Book Description
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.
This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
Customer Reviews:
Very Good.......2007-05-09
This book is a classic. It is probably the best reference book although it is tough to read from the beginning untill the end. The style is heavy and you need strong mathematical background to understand it.
Anyway, if you need a result on convex functions or convex analysis it is very likely that you will find it in ths book.
the only thing it lacks is diagrams.......2007-01-12
This book perhaps ranks with Halmos' "Finite Dimensional Vector Spaces" as an unusually clear description of its subject. Rockafellar's book has been through numerous printings in 40 years. The theorem proofs can be intricate. But the thread of logical development makes reading it worthwhile. Certainly, it is beautiful how the crucial assumption of convexity makes all the derivations possible.
The level of discussion is suitable for a 3rd year undergrad [or higher], who is majoring in maths.
By current standards of maths texts, it does lack diagrams. In fact, there doesn't seem to be a single one! Something to get used to, if you are a current undergrad weaned on recent texts. [Since the author is still alive, perhaps he might consider adding diagrams to a future edition.]
a beauty mummified .......2005-12-02
convex programming is a beautiful topic which admits amazing geometric interpretation.
books like this manage to destroy one's appreciation of the topic by not providing even one (gasp!) figure. damn Bourbaki style.
Excellent introduction to Topology........2001-05-10
This is a good book for the first year in PhD studies. I recommend amply this book, it's very clear in the explanation, if you have any doubts about topology, Rockafellar explained in this book very simple the theory and all you need about Topology.
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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)
V.L. Kocic , and
G. Ladas
Manufacturer: Springer
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ASIN: 079232286X |
Book Description
This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the very frontiers of the subject, important open problems are also formulated.
The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices.
For graduate students and researchers whose work involves difference and differential equations.
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Nonlinearity & Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis (Pure and Applied Mathematics, a Series of Monographs and Tex)
Melvyn S. Berger
Manufacturer: Academic Press
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ASIN: 0120903504 |
Book Description
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.
Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember.
The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology.
Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.
Customer Reviews:
A geometric approach to differential forms.......2007-06-27
Easy to read, but not too deep in theory or algebraic properties of differntial forms. Interesting for many exercices to solve ( with solutions !) Useful to grasp an intuitive approach to the concept, but if you are seeking a thoroughtly book on the subject this is not the book.
A Very Accessable Intro to Forms.......2007-03-11
I highly recommend this text for anyone looking for a "gentle" introduction to forms and manifolds.
When learning a topic, I believe that it is important to develop both computational proficiency and a deep conceptual understanding. I have come to understand that manipulating symbols is not sufficient and that whenever possible, understanding the underlying geometry is critical.
For whatever reason, I struggled to understand forms from other sources. (Maybe I was too focused on the algebra of the wedge product.) However, Bachmann's exposition was easy to follow and very insightful. It was a revelation that all integrands are not differential forms. Also, I had read elsewhere that forms are a basis for the tangent space of a manifold. I could say the words but they contained little meaning for me. Within the first couple of days with Bachmannn's book, this as well as some other basic ideas became crystal clear. I particularly liked that he at times presents more than one geometric interpretation of an concept.
Anyone who has already seen some vector calculus and now wants a very quick introduction to forms with a minimum time investment can benefit greatly from this text. In total, I spent about a month reading, A Geometric Approach to Differential Forms and I am now confident that I am ready to tackle more advanced texts on the topic.
A word of caution, in the book's Preface, it is suggested that there are three possible tracks one can take with this text. In addition to an upper division track that focuses on forms and manifolds, one is a vector calculus track and another is a multi-variable calculus track. In either of the latter two cases, if that is your main interest, I would recommend a text like Marsden's Vector Calculus. It encompasses a broader base of material and it is also very well written.
Book Description
This introductory text offers simple presentations of the fundamentals of nonlinear analysis, with direct proofs and clear applications. Its full treatment ranges from smooth to nonsmooth functions, from convex to nonconvex variational problems, and from economics to mechanics. 1984 edition.
Customer Reviews:
basically a notebook.......2007-08-27
Unfortunately, this book was not worth purchasing. I purchased this book hoping for an engineers look at nonlinear analysis. The three major flaws:
1) It has virtually no prose in it. It is page after page of theorems.
2) The math notation used is not explained, so unless you are a mathematics PhD student or above I don't think you will be able to follow this book.
3) All the nonlinear analysis is focused on optimization.
I wish there had been some reviews of this book before I purchased it.
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Nonlinear Functional Analysis
Klaus Deimling
Manufacturer: Springer-Verlag
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Nonlinear Analysis (Series in Mathematical Analysis and Applications)
Leszek Gasinski , and
Nikolaos S. Papageorgiou
Manufacturer: Chapman & Hall/CRC
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ASIN: 1584884843 |
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Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.
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Semi-Linear Hyperbolic Problems in Bounded Domains (Mathematical Reports, Vol 3, Pt 1)
A. Haraux
Manufacturer: Routledge
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ASIN: 3718604604 |
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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.
Book Description
From Robert James Waller comes a wonderful collection of 19 essays--all of them as romantic, reflective, and timeless as readers have come to expect from the author of The Bridges of Madison County--a celebration of life and loss, of what things still can be.
