Applied functional analysis

Description

This is the first part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schrodinger approach and the Feynman approach to quantum physics, and quantum statistics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus.

First Sentence

In a Banach space, the so-called norm ||u|| = nonnegative number is assigned to each element u.

Excerpt

In a Banach space, the so-called norm ||u|| = nonnegative number is assigned to each element u.

Description

This is the second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws (the Noether theorem), the quark model, and gauge theory in elementary particle physics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus.

Subjects

Series Statement

• Applied mathematical sciences ;

Other Editions

• Applied functional analysis: main principles and their applicationsSpringer-Verlag1995-01-01
• Applied functional analysisSpringer-Verlag1995-01-01
• Applied Functional AnalysisSpringer1999-08-13
• Applied Functional AnalysispaperbackSpringer2012-09-28