1. 31: Potential Theory Gives a brief description of potential theory with some indications oftextbooks/tutorials and links to other web resources. http://www.math.niu.edu/~rusin/known-math/index/31-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 31: Potential theory Introduction Potential theory may be viewed as the mathematical treatment of the potential-energy functions used in physics to study gravitation and electromagnetism. If some electrically charged particles are distributed in space, then a function U is defined on all of space (except right where the particles are) which measures the potential energy at each point. This function is harmonic , that is, it satisfies the Laplace equation d^2 U / dx^2 + d^2 U / dy^2 + d^2 U / dz^2 = 0, a condition which, for example, forces the value of U at a point to be the average of its values on a ball centered at that point. Classical problems include the determination of harmonic functions taking prescribed values at a point, on a sphere, and so on (the Dirichlet problem) that is, determining the force field which results from a particular arrangement of force sources. Harmonic functions in the plane include the real and complex parts of analytic functions, so Potential Theory overlaps Complex Analysis. (Actually potential theory in the plane is rather different from in higher dimensions, since the fundamental solution of the Laplace equation, corresponding to a single point charge, is 1/r^(n-2) in n-dimensional space, but log(r) in the plane. Nonetheless, the results in all dimensions often have cognates in complex analysis.)

2. Index Two texts by V.I. Fabrikant Applications of potential theory in Mechanics, Selection of New Results (1989); Mixed Boundary Value Problems of potential theory and their Applications in Engineering (1991). Text in PDF with figures separately in JPG. http://www.geocities.com/fabrikant_books/

UPDATE: My third book is now finished. If you are interested, click here Two books are presented here. They were originally published by Kluwer Academic in 1989 and 1991 respectively. The form of presentation does not correspond exactly to the original publications: all the noticed misprints and errors were corrected and some additional formulae are given. The book text is given in PDF format and all the figures are given separately in JPG format. You can read the books or download free of charge. Just click the appropriate book title below. If you have any question about the use of the web site or need help on any subject described in the book, you can communicate with me using the following E-mail: valery_fabrikant@hotmail.co m. If you download book 1 or book 2, I suggest that you send me e-mail at valery_fabrikant@hotmail.co m stating which book you downloaded. You private information will be kept strictly confidential and will be used in one case only: when a misprint or an error in the book is discovered, you will receive an e-mail with necessary information about the error or misprint. 1. V.I. Fabrikant, Applications of Potential Theory in Mechanics.

3. Complex Potential Theory Feza Gursey Institute, Istanbul, Turkey; Summer 1999. http://www.gursey.gov.tr/complex.html

Home General Research Semesters People ... Share your links Summer Research Semester on Complex Potential Theory and its Applications Feza Gursey Institute, Istanbul Turkey application form Feza Gursey Institute shall host a research-teaching semester (July 5 - Aug. 6 and Aug. 16 - 21, 1999) on Complex Potential Theory (CPT) and its applications. There will be a workshop in Edirne Aug. 9 - 16, 1999 emphasizing the connection between functional analysis and complex analysis. The principal organizers of this mini-semester are A. Aytuna (METU), T.Terzioglu (Sabanci University), and V. Zahariuta (Feza Gursey Institute). CPT is a relevant potential theory for the multidimensional complex analysis and deals with plurisubharmonic functions and maximal plurisubharmonic functions; it is strongly connected with the study of the complex Monge-Ampere equation. CPT is an active area of research in Mathematics with applications in Approximation and Interpolation Theory, Partial Differential Equations, Complex Dynamical Systems, Differential Geometry, Number Theory and so on. Our aim, during the semester, is to impart the main ideas of CPT to advanced graduate students and other interested mathematicians through a series of lectures by leading researchers in the field as well as to proceed scientific discussions of the most advanced results and some actual problems in CPT. The following specialists have been contacted and accepted to provide 10-15 hour courses of lectures each:

4. International Conference On Complex Analysis And Potential Theory Kyiv (Kiev) Ukraine; 712 August 2001. http://www.imath.kiev.ua/~captconf/

INTERNATIONAL CONFERENCE ON COMPLEX ANALYSIS AND POTENTIAL THEORY IN KIEV ON 7 - 12 AUGUST 2001 SECOND ANNOUNCEMENT The registration of participants will be held on 7 August at 9.00-19.00 and on 8 August at 9.00-9.30 in the Institute of Mathematics (IM) (the interactive map of Kiev is available at http://www.isgeo.kiev.ua; type "Tereshchenkivs'ka" instead of "Tereshchenkivska" at the streets window on searching of the IM area at this map). Please inform us about your itinerary including the time of arrival and departure, flights or trains and so on. Institute of Mathematics (IM) is located in the center of Kiev (new spelling "Kyiv") near the Metro Station "Theatralna". There is a good connection with the Kiev airports "Boryspil" and "Zhulyany" (now it is called "Kyiv") as well as with the main railway Station, which is called "Vokzal", more explicitly: from Vokzal two stops by Metro, from the airport "Kyiv" by trolley No. 9 or by a special taxi No. 9 to the Tereshchenkivska St., which is the last stop; from the airport "Boryspil" by special bus "Polit" to the stop "Metro University" or by Shuttle bus The corrected schedule of the Conference is the following. The Opening will be held on 8 August at 9.45 in the Conference Hall of IM. Scientific sessions will be held in three from 10.00 on 8 August till 13.00 on 12 August.

