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# ðŸ“™ Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables by Mariano Giaquinta, Giuseppe Modica (auth.) â€” epub download

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*Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables* builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.

The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory â€“ Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.

This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.

- Author:
**Mariano Giaquinta, Giuseppe Modica (auth.)** - Year:
**2012** - Publisher:
**BirkhÃ¤user Basel** - Language:
**English** - ISBN:
**9780817683092,0817683097**

- File size:
**4 534 315** - Format:
**pdf**

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Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volum...

Having successfully replaced elements used in traditional, pollution-prone, energy-consuming separation processes, nanoporous materials play an important role in chemical processing. Although their unique structural or surface physicochemical properties c...

Mathematical and Computer Programming Techniques for Computer Graphics introduces the mathematics and related computer programming techniques used in Computer Graphics. Starting with the underlying mathematical ideas, it gradually leads the reader to a su...

This is the first book to focus on the use of nonlinear analysis and synthesis techniques for aircraft control. It is also the first book to address in detail closed-loop control problems for aircraft "on-ground" â€“ i.e. speed and directional control of ...

If you love Essbase and hate seeing it misused, then this is the book for you. Written by 12 Essbase professionals that are either acknowledged Essbase gurus or certified Oracle ACEs, Developing Essbase Applications: Advanced Techniques for Finance and IT...

This in-depth, detailed reference presents for the first time a comprehensive treatment of recent advances in optical performance monitoring. Written by leading experts in the field, the book provides an overview of recent developments in the area and the...

The increased efficiency and quality constraints imposed on electrical energy systems have inspired a renewed research interest in the study of formal approaches to the analysis and control of power electronics converters. Switched systems represent a use...

It is unlikely that any frontier of economics/econometrics is being pushed faster, further than that of computational techniques. The computer has become a tool for performing as well as an environment in which to perform economics and econometrics, takin...

This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Di...