Mathematical Analysis II

1. Front Matter

   Pages I-X

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2. Numerical series

   Pages 1-32

3. Series of functions and power series

   Pages 33-73

4. Fourier series

   Pages 75-109

5. Functions between Euclidean spaces

   Pages 111-154

6. Differential calculus for scalar functions

   Pages 155-200

7. Differential calculus for vector-valued functions

   Pages 201-259

8. Applying differential calculus

   Pages 261-296

9. Integral calculus in several variables

   Pages 297-364

10. Integral calculus on curves and surfaces

    Pages 365-418

11. Ordinary differential equations

    Pages 419-505

12. Back Matter

    Pages 507-523

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The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined.

• Differential Equations
• Fourier series
• Functional Analysis
• calculus
• differential equation
• equation
• function
• ordinary differential equation
• proof
• variable
• ordinary differential equations
• partial differential equations

From the reviews:

“This text provides a … thorough coverage of the usual material of a second-year calculus course. … The book is very readable. Each chapter begins with definitions and examples, and closes with a fairly extensive set of exercises, and answers to the exercises, sometimes with a sketch of how the answer is found, are given immediately following each set of exercises. … The book looks like a good candidate for a textbook upon which to base a second course in calculus.” (Gerald A. Heuer, Zentralblatt MATH, Vol. 1200, 2011)

• Dipartimento di Matematica, Politecnico di Torino, Italy

  Claudio Canuto, Anita Tabacco

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