An Introduction to Nonlinear Analysis (Cambridge Studies in Advanced Mathematics, Series Number 95)

Main subject categories: • Nonlinear analysisThe techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. 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. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study. The Techniques That Can Be Used To Solve Non-linear Problems Are Far Different Than Those That Are Used To Solve Linear Problems. 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. An Understanding Of The Tools For Solving Non-linear Problems Is Developed Whilst Demonstrating Their Application To Problems In One Dimension And Then Leading To Higher Dimensions. The Reader Is Guided Using Simple Exposition And Proof, Assuming A Minimal Set Of Pre-requisites. For Completion, A Set Of Appendices Covering Essential Basics In Functional Analysis And Metric Spaces Is Included, Making This Ideal As An Accompanying Text On An Upper-undergraduate Or Graduate Course, Or Even For Self-study. Martin Schechter. Includes Bibliographical References (p. 353-354) And Index. Professor Martin 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 developed while demonstrating their application to problems first in one dimension, and then in higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of prerequisites. To complete, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as a text for an upper-undergraduate or graduate course, or even for self-study.

This work is a substantial contribution to the history of philosophy. Its subject, the ninth-century philosopher John Scottus Eriugena, developed a form of idealism that owed as much to the Greek Neoplatonic tradition as to the Latin fathers and anticipated the priority of the subject in its modern, most radical statement: German idealism. Moran has written the most comprehensive study yet of Eriugena's philosophy, tracing the sources of his thinking and analyzing his most important text, the Periphyseon. This volume will be of special interest to historians of mediaeval philosophy, history, and theology.

Contents......Page 8 Preface......Page 14 Extrema......Page 20 Critical points......Page 64 Boundary value problems......Page 106 Saddle points......Page 142 Calculus of variations......Page 164 Degree theory......Page 190 Conditional extrema......Page 226 Mini-max methods......Page 256 Jumping nonlinearities......Page 264 Higher dimensions......Page 272 Appendix A Concepts from functional analysis......Page 332 Appendix B Measure and integration......Page 350 Appendix C Metric spaces......Page 360 Appendix D Pseudo-gradients......Page 364 Bibliography......Page 372 Index......Page 374 The techniques used to solve nonlinear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems and principles from first principles, this textbook gives upper undergraduates and graduate students a thorough understanding using as little background material as possible. The techniques used to solve non-linear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems from first principles, this 2005 textbook should give upper undergraduates and graduate students a thorough understanding using as little background material as possible. Schechter's book deploys nonlinear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application Eriugena, an early mediaeval author, wrote during a period of cultural instability when much of the wealth of Greek philosophy had been lost or forgotten. One of the most powerful tools in dealing with nonlinear problems is critical point theory.