Analysis for Computer Scientists: Foundations, Methods, and Algorithms

✍ Scribed by Michael Oberguggenberger, Alexander Ostermann (auth.)

• Publisher: Springer-Verlag London
• Year: 2011
• Tongue: English
• Leaves: 338
• Series: Undergraduate Topics in Computer Science
• Edition: 1
• Category: Library

✦ Synopsis

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.

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.

✦ Table of Contents

Front Matter....Pages I-X
Numbers....Pages 1-11
Real-Valued Functions....Pages 13-24
Trigonometry....Pages 25-35
Complex Numbers....Pages 37-44
Sequences and Series....Pages 45-62
Limits and Continuity of Functions....Pages 63-72
The Derivative of a Function....Pages 73-93
Applications of the Derivative....Pages 95-110
Fractals and L-Systems....Pages 111-125
Antiderivatives....Pages 127-133
Definite Integrals....Pages 135-147
Taylor Series....Pages 149-157
Numerical Integration....Pages 159-167
Curves....Pages 169-189
Scalar-Valued Functions of Two Variables....Pages 191-210
Vector-Valued Functions of Two Variables....Pages 211-218
Integration of Functions of Two Variables....Pages 219-231
Linear Regression....Pages 233-250
Differential Equations....Pages 251-266
Systems of Differential Equations....Pages 267-285
Numerical Solution of Differential Equations....Pages 287-294
Appendix A: Vector Algebra....Pages 295-305
Appendix B: Matrices....Pages 307-315
Appendix C: Further Results on Continuity....Pages 317-327
Appendix D: Description of the Supplementary Software....Pages 329-330
Back Matter....Pages 331-341

✦ Subjects

Math Applications in Computer Science; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Discrete Mathematics in Computer Science