Mathematical Analysis II

✍ Scribed by Claudio Canuto, Anita Tabacco

• Publisher: Springer
• Year: 2015
• Tongue: English
• Leaves: 563
• Series: UNITEXT 85
• Edition: 2ed.
• Category: Library

✦ Synopsis

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the corresponding key techniques and find the proofs of the main results. The second level enables the strongly motivated reader to explore further into the subject, by studying also the material contained in the appendices. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis

✦ Table of Contents

Front Matter....Pages I-XIII
Numerical series....Pages 1-32
Series of functions and power series....Pages 33-74
Fourier series....Pages 75-109
Functions between Euclidean spaces....Pages 111-154
Differential calculus for scalar functions....Pages 155-200
Differential calculus for vector-valued functions....Pages 201-259
Applying differential calculus....Pages 261-296
Integral calculus in several variables....Pages 297-365
Integral calculus on curves and surfaces....Pages 367-420
Ordinary differential equations....Pages 421-507
Back Matter....Pages 509-559