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Mathematical Analysis: Linear and Metric Structures and Continuity,New
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One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system. We have already discussed real functions of one real variable and a few examples of functions of several variables but there are many more examples of functions that the real world, physics, natural and social sciences, and mathematics have to offer: (a) not only do we associate numbers and points to points, but we as ciate numbers or vectors to vectors, (b) in the calculus of variations and in mechanics one associates an ergy or action to each curve y(t) connecting two points (a, y(a)) and (b,y(b)): b Lea ~(y) / 9 F(t, y(t), y' (t))dt t. J a in terms of the socalled Lagrangian F(t, y, p), (c) in the theory of integral equations one maps a function into a new function b /1, dr / o. J a by means of a kernel K(s, T), (d) in the theory of differential equations one considers transformations of a function x(t) into the new function t t f f( a where f(s, y) is given. 1 in M. Giaquinta, G. Modica, Mathematical Analysis. Functions of One Va able, Birkh~user, Boston, 2003, which we shall refer to as [GM1] and in M. G quinta, G. Modica, Mathematical Analysis. Approximation and Discrete Processes, Birkhs Boston, 2004, which we shall refer to as [GM2].
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- Q: What is the main focus of 'Mathematical Analysis: Linear and Metric Structures and Continuity'? A: The book primarily focuses on the notion of functions in mathematical analysis, exploring relationships among variable quantities and transformations within various mathematical contexts.
- Q: Who is the author of this book? A: The author of 'Mathematical Analysis: Linear and Metric Structures and Continuity' is Mariano Giaquinta.
- Q: What is the publication date of this book? A: This book was published on September 4, 2007.
- Q: What is the condition of the book? A: The book is listed as 'New' in condition.
- Q: How many pages does this book have? A: The book contains a total of 486 pages.
- Q: What is the binding type of this book? A: The book is available in paperback binding.
- Q: What academic category does this book fall under? A: This book falls under the category of Differential Equations.
- Q: What is the edition of this book? A: The edition of this book is from the year 2007.
- Q: Is this book suitable for beginners in mathematical analysis? A: While the book covers foundational concepts, it is primarily aimed at readers with some prior knowledge of mathematical analysis.
- Q: Does this book include examples of functions in real-world applications? A: Yes, the book discusses various examples of functions used in real-world scenarios across physics, natural sciences, and social sciences.