An Introduction to Nonlinear Analysis: Theory
- © 2003
- Zdzisław Denkowski 0 ,
- Stanisław Migórski 1 ,
- Nikolas S. Papageorgiou 2
Faculty of Mathematics, Physics and Computer Science Institute of Computer Science, Jagiellonian University, Cracow, Poland
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Department of Mathematics, National Technical University, Athens, Greece
- Covers some important aspects of the subject and emphasizes some parts not included in the classical treatment of nonlinear analysis
- Uses results and techniques from different areas of analysis
- Self-contained and accessible to the newcomer
- Presents foundations, theory and a background for studying the applications on Nonlinear Analysis
- Includes exercises and solutions at the end of each chapter
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Table of contents (5 chapters)
Front matter, elements of topology.
- Zdzisław Denkowski, Stanisław Migórski, Nikolas S. Papageorgiou
Elements of Measure Theory
Banach spaces, set-valued analysis, nonsmooth analysis, back matter.
- Banach Space
- differential equation
- functional analysis
About this book
Authors and affiliations.
Zdzisław Denkowski, Stanisław Migórski
Nikolas S. Papageorgiou
Bibliographic Information
Book Title : An Introduction to Nonlinear Analysis: Theory
Authors : Zdzisław Denkowski, Stanisław Migórski, Nikolas S. Papageorgiou
DOI : https://doi.org/10.1007/978-1-4419-9158-4
Publisher : Springer New York, NY
eBook Packages : Springer Book Archive
Copyright Information : Springer Science+Business Media New York 2003
Hardcover ISBN : 978-0-306-47392-0 Published: 31 January 2003
Softcover ISBN : 978-1-4613-4814-6 Published: 24 November 2013
eBook ISBN : 978-1-4419-9158-4 Published: 01 December 2013
Edition Number : 1
Number of Pages : XVI, 690
Topics : Analysis , Calculus of Variations and Optimal Control; Optimization , Geometry , Mathematical Modeling and Industrial Mathematics , Applications of Mathematics
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Browse Course Material
Course info.
- Klaus-Jürgen Bathe
Departments
- Mechanical Engineering
As Taught In
- Solid Mechanics
- Computational Modeling and Simulation
- Numerical Simulation
Learning Resource Types
Finite element procedures for solids and structures, lecture 1: introduction to nonlinear analysis.
Topics: Introduction to nonlinear analysis
- Introduction to the course
- The importance of nonlinear analysis
- Four illustrative films depicting actual and potential nonlinear analysis applications
- General recommendations for nonlinear analysis
- Modeling of problems
- Classification of nonlinear analyses
- Example analysis of a bracket, small and large deformations, elasto-plastic response
- elasto-plastic large deformation response of a plate with a hole
- large displacement response of a diamond-shaped frame
- The basic approach of an incremental solution
- Time as a variable in static and dynamic solutions
- The basic incremental/iterative equations
- A demonstrative static and dynamic nonlinear analysis of a shell
Instructor: Klaus-Jürgen Bathe
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- Download transcript
Study Guide ( PDF )
Section 6.1
Problems 6.1-6.4
Ishizaki, T., and K. J. Bathe. “ On Finite Element Large Displacement and Elastic-Plastic Dynamic Analysis of Shell Structures. ” Computers & Structures 12 (September 1980): 309-318.
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Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered throughout the literature from the methodology point of view, and presents them in a systematic way.
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and …. View full aims & scope.
Nonlinear analysis in engineering mechanics can be an art. Nonlinear analysis can be a frustration. It always is a great challenge. Transparency. 1-2. Some important engineering phenomena can only be assessed on the basis of a nonlinear analysis: Collapse or buckling of structures due to sudden overloads.
Dušan D. Repovš. Introduces the basic methods used in the qualitative mathematical analysis of nonlinear models. Reveals a number of surprising interactions between several fields of mathematics, including topology, functional analysis, mathematical physics, and potential theory.
About this book. An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field.
Professor Schechter’s book is devoted to nonlinear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving nonlinear problems is devel-oped while demonstrating their application to problems first in one di-mension, and then in higher dimensions.
Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques.
Topics: Introduction to nonlinear analysis. Introduction to the course; The importance of nonlinear analysis; Four illustrative films depicting actual and potential nonlinear analysis applications; General recommendations for nonlinear analysis; Modeling of problems; Classification of nonlinear analyses