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.

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.

Zusammenfassung

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.