Product Description

Measure theory, integration, weak differentiation of functions, and basic introduction to functional analysis are topics studied by virtually all graduate students in mathematics and applied sciences. Analysis: Foundations and Applications covers the core mathematical topics of the subject, and will particularly attract the reader with a more applied view. The focus of this modern text is to prepare the potential researcher to a way of thinking in applied mathematics and partial differential equations. Topics & Features - clear, user-friendly exposition covers a great deal of territory in a minimal number of pages - sufficient motivation and examples throughout - standalone chapters 1-5 and 7 contain standard material for a two-quarter graduate-level course in analysis - carefully chosen topics, some not touched upon in competing texts; these include fine properties of integrable functions as they arise in applied mathematics and pdes-Radon measures, the Lebesgue Theorem for general Radon measures, the Besicovitch covering Theorem, the Rademacher Theorem; topics in Marcinkiewicz integrals, functions of bounded variation, Legendre transform and the characterization of compact subset of some metric function spaces and in particular of Lp spaces - unique presentation of the Stone-Weierstrass Theorem; its value emphasized as a fact of approximation theory, while identifying the structure of classes of functions that can be approximated by polynomials

Product Details

• Amazon Sales Rank: #2947029 in Books
• Published on: 2002-04-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 512 pages

Synopsis
Measure theory, integration, weak differentiation of functions, and basic introduction to functional analysis are topics studied by virtually all graduate students in mathematics and applied sciences. Analysis: Foundations and Applications covers the core mathematical topics of the subject, and will particularly attract the reader with a more applied view. The focus of this modern text is to prepare the potential researcher to a way of thinking in applied mathematics and partial differential equations.

Topics & Features - clear, user-friendly exposition covers a great deal of territory in a minimal number of pages - sufficient motivation and examples throughout - standalone chapters 1-5 and 7 contain standard material for a two-quarter graduate-level course in analysis - carefully chosen topics, some not touched upon in competing texts; these include fine properties of integrable functions as they arise in applied mathematics and pdes-Radon measures, the Lebesgue Theorem for general Radon measures, the Besicovitch covering Theorem, the Rademacher Theorem; topics in Marcinkiewicz integrals, functions of bounded variation, Legendre transform and the characterization of compact subset of some metric function spaces and in particular of Lp spaces - unique presentation of the Stone-Weierstrass Theorem; its value emphasized as a fact of approximation theory, while identifying the structure of classes of functions that can be approximated by polynomials