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This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. 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. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH.

Analytic functions. --- Electronic books. -- local. --- Functions of several complex variables. --- Mathematical analysis. --- Mathematical analysis --- Engineering & Applied Sciences --- Applied Mathematics --- Complex variables --- Several complex variables, Functions of --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- 517.1 Mathematical analysis --- Mathematics. --- Analysis (Mathematics). --- Measure theory. --- Differential equations. --- Functions of complex variables. --- Calculus of variations. --- Analysis. --- Measure and Integration. --- Calculus of Variations and Optimal Control; Optimization. --- Several Complex Variables and Analytic Spaces. --- Ordinary Differential Equations. --- Functions of complex variables --- Series, Taylor's --- Global analysis (Mathematics). --- Mathematical optimization. --- Differential equations, partial. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Variables (Mathematics) --- Mathematical constants --- Mathematics --- Elliptic functions --- Functions of real variables --- Isoperimetrical problems --- Variations, Calculus of --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)