Customer Reviews:
I love this book.......2006-12-01
Since this is a group of essays, it is easy to pick up and read any particular portion at will. I've read "...Rachael's room" several times, cry every time, and it makes me give thanks AND say a prayer for our own son. Love the flow. Each story is unique, and living. I've given a number of these books as gifts, and will again. I'm glad Mr. Waller shared these stories with us.
Robert James Waller - A Mentor for Writers.......2006-10-25
I found "Old Songs in a New Cafe" to be the choice selection of Waller's essays, although "One Good Road Is Enough" and "Just Beyond The Firelight" contain excellent essays as well. Waller is a master of dressing emotions in words and for me a new experience. After finding this author, I read his fiction as well. I don't care for some of the subject matter of the fiction but was intrigued with the sensitive prose. Behind it all is a seeker who has "been circling a thousand years and still does not know whether he is a Falcon, or a storm, or a great song." Waller sets me on a high plains afternoon remembering the flowers and the wind, dancing through the late autumn dust remembering those who were free.
Trish New, author of The Thrill of Hope, Concepts to Ponder and South State Street Journal, Secrets of The Heart.
Wonderful Read.......2004-03-06
I enjoyed reading this biography of writings by Robert James Waller. I, too, felt he was very similar to Robert Fulghum in his approach to life; a reverence for all that is simple and beautiful in this world. After reading only his fictional works, I gained a deep appreciation of the author himself and am refreshed that someone with a PhD in business can have a soul.
What an amazing biography!.......2002-03-13
Reads a tremendous lot like Robert Fulghum, but beyond that...
Through essays, the presumably all true story of a man who lived as if he was born with a detailed, incredibly accurate set of instructions and near-Godlike wisdom. Learns pool and billiards as an eleven-year-old kid and beats the town champ. Takes up basketball, making his high school team as a freshman and becoming a good major-school college player. Starts a loving marriage in college that remains super-strong over 25 years later. Plays guitar, and with his small combo is chosen for national TV appearances with Charles Kuralt and Robert Kennedy. Despite all his independent thought, establishes a solid - actually distinguished - career in academia. And, in the decade after this book, writes a novel that may have sold more copies - and tickets to its subsequent movie - than ANY in the 1990's!
And guess what? NONE of this - not even a SCRAP of it, according to the essays - ever misled him or cost him anything! He didn't drop out of school to hustle pool, ignore academics to over-concentrate on basketball, discover his wife who he chose at age 22 didn't fit his ever-evolving life at age 50, go for a low-paying full-time music career, QUIT music altogether and lose the fun of playing recreationally, or constrict his thinking by getting it in line with the PC work setting of a university.
Not only did he seem to be always doing the exact right thing at the right time, he avoided every trap there was.
Amazing! Have never seen a life so comprehensively superb since Jennifer Beals' in Flashdance, and she was FICTIONAL!
So, Robert James, we have two ways to interpret you. You can be one of the most premier renaissance men of our time, or an archly annoying "perfect" person akin to Martha Stewart. So, my challenge to you is - write an essay, telling us in detail, how in at least one instance YOU, not circumstances, luck or the people around you - have FAILED. Have you done it? Can you do it?
Beautiful, Absolutely Beautiful.......2000-03-09
I was 15 years old when I was first introduced to this book and author. The essay "Slow Waltz for Georgia Ann" was the most touching story iv ever hurd. It was love, and reckless, and compation, and solitude all wrapped up into one. Every time I need something to make me smile I read this story. I have incouraged every one I have met, who also loves to read, to read this book. The cat, his daughter, the birds and the romance tie it all together to make this book, in my opinion, the greatest ever writen. If you were to pass this up without at least reading once you are a fool. I am 20 now and the original paperback that was givin to me 5 years ago is still laying on my nightstand next my bed.
Book Description
On an island teeming with masters of the short story, Mary Lavin's distinct voice and devoted following set her apart. Before her death in 1996, this Irish writer had received many honors and prizes not only for her luminous short stories but also for several highly regarded novels. William Trevor praised Lavin's ability to "make moments timeless, to illuminate people and places, words and things, by touching them with the magic of the rarely-gifted storyteller." In a Cafe makes available for the first time in the United States a collection of her most beloved pieces as compiled by her daughter. In masterworks such as the title story, an unsettling portrayal of widowhood, and "The Will," which Lavin considered the finest expression of her art, we recognize the justice in Trevor's declaration that "the short story of today owes her a very great debt."
"I envy the skill of Mary Lavin. . . . In her capacity to make much out of little, to compress an entire ethos into an apparently banal situation, she reminds us what literature is all about." --Anthony Burgess
"I cannot think of any Irish writer who has gone so profoundly without fear into the Irish heart." --V. S. Pritchett
Books:
- Design Theory (Encyclopedia of Mathematics and its Applications)
- Diffraction by an Immersed Elastic Wedge
- Discrete Event Systems: Modeling and Performance Analysis (The Aksen Associates Series in Electrical and Computer Engineering)
- Dynamic Economics: Quantitative Methods and Applications
- Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring and Optimal Control (Advances in Industrial Control)
- Elliptic and Parabolic Problems : A Special Tribute to the Work of Haim Brezis (Progress in Nonlinear Differential Equations and Their Applications) (Progress ... Equations and Their Applications)
- Emerging Technologies and Techniques in Porous Media (NATO Science Series II: Mathematics, Physics and Chemistry)
- Environmental Engineering
- Far Side Gallery 3
- Finite Mathematics and Calculus with Applications (7th Edition) (Lial/Greenwell/Ritchey Series)
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