61. Centre For Mathematical Modeling - Activities - Groups - Math. Biology activities, of a unified Fourier transform method for the asymptotic analysis of a wide class of scalar or matrix differential equations with polynomial http://www.swin.edu.au/cmm/activities/groups_mac.htm

consultation research groups seminars ... publications Mathematical Analysis and Computation The main goal of our research is the development and the application of a unified Fourier transform method for the asymptotic analysis of a wide class of scalar or matrix differential equations with polynomial coefficients arising in spectral and scattering problems of mathematical physics. The method is based on the concept of the Strokes Structure, an algebraic structure generated by the differential equation. The principal idea of this method is to investigate the Strokes Structure as an independent object by finding and applying proper (adjusted) fourier transform to the Strokes Structure rather than to the original differential equation. The method consists of a chain of steps that can be realised algorithmically. Whereas the classical Fourier transform technique can be applied only for a very restrictive class of differential equations, the range of applications of this method is much wider. Pilot results obtained by this method show its power and great potential for various applications. Vladimir Gurarii

62. Speaking Invitations SPEAKING INVITATIONS AND OTHER NOTABLE activities Professor Douglas Arnold was on Stable and Unstable Discretization of Partial differential equations . http://www.math.umn.edu/arb/newsletter04/speaking_invite.html

Welcome From the Department Head Promotions and Awards Academic Visitors ... Newsletter 2003 SPEAKING INVITATIONS AND OTHER NOTABLE ACTIVITIES Professor Douglas Arnold was recently elected to a three-year term on the Council of the Society for Industrial and Applied Mathematics (SIAM), SIAM's main policy-making body. He is also a member of a number of scientific advisory boards. As many of our readers are aware, since September 2001, he is serving as the Director of the Institute for Mathematics and its Applications which is associated with our department. In October 2003, Professor Arnold was a ncm2 Distinguished Lecturer (ncm2 is the Network for Computing and Mathematical Modeling, a Canadian initiative based in Montreal). The title of his lecture was "From Exact Sequences to Colliding Black Holes: Differential Complexes in Numerical Analysis". In January 2004 he spoke at the Oxford University Colloquium on "Stable and Unstable Discretization of Partial Differential Equations".

63. Differential Equations With The TI-86 a Function From its Derivative A Graphical Approach (398 KB)* Biological Models with differential equations (364 KB)*. * For additional activities, see our http://education.ti.com/us/product/book/86dif.html

Advanced Differential Equations with the TI-86 by Ray Barton and Dennis Pence The TI-86 includes a differential equation graphing mode that allows students to augment traditional analytic solutions to differential equations with graphic and numeric solutions. We believe these graphic and numeric solutions will greatly enhance student understanding. Students can also use this graphing mode to model real-life problems and solve differential equations that would be very difficult to solve using only analytic methods. This technology provides student access to advanced topics in differential equations at a much earlier stage in the curriculum. Table of Contents View Sample Activity: Recovering a Function From its Derivative: A Graphical Approach (398 KB)* Biological Models with Differential Equations (364 KB)* * For additional activities, see our Online Activity Subscriptions Top Table of Contents Activity 1: Recovering a Function From its Derivative: A Graphical Approach (398 KB)* Activity 2: Recovering a Function From its Derivative: A Numerical Approach Activity 3: Higher Order Differential Equations Activity 4: Projectile Motion Activity 5: Harmonic Motion Activity 6: Biological Models with Differential Equations (364 KB)* Activity 7: Nonlinear Pendulum Problems Activity 8: Numerical Methods and Series Activity 9: Space Trajectories Activity 10: Numerical Methods for Boundary Value Problems Appendix A: Appendix B: References Top About The Author RAY BARTON teaches mathematics at Olympus High School in Salt Lake City. He received Utah's Presidential Award for Excellence in Mathematics Teaching in 1995. Ray is an instructor for the Teachers Teaching With Technology (T

