Mathematical analysis
著者
書誌事項
Mathematical analysis
（Collana unitext, v. 84-85 . La matematica per il 3+2）
Springer, c2015
2nd ed
- 1 : [pbk.]
- 2 : [pbk.]
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注記
Vol.1: xi, 483 p. ; v. 2: xiii, 550p.
Includes index
内容説明・目次
- 巻冊次
-
2 : [pbk.] ISBN 9783319127569
内容説明
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.
目次
1 Numerical series.- 2 Series of functions and power series.- 3 Fourier series.- 4 Functions between Euclidean spaces.- 5 Differential calculus for scalar functions.- 6 Differential calculus for vector-valued functions.- 7 Applying differential calculus.- 8 Integral calculus in several variables.- 9 Integral calculus on curves and surfaces.- 10 Ordinary differential equations.- 11 A.1 Complements on differential calculus.- 12 A.2 Complements on integral calculus.- 13 Basic definitions and formulas.
- 巻冊次
-
1 : [pbk.] ISBN 9783319127712
内容説明
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 requires the 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.
目次
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.
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