Mathematical Analysis II

1. Front Matter

   Pages I-XIII

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2. Numerical series

   • Claudio Canuto, Anita Tabacco

   Pages 1-32

3. Series of functions and power series

   • Claudio Canuto, Anita Tabacco

   Pages 33-74

4. Fourier series

   • Claudio Canuto, Anita Tabacco

   Pages 75-109

5. Functions between Euclidean spaces

   • Claudio Canuto, Anita Tabacco

   Pages 111-154

6. Differential calculus for scalar functions

   • Claudio Canuto, Anita Tabacco

   Pages 155-200

7. Differential calculus for vector-valued functions

   • Claudio Canuto, Anita Tabacco

   Pages 201-259

8. Applying differential calculus

   • Claudio Canuto, Anita Tabacco

   Pages 261-296

9. Integral calculus in several variables

   • Claudio Canuto, Anita Tabacco

   Pages 297-365

10. Integral calculus on curves and surfaces

    • Claudio Canuto, Anita Tabacco

    Pages 367-420

11. Ordinary differential equations

    • Claudio Canuto, Anita Tabacco

    Pages 421-507

12. Back Matter

    Pages 509-559

    PDF

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 graspthe 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.

• Differential equations
• Integrals over curves and surfaces
• Multi-dimensional differential calculus
• Multiple integrals
• Sequences and Series of functions
• partial differential equations

From the book reviews:

“This is the second part of a textbook written for students whose interest is not mainly in mathematics, yet mathematics plays an important role in their curricula. Second-year students will benefit from this very well written textbook with appropriate examples and good material presentation.” (George Stoica, zbMATH, Vol. 1305, 2015)

• Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy

  Claudio Canuto, Anita Tabacco

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

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

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