Mathematical Analysis I

✍ Scribed by Claudio G Canuto, Anita Tabacco

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 435
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Mathematical Analysis I......Page p0002.djvu
1-Basic notions......Page p0012.djvu
2-Functions......Page p0042.djvu
3-Limits and continuity I......Page p0075.djvu
4-Limits and continuity II......Page p0098.djvu
5-Local comparison of functions. Numerical sequences and series......Page p0131.djvu
6-Differential calculus......Page p0174.djvu
7-Taylor expansions and applications......Page p0230.djvu
8-Geometry in the plane and in space......Page p0263.djvu
9-Integral calculus I......Page p0305.djvu
10-Integral calculus II......Page p0360.djvu
11-Ordinary differential equations......Page p0391.djvu
back-matter......Page p0426.djvu