64. :: Ez2Find :: Differential Equations differential equations at Glasgow Site Info - Translate - Open New Window The site describes research activities of the differential equations group in http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Differential_Eq

Guide : Differential Equations Global Metasearch Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode All Words Any Word Phrase Results Timeout Depth Adult Filter Add to Favorites Other Search Web News Newsgroups Images Guides Differential Equations ez2Find Home Directory Science Math : Differential Equations Courses Difference Equations Dynamical Systems Education ... Software Related Categories Science: Math: Calculus Science: Physics: Mathematical Physics Web Sites Analytic Solution for the Burgers Equation [Site Info] [Translate] [Open New Window] Provides the general analytic solution for the Burgers equation in the form of a 4-D commutative hypercomplex function. The solution exhibits the main dynamic features in a Burgers medium: propagation of disturbances, shock waves, propagating state change fronts, and solitons. A page is included to explain the hypercomplex mathematics. URL: http://home.usit.net/~cmdaven/burgers.htm

65. Reserch Activities Of Kenzi ODANI Reserch activities of K. Odani. 5, The integration of polynomial Li?ard systems by elementary functions, differential equations and Dynamical Systems 5 (3/4 http://auemath.aichi-edu.ac.jp/~kodani/research.html

Reserch Activities of K. Odani Research Papers No Title of Article (Co-author) Journal Vol. (No.), Year, Pages Home Publisher View Algebraic solutions for Lotka-Volterra equations in preparation On the limit cycle of the Liénard equation Archivum Mathematicum (Brno) (1), 2000, pp. 2531. Home Masaryk Univ. (Czech) PDF On a Lotka-Volterra model which can be projected to a sphere (with T. Uno) Nonlinear Analysis (3), 1997, pp. 14051410. Home Pergamon, Elsevier Science (Netherlands) PDF The integration of polynomial Liénard systems by elementary functions Differential Equations and Dynamical Systems (3/4), 1997, pp. 347354. Research Square Publications (India) PDF Existence of exactly N periodic solutions for Liénard systems Funkcialaj Ekvacioj (2), 1996, pp. 217234. Home Division of Functional Equations, Mathematical Society of Japan PDF The limit cycle of the van der Pol equation is not algebraic Journal of Differential Equations (1), 1995, pp. 146152. Home Academic Press (USA) Generic homeomorphisms have the pseudo-orbit tracing property Proceedings of American Mathematical Society (1), 1990, pp. 281284

66. FIM - Adaptive Methods For Solving Differential Equations Adaptive methods for solving differential equations. Rolf Rannacher, Universität Heidelberg, Deutschland Beginning Thursday, April http://www.fim.math.ethz.ch/activities/eth_lectures/archive/ss2002/rannacher

Contact Guests Information for Guests Contact ... WS 99/00 Adaptive methods for solving differential equations Rolf Rannacher , Universität Heidelberg, Deutschland Beginning: Thursday, April 11, 2002 Time: Thursday 10:00-12:00 Room: HG G 43 (Hermann-Weyl-Zimmer) Abstract The lectures discuss "adaptivity" in solving differential equations by discretization with emphasis on Galerkin finite element methods. The key issues are "a posteriori error estimation" and "automatic mesh adaptation". Beside the traditional approach of "energy-error control" a new duality-based technique for "goal-oriented error estimation" will be discussed in detail. This method aims at economical computation of certain quantities of physical interest, which is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. Tentative contents The goals of numerical simulation Approaches to a posteriori error estimation How to organize mesh adaptation?

