Postmodern Analysis

• Κύριος συγγραφέας: Jost, Jürgen (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Έκδοση: Third Edition.
• Σειρά: Universitext
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Analysis.; Partial Differential Equations.

What is the title of this book intended to signify, what connotations is the adjective “Postmodern” meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the - proach to analysis presented here from what has by its protagonists been cal...

Πίνακας περιεχομένων:

• Calculus for Functions of One Variable
• Prerequisites
• Limits and Continuity of Functions
• Differentiability
• Characteristic Properties of Differentiable Functions. Differential Equations
• The Banach Fixed Point Theorem. The Concept of Banach Space
• Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
• Integrals and Ordinary Differential Equations
• Topological Concepts
• Metric Spaces: Continuity, Topological Notions, Compact Sets
• Calculus in Euclidean and Banach Spaces
• Differentiation in Banach Spaces
• Differential Calculus in $$\mathbb{R}$$ d
• The Implicit Function Theorem. Applications
• Curves in $$\mathbb{R}$$ d. Systems of ODEs
• The Lebesgue Integral
• Preparations. Semicontinuous Functions
• The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets
• Lebesgue Integrable Functions and Sets
• Null Functions and Null Sets. The Theorem of Fubini
• The Convergence Theorems of Lebesgue Integration Theory
• Measurable Functions and Sets. Jensen’s Inequality. The Theorem of Egorov
• The Transformation Formula
• and Sobolev Spaces
• The Lp-Spaces
• Integration by Parts. Weak Derivatives. Sobolev Spaces
• to the Calculus of Variations and Elliptic Partial Differential Equations
• Hilbert Spaces. Weak Convergence
• Variational Principles and Partial Differential Equations
• Regularity of Weak Solutions
• The Maximum Principle
• The Eigenvalue Problem for the Laplace Operator.