Mathematical Analysis I

Claudio Canuto, Anita Tabacco (Autoren)

Buch | Softcover

XI, 492 Seiten

2014 | 2nd ed. 2015
Springer International Publishing (Verlag)
978-3-319-12771-2 (ISBN)

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The purpose of the volume is to provide a support for a first course in Mathematics. 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. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requiresthe additional study of the material contained in the appendices, which enable the strongly motivated reader to explore further into the subject. 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. This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics.

Prof. Canuto Tabacco, Dept. of Mathematical Sciences, Politecnico di Torino, Torino, Italy Prof. Anita Tabacco, Dept. of Mathematical Sciences, Politecnico di Torino, Torino, Italy

1 Basic notions.- 2 Functions.- 3 Limits and continuity I.- 4 Limits and continuity II.- 5 Local comparison of functions. Numerical sequences and series.- 6 Differential calculus.- 7 Taylor expansions and applications.- 8 Geometry in the plane and in space.- 9 Integral calculus I.- 10 Integral calculus II.- 11 Ordinary differential equations.- 12 A.1 The Principle of Mathematical Induction.- 13 A.2 Complements on limits and continuity.- 14 A.3 Complements on the global features of continuous maps.- 15 A.4 Complements on differential calculus.- 16 A.5 Complements on integral calculus.- 17 Tables and Formulas.

From the book reviews:

"I enjoyed reading the present textbook. It provides a good coverage of the material, a very good choice of exercises, and an impeccable graphical presentation. The textbook is written for first-year students whose interest is not mainly in mathematics, yet mathematics plays an important role in their curricula. The authors attained their goal." (George Stoica, zbMATH, Vol. 1305, 2015)

Erscheint lt. Verlag	31.10.2014
Reihe/Serie	La Matematica per il 3+2
Reihe/Serie	UNITEXT
Zusatzinfo	XI, 492 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Differential Equations • Integral calculus • Limits and continuity • One variable differential calculus • Ordinary differential equations • Partial differential equations • PDE
ISBN-10	3-319-12771-3 / 3319127713
ISBN-13	978-3-319-12771-2 / 9783319127712
Zustand	Neuware