67. Linear Differential Equations Linear differential equations. Local 30. Scheduled activities, Lecture = 24, Tutorial = 6. Min Student Numbers, 20, Max Student Numbers, 60. http://www.tech.port.ac.uk/tud/db/UnivPort/level_2/MTH209.htm

Linear Differential Equations Local Key Hemis Key Base Key Credit Points Lecturer Mr Barrie Davies Coordinator Mr Barrie Davies Delivery Mode Campus - Semesterised Release Status A Materials Normal Level Notional Study Hours Standard Hours Scheduled Activities Lecture = 24, Tutorial = 6. Min Student Numbers Max Student Numbers Prereq Named Postreq Named None Coreq Named None Excluded Combinations None Dependancies None Prereq Statement Students should have knowledge of elementary calculus. Ass Weight Exam Ass Weight Con Ass Weight Other Abstract This unit is about analytical methods of solving ordinary differential equations. Aims To extend students' knowledge of ordinary differential equations, and introduce a range of analytical solution methods. Learning Outcomes On successful completion of this unit, students should be able, at threshold level, to: Solve ordinary differential equations in terms of complementary function plus particular integral. Solve ordinary differential equations in terms of series. Solve ordinary differential equations using Laplace transform methods. Learning and Teaching Strategy Assessment Schedule and Strategy In-Class Test of 1 hour 15 minutes duration - open book, to cover learning outcome 3.

68. Events & Activities - PIMS U Of A The initial approach would be to define the governing partial differential equations in each region. Transform these equations into Laplace Space. http://pims.math.ualberta.ca/problem2description.htm

Wellbore Modelling - Boundary Value Problems in the Recovery of Petroleum Fluids from an Oil Reservoir Submitted by: Bruce C. W. McGee and McMillan-McGee Corp. NEOppg Corp. This practical problem falls into the area of Boundary Value Problems and Mathematical Physics. It is a practical problem in the recovery of petroleum fluids from an oil reservoir using electrical energy. The geometry of the problem best fits the cylindrical coordinate system, as shown in the following Figure: Some assumptions: All fluid flow is laminar and incompressible, Field symmetry in the angular direction, The pipe is made from steel and has a thermal conductivity of 50.0 [W m o C The inductor heater is made from a material that has a thermal conductivity of 1.8 [W m o C Radial fluid velocity is initially uniform and radial into the wellbore. A non-linearity is introduced into the problem if the radial velocity is a function of temperature as follows (the velocity increases as the temperature increases): The zone of induced heat in the pipe extends from one end of the induction heater to the other.

69. FORTH / IACM Computing Group targets its activities towards the development of numerical methods for the solution of partial differential equations with applications in http://www.iacm.forth.gr/activities.html

FORTH Institutes IACM Scientific and Research Interests The activities of the research groups of IACM are directed towards: Research in Applied Mathematics Mathematical and computational methods for wave propagation with emphasis in underwater acoustics. Development of numerical methods and techniques for the solution of Partial Differential Equations which describe physical phenomena and technological processes. Studies of non-linear partial differential equations associated with the mechanics of continuous media. Development of mathematical models and statistical methods for regional analysis and decision making problems. Development of computational platforms for solving applied problems Integrated computer environments for the solution of wave propagation and acoustic tomography problems in the sea. User-friendly environments for pre and post - processing of scientific computations. Development of integrated decision making tools and Geographical Information Systems (GIS) in regional planning problems. Development of simulation algorithms of the workings and properties of the human neural system and especially of the oculomotor system.

70. KemSU OnLine | Chairs | Mathematical Faculty | Chair Of Differential Equations Educational activities of the Chair The Chair provides lectures and General differential equations (fulltime education, correspondence education);; Functional http://mmedia2.kemsu.ru/chairs/mathematics/diff_equat.xsql.en

K emerovo . June 9, 2004 4:41 AM WHERE AM I? Kemerovo State University Chairs Mathematical Faculty Chair of Differential Equations ... Faculty of Physical Training and Sports CHAIRS Physical Faculty Chemical Faculty Economic Faculty Faculty of Law Tip If you want to print out this or that document use one of alternate formats: pdf or rtf All Tips Advertising CHAIRS Mathematical Faculty Chair of Mathematical Analysis Chair of Calculating Mathematics Chair of Mathematical Cybernetics Chair of Automation of Investigations and Technical Cybernetics ... Chair of Algebra and Geometry Chair of Differential Equations Contacts E-mail: stkna@ic.kemsu.ru The Chair page on the site of the Mathematical Faculty: http//www.math.kemsu.ru/departs/mathciber/index.htm Brief historical reference The Chair was founded in 1978. Since the moment of opening the Chair its Head has been Professor Kucher N. A. The Chair specialization on Differential Equations is introduced with a view of training highly qualified multifunctional specialists able to solve both purely mathematical problems in the qualitative theory of differential equations and problems of the applied kind arising during simulation of different processes in mechanics of continua. Educational activities of the Chair The Chair provides lectures and practical classes at the Mathematical Faculty on the following basic disciplines: General Differential Equations (full-time education, correspondence education);

