Autorentext

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.

Klappentext

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.

Inhalt

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