This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science.
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Posts Tagged ‘Mathematics’
Unsolved Problems in Mathematical Systems and Control Theory
Thursday, November 5th, 2009Why the Boundary of a Round Drop Becomes a Curve of Order Four
Thursday, November 5th, 2009Description:
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary.
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A Problem Course in Mathematical Logic
Thursday, November 5th, 2009A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.
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A Problem Text in Advanced Calculus
Thursday, November 5th, 2009This is a text on Advanced Calculus written for a more “theoretical” course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), it concentrates on conceptual development and proofs. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from.
A Course of Modern Analysis
Thursday, November 5th, 2009This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever
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A Concise Course in Algebraic Topology
Wednesday, November 4th, 2009Description:
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields
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A Century of Mathematics in America
Monday, November 2nd, 2009In the 100 years since the founding of the AMS, the American mathematical community has grown from a small group heavily dependent on European mathematicians to a large and influential group that in many areas sets the standard for the rest of the world. By the 1930s, there was a flourishing mathematical community to welcome the influx of mathematicians fleeing Europe. This volume, the first in the History of Mathematics series, brings together a variety of perspectives on the political, social, and mathematical forces that have shaped the American mathematical community in the past century.
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(3 volumes, 35 PDF files, 74MB)
Derivations of Applied Mathematics
Sunday, September 20th, 2009This is a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here. The book’s purpose is to convey the essential ideas underlying the derivations of a large number of mathematical results useful in the modeling of physical systems. To this end, the book emphasizes main threads of mathematical argument and the motivation underlying the main threads, deemphasizing formal mathematical rigor. It derives mathematical results from the purely applied perspective of the scientist and the engineer. This book defines applied mathematics to be correct mathematics useful to scientists, engineers and the like; proceeding not from reduced, well defined sets of axioms but rather directly from a nebulous mass of natural arithmetical, geometrical and classical-algebraic idealizations of physical systems; demonstrable but generally lacking the detailed rigor of the professional mathematician.
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Handbook of Mathematical Functions
Wednesday, September 2nd, 2009Description:
Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places.
Basic Engineering Mathematics
Thursday, August 13th, 2009Multiple Integrals
1. Double Integrals
(a) Regions of Integration
(b) Iterated Integrals
(c) Double Integrals in Polar Coordinates
Triple Integrals
2.
Innite Sequences & Series
1. Sequences and Series
2. Convergence and Tests for Convergence
Vectors
Vectors in the Plane
1.
2. Dot and Cross product
3. Lines and Planes in Space
3
4. Vector Methods for Measuring Distance in R
Laplace Transforms
1. Denition
(a) Linearity
(b) Inverse Laplace Transform
Properties of Laplace Transforms
2.
(a) Dierentiation
(b) Integration
(c) Shifting on the s-axis
(d) Shifting on the t-axis
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