71. Wauu.DE: Science: Math: Differential Equations http//www.mgnet.org/. Nonlinear differential equations at Glasgow The site describes research activities of the differential equations group in the mathematics http://www.wauu.de/Science/Math/Differential_Equations/

Home Science Math : Differential Equations Search DMOZ-Verzeichnis: All Categories Categories Onlye Kategorien: Courses Difference Equations Dynamical Systems Events ... People Links: Analytic Solution for the Burgers Equation Provides the general analytic solution for the Burgers equation in the form of a 4-D commutative hypercomplex function. The solution exhibits the main dynamic features in a Burgers medium: propagation of disturbances, shock waves, propagating state change fronts, and solitons. A page is included to explain the hypercomplex mathematics. http://home.usit.net/~cmdaven/burgers.htm arXiv Front: AP Analysis of PDEs PDEs section of the mathematics e-print arXiv. http://front.math.ucdavis.edu/math.AP Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equation Courses Online course material http://math.bu.edu/DYSYS/ode-bif/ode-bif.html C*ODE*E Consortium of ODE Experiments. Newsletter, graphics, links http://www.math.hmc.edu/codee/main.html Computational PDEs Unit School of Computing, University of Leeds. Research details, publications, software and resources. http://www.scs.leeds.ac.uk/cpde/

72. Math4113DifferentialEquation.html MATERIALS (Required Textbook) Elementary differential equations and Boundary following expositorydiscussion, demonstration, inquiry, and group activities. http://arapaho.nsuok.edu/~linded/Dr. Linde/Math4113DifferentialEquations2.htm

Northeastern State University College of Mathematics, Science and Nursing Department of Mathematics Tahlequah, OK INSTRUCTOR Dr. Darryl A. Linde, Associate Professor. Office: Sc 119. Office Hours: 10:00 -11:00 and 1:00 - 2:00 MWF in Tahlequah 3:00 - 4:30 T Th at OSU-Tulsa and by appointment at other times. Telephone: 918-456-5511 ext. 3809. FAX: 918-458-2325 E-mail: linded@nsuok.edu COURSE TITLE AND NUMBER MATH 4113, Differential Equations 9:00- 9:50 a.m. MWF Fall 2001 PREREQUISITES Math 2624, Calculus II CATALOG DESCRIPTION OF COURSE Introduction to the theory and application of ordinary differential equations, linear and nonlinear first order equations, second order linear equations and higher order linear equations. Introduction to the Laplace transform and applications. COURSE PURPOSE This course provides students an opportunity to develop their calculus skills in a more sophisticated setting than the first year calculus sequence. Students use differential equations to model physical phenomena, business applications, and applications in medicine and biology. The course is particularly useful to a student studying a physical science or mathematics. The student will see connections to a broad range of mathematics including complex functions, linear algebra, advanced calculus, topology, numerical analysis, special functions, and discrete mathematics. EXPECTED COURSE OUTCOMES The student will be expected to achieve the following objectives:

73. Modelica Activities At PELAB Partial differential equations in Modelica (Levon Saldamli). In Modelica, models are defined using equations and connections between components. http://www.ida.liu.se/labs/pelab/modelica/index1.html