5. Introduction Hejnice, Czech Republic; 26 September 2 October 2004. http://www.karlin.mff.cuni.cz/PTRT04/

TECHNICAL UNIVERSITY LIBEREC HHU MI Special conference Potential Theory and related topics progress, prospects and perspectives Preliminary announcement First announcement Second announcement Last announcement September 26 October 2, 2004 Hejnice, Czech Republic

6. Potential Theory Karlin's page, which is a good place to find out who is doing work in potential theory. http://www.karlin.mff.cuni.cz/lat/katedry/kma/pt/

7. 31 Potential Theory Gives a brief description of potential theory with some indications of textbooks/tutorials and links to other web resources. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Potential Theory Basic 2D potential theory We shall discuss 2-D incompressible potential flowand just mention the extension to linearized compressible flow. http://www.desktopaero.com/appliedaero/potential/potentialtheory.html

Basic 2-D Potential Theory We outline here the way in which the "known" solutions used in panel methods can be generated and obtain some useful solutions to some fundamental fluid flow problems. Often the known solutions just come out of thin air and can be applied, but sometimes other approaches are possible. The simplest case, two-dimensional potential flow illustrates this process. We shall discuss 2-D incompressible potential flow and just mention the extension to linearized compressible flow. For this case the relevant equation is Laplace's equation: There are several ways of generating fundamental solutions to this linear, homogeneous, second order differential equation with constant coefficients. Two methods are particularly useful: Separation of variables and the use of complex variables. Complex variables are especially useful in solving Laplace's equation because of the following: We know, from the theory of complex variables, that in a region where a function of the complex variable z = x + iy is analytic, the derivative with respect to z is the same in any direction. This leads to the famous Cauchy-Riemann conditions for an analytic function in the complex plane. Consider the complex function: W = f + i y The Cauchy-Riemann conditions are: Differentiating the first equation with respect to x and the second with respect to y and adding gives: Thus, analytic function of a complex variable is a solution to Laplace's equation and may be used as part of a more general solution.

9. ~l-helms Homepage Author of 'Introduction to potential theory'. Contains information about his forthcoming book 'potential theory, the Dirichlet Problem, and the Other Problem'. http://www.math.uiuc.edu/~l-helms/

Lester L. HelmsHome Page Emeritus Professor, Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801 Office: 309 Altgeld Hall Office Telephone: 333-3699 e-mail: l-helms@math.uiuc.edu General Information Ph. D., Purdue University, 1956 Mathematical Interests My interests lie in three interrelated topics: heat equations associated with second-order elliptic operators, Markov or diffusion processes, and potential theory. In the early 1950s, W. Feller characterized one-dimensional diffusions by representing their infinitesimal generators intrinsically and determined all possible boundary conditions which determine the domain of the generator. In 1959, Ventcel characterized the infinitesimal generators of general diffusion processes on bounded domains in higher dimensions as a second-order elliptic operator subject to boundary conditions involving diffusion, absorption, reflection, and viscosity at the boundary. The problem of showing that a second-order elliptic operator subject to such boundary conditions generates a Markov or diffusion process is in its infancy. The best results obtained so far involve a nondegenerate second-order elliptic operator subject to oblique derivative boundary conditions. Selected Publications and Comments Books Tables of contents for the second and third books of the following list can be viewed.

10. Digital Physics *** In C. Freksa, Ed., Foundations Of Computer In C. Freksa, ed., Foundations of Computer Science Potential Theory - Cognition Lecture Notes in Computer Science, pp. 201-208, Springer, 1997. A http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Potential Theory potential theory in Gravity and Magnetic Applications This book bridges thegap between the classic texts on potential theory and modern books on http://pangea.stanford.edu/~blakely/potential.html

Potential Theory in Gravity and Magnetic Applications Richard J. Blakely Cambridge University Press 1995 Hardcover: 441 pages, list $59.95, ISBN 0-521-41508-X Paperback: 441 pages, list $34.95, ISBN 0-521-57547-8 This book bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It begins with Newton's second law of motion and concludes with topics on state-of-the-art interpretations of gravity and magnetic data. It was published as part of the Stanford-Cambridge Program The introductory chapters discuss potential theory, with emphasis on those aspects important to earth scientists, such as Laplace's equation, Newtonian potential, magnetostatic and electrostatic fields, conduction of heat, and spherical harmonic analysis. Difficult concepts are illustrated with easily visualized examples from steady-state heat flow. Later chapters apply these theoretical concepts specifically to the interpretation of gravity and magnetic anomalies, with emphasis on anomalies caused by crustal and lithospheric sources. Many of these examples are drawn from the modern geophysical literature. Topics include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book contains over 100 black-and-white figures , problem sets at the end of each chapter, and exercises dispersed throughout the text. It also includes an appendix of

