometry 25 Complex Numbers 36 Sequences and Series 45 Limits and Continuity of Functions 63 The Derivative of a Function 73 Applications of the Derivative 95
 ScalarValued Functions of Two Variables 191 VectorValued Functions of Two Variables 211 Integration of Functions of Two Variables 219 Linear Regression 232 Differential Equations 251 Systems of Differential Equations 267 Numerical Solution of Differential Equations 287 Appendix A Vector Algebra 295

 Fractals and LSystems 111 Antiderivatives 126 Definite Integrals 135 Taylor Series 148 Numerical Integration 159 Curves 168
 Appendix B Matrices 306 Appendix C Further Results on Continuity 317 Appendix D Description of the Supplementary Software 328 References 331 Index 333 Copyright