Mathematical Analysis I: v. 1

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The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution.

Author(s): Claudio G Canuto, Anita Tabacco
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2008

Language: Italian
Pages: 435
City: Berlin
Tags: Математика;Математический анализ;

Mathematical Analysis I......Page 2
1-Basic notions......Page 12
2-Functions......Page 42
3-Limits and continuity I......Page 75
4-Limits and continuity II......Page 98
5-Local comparison of functions. Numerical sequences and series......Page 131
6-Differential calculus......Page 174
7-Taylor expansions and applications......Page 230
8-Geometry in the plane and in space......Page 263
9-Integral calculus I......Page 305
10-Integral calculus II......Page 360
11-Ordinary differential equations......Page 391
back-matter......Page 426