12. Harmonic Function Theory And Mathematica Harmonic Function Theory. Some of the algorithms used by this software are explained in the paper listed below. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Potential Theory--Subroutines potential theory in Gravity and Magnetic Applications contin, Analyticallycontinue a gridded potential field from one horizontal level to another http://pangea.stanford.edu/~blakely/subroutines.html

Potential Theory in Gravity and Magnetic Applications Subroutines The textbook contains an appendix of computer subroutines written in FORTRAN that provide insight into underlying theories discussed in the text. The subroutines are used in some of the problem sets that follow each chapter, and they provide a reference source with which readers can develop their own computer programs. The subroutines are listed in the following table. They can be downloaded individually by selecting the appropriate subroutine name, or they can be downloaded en masse if preferred. Name Function contin Analytically continue a gridded potential field from one horizontal level to another cross Calculate vector products cylind Calculate the gravitational attraction of an infinitely extended cylinder dipole Calculate the magnetic induction of a dipole dircos Calculate direction cosines expand Add tapered rows and columns to a grid fac Calculate factorials facmag Calculate magnetic induction of one polygonal facet of a polyhedron fork Calculate the one-dimensional Fourier transform and its inverse fourn Calculate an n-dimensional Fourier transform and its inverse gbox Calculate the gravitational attraction of a right rectangular prism gfilt Calculate the earth filter (gravity case) for a horizontal layer glayer Calculate the gravitational attraction of a flat, horizontal layer

14. Foundations Of Computer Science. Potential-Theory-Cognition (Lecture Foundations of Computer Science. PotentialTheory-Cognition (Lecture Notes in Computer Science Vol. 1337), vergleicht Verf gbarkeit, Preise http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Potential Theory -- From MathWorld REFERENCES. Kellogg, OD Foundations of potential theory. New York Dover, 1953 . potential theory. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/PotentialTheory.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Harmonic Analysis Harmonic Functions Potential Theory The study of harmonic functions (also called potential functions SEE ALSO: Harmonic Function Scalar Potential Vector Potential [Pages Linking Here] REFERENCES: Kellogg, O. D. Foundations of Potential Theory. New York: Dover, 1953. MacMillan, W. D. The Theory of the Potential. New York: Dover, 1958. Weisstein, E. W. "Books about Potential Theory." http://www.ericweisstein.com/encyclopedias/books/PotentialTheory.html CITE THIS AS: Eric W. Weisstein. "Potential Theory." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/PotentialTheory.html Wolfram Research, Inc.

16. Springer - Your Publishers Of Books, Journals, And Electronic Media (Kluwer) Devoted to the interactions between potential theory, Probability Theory, Geometry and Functional Analysis. Abstracts and contents from vol.4 (1995). Full text to subscribers. http://www.wkap.nl/journalhome.htm/0926-2601

Springeronline.com - Our new domain Please choose your location on the buttons above for information, special sales and services targeted to where you live. Springeronline.com - Europe Please select an item from the list below. General Springer Springer Germany Springer United Kingdom Springer Switzerland Springeronline.com - North America Springeronline.com - South America Springeronline.com - Europe Springeronline.com - Africa Springeronline.com - Asia Springeronline.com - Australia and Oceania

17. Potential Theory potential theory in Gravity and Magnetic Applications http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. David Quantick - Function Spaces And Potential Theory Grundlehren ber David Quantick Beck (Kill Your Idols Series) und Function Spaces and potential theory Grundlehren der mathematischen Wissenschaften A Series http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Studies In Potential Theory Studies in potential theory. MA Monterie. The thesis consists of three parts inwhich two problems of potential theory are studied. http://www.geocities.com/marcelmonterie/other/thesis.htm

Studies in potential theory M.A. Monterie The thesis consists of three parts in which two problems of potential theory are studied. The first two parts concern distributions of electric charge on conductors in R and R For planar continua, upper and lower bounds are given for the growth of the associated Fekete polynomials and potentials. For continua K of capacity 1 whose outer boundary is an analytic Jordan curve, the family of Fekete polynomials is bounded on K . The difference between the Fekete potential and the equilibrium distribution is estimated with order log N/N. The work is based on fundamental results of Pommerenke and on potential theory, including the exterior Green function with pole at infinity. For convex surfaces, and certain smooth surfaces, a similar technique is used and the order 1/x is obtained. In the last part, a Nevanlinna-like criterion for positive capacity of Cantor-type sets K is proved. Using this criterion, examples are constructed of such K with capacity zero such that the projections of the square of K in all but two directions have positive capacity.

20. IWPT 2004 International Workshop on potential theory in Matsue 2004 Third Announcement http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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