Mathematical Analysis

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.

The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.

Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.

• analysis
• differential calculus
• integral calculus
• ordinary differential equations

From the reviews:

"This is a comprehensive introduction to the study of functions of several variables that includes several areas not commonly included in comparable textbooks. … The Current book has a generally broader scope … . There is a huge amount of mathematics here, presented carefully and with style. … The treatment of holomorphic functions here is nicely done … . In the end, I find that this text would be an agreeable source for most of its individual topics … ." (William J. Satzer, The Mathematical Association of America, August, 2009)

“This is a classical textbook on functions of several variables. On 348 pages it covers the content of a graduate course of mathematical analysis devoted to the higher dimensional spaces. … The textbook is suitable for students of mathematics, physics, engineering and technology, as well as for researchers.” (Vladimír Janiš, Zentralblatt MATH, Vol. 1177, 2010)

“This is a part of an ampler project of the authors … . The applications and the examples included in the book make it more attractive. There are also exercises at the end of each chapter. … will supply the reader with a fairly complete account of the fundamental results in mathematical analysis and applications, including Lebesgue integration in Rⁿ and complex analysis of one variable. … can be used for courses in real or complex analysis and their applications.” (Tiberiu Trif, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)

“This is a textbook on analysis of functions of several real variables and of functions of one complex variable. … The book is concise and nicely written and may well serve as source for (graduate) courses in the areas covered as well as a textbook for students and as a reference book for the working mathematician.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 165 (3-4), March, 2012)

• Scuola Normale Superiore, Pisa, Italy

  Mariano Giaquinta

• Dipartimento di Matematica Applicata, Università di Firenze, Firenze, Italy

  Giuseppe Modica