This page http://www.ida.liu.se/~pelab/modelica describes research projects at PELAB Modelica - an object oriented modeling language. Main projects Modelica language and environment design (Peter Fritzson) Open Modelica (Peter Fritzson) Modelica, CAD and visualization (Vadim Engelson) Compilation of Modelica for parallel computers (Peter Aronsson) Debugging of equation systems (Peter Bunus) Partial Differential equations in Modelica (Levon Saldamli) Other projects Distributed simulation on Windows/UNIX cluster (Vadim Engelson) RealSim (Real-time Simulation for Multi-Physics Systems) sponsored by European Commission VISP ,(V Previous projects Information for students Modelica language and environment design We participate in efforts of Modelica Association in language design. Visit the main site www.Modelica.org for latest Modelica documents, libraries, publications and meetings. Paper on object oriented aspects of Modelica language Paper Modelica Natural Semantics . The formal definition is used for compiler generation.

74. William E. Boyce,Richard C. DiPrima, Elementary Differential Equations And Bound WILLIAM E. BOYCE,RICHARD C. DIPRIMA, ELEMENTARY differential equations AND BOUNDARY VALUE cost just £9.99 but each provides four exciting activities at two http://www.reviewcentre.com/reviews30916.html

William E. Boyce,Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems Login/Register List Your Site Tell a Friend Bookmark ... Cookery Books Search All Items Activity Holidays America Attractions Beauty Book Reviews Buying a car Car Accessories Car Reviews Caravans Careers Caribbean Catalogues City Breaks Computer Game Reviews Computer Hardware Computer Software Cruises Digital Camera Reviews DIY Drink Reviews DVD Players and Televisions Education Electrical Appliances Entertainment Reviews Far East and Asia Fashion Film Cameras Film Reviews Finance Reviews Food Reviews Gadgets Gardening Golf HiFi Reviews High Street Shop Reviews Holiday Reviews Insurance Internet Magazine Reviews Mobile Phone Reviews Motorcycles Motoring Music Reviews Musical Instrument Reviews Office Equipment Online Shop Reviews Parenting Pets Recreation Reference Restaurant Reviews Shooting Skiing Holidays Sports Equipment Reviews Toy Reviews Travel Services Utility Companies Water Sports Book Reviews Magazine Reviews You are here : Welcome Books Book Reviews Compare Mathematic Books William E. Boyce,Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems WILLIAM E. BOYCE,RICHARD C. DIPRIMA, ELEMENTARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS

75. WE Boyce, Elementary Differential Equations And Boundary Value Problems 7e Cours WE BOYCE, ELEMENTARY differential equations AND BOUNDARY VALUE PROBLEMS 7E COURSE ADVANTAGE cost just £9.99 but each provides four exciting activities at two http://www.reviewcentre.com/reviews30928.html

WE Boyce, Elementary Differential Equations and Boundary Value Problems 7e Course Advantage Edition +CD (Wse) Login/Register List Your Site Tell a Friend Bookmark ... Cookery Books Search All Items Activity Holidays America Attractions Beauty Book Reviews Buying a car Car Accessories Car Reviews Caravans Careers Caribbean Catalogues City Breaks Computer Game Reviews Computer Hardware Computer Software Cruises Digital Camera Reviews DIY Drink Reviews DVD Players and Televisions Education Electrical Appliances Entertainment Reviews Far East and Asia Fashion Film Cameras Film Reviews Finance Reviews Food Reviews Gadgets Gardening Golf HiFi Reviews High Street Shop Reviews Holiday Reviews Insurance Internet Magazine Reviews Mobile Phone Reviews Motorcycles Motoring Music Reviews Musical Instrument Reviews Office Equipment Online Shop Reviews Parenting Pets Recreation Reference Restaurant Reviews Shooting Skiing Holidays Sports Equipment Reviews Toy Reviews Travel Services Utility Companies Water Sports Book Reviews Magazine Reviews You are here : Welcome Books Book Reviews Compare Mathematic Books WE Boyce, Elementary Differential Equations and Boundary Value Problems 7e Course Advantage Edition +CD (Wse) WE BOYCE, ELEMENTARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS 7E COURSE ADVANTAGE EDITION +CD (WSE)

76. Scientific Activities October 30November 04, The structure of amenable systems, BIRS. November 06-11, Functional differential equations , BIRS. Past activities. http://www.pims.math.ca/science/activities-all.html

Scientific Activities Past Activities Current Activities Future Activities Current Activities (January 2004 - December 2004) January 03-04 2nd PIMS-MITACS Crystal Growth Workshop, PIMS-UBC January 08-13 PIMS Graduate Weekend , UBC, SFU, UVic March 05 Biological Molecular Algorithms - A Mathematicians Perspective on Molecular Biology (Barry Merriman, UCLA) , Axa Pacific Lecture room, Harbour Centre, Vancouver March 13-17 Cohomogeneity One Manifolds with Positive Sectional , BIRS March 13-18 Interactions between model theory and geometry , BIRS March 13-27 Modular invariants and NIM-reps , BIRS March 18-20 Human Infant Speech Perception and Language Acquisition , BIRS March 20-25 Topology of Manifolds and Homotopy Theory , BIRS March 25-27 2-day Retreat on Mathematical Ecology and Evolution , BIRS March 27-28 Young Researchers' Forum in Mathematical and Statistical Sciences , University of Alberta March 27-April 01 Orthogonal Polynomials; Interdisciplinary Aspects , BIRS April 03-08 Model Reduction Problems and Matrix Methods , BIRS April 09-10 West Coast Optimization Meeting , University of Washington April 10-15 Analytic and Geometric Aspects of Stochastic Processes , BIRS April 15-17 PIMS PDF Meeting , BIRS April 17 Pacific Northwest Number Theory Seminar , Oregon State University April 17-22 BIRS Workshop in Creative Scientific Writing , BIRS April 17-22 Celestial Mechanics , BIRS April 22-24 Mathfair Workshop , BIRS April 24-29 Microeconometrics of Spatial and Grouped Data , BIRS May 01 The First Pacific Northwest Theory Day , Microsoft Research, Redmond, Washington

77. H. Amann's Editorial Activities Editorial activities. Member of the following editorial boards Journals. Abstract and Applied Analysis (AAA); Advances in differential equations; Advances in http://www.math.unizh.ch/amann/editorial_activities.html

Herbert Amann Editorial activities Member of the following editorial boards: Journals Abstract and Applied Analysis (AAA) Advances in Differential Equations Advances in Mathematical Sciences and Applications Advanced Nonlinear Studies Cubo Matemática Educacional Differential and Integral Equations Houston Journal of Mathematics Journal of Evolution Equations (JEE) Journal of Mathematical Fluid Mechanics Nonlinear Differential Equations and Applications (NoDEA) Questiones Mathematicae Scientiae Mathematicae Japonicae Retired from Proceedings of the Royal Scociety of Edinburgh (1978-1988) Mathematische Annalen (1979-1999, managing editor 1993-1999) Dynamics Reported (1987-1995) Book Series Monographs in Mathematics Retired from Research Notes in Mathematics Series (formerly: Pitman Research Notes in Mathematics) Monographs and Surveys in Pure and Applied Mathematics (formerly: Pitman Monographs and Surveys in Pure and Applied Mathematics) home

78. Differential Equations Store Groetsch (Author) (Paperback December 1999) Inverse Problems activities for Undergraduates on 10-5-2003, Theory of Ordinary differential equations by Earl E http://www.mathbook.com/d/Differential_Equations/index2.htm

For Age: 4 years and up LeapPad by LeapFrog At Amazon on 4-15-2003. More Info This talking book comes with an interactive ''magic pen'' that works like a hand-held computer mouse pointer. Children can opt to turn the paper pages and listen to the story read with different voices for each character. Or they can interrupt the read-aloud session to play with the magic pen (permanently attached with a wire). They can point the pen tip to any word on a page and hear it pronounced, or touch a picture and hear a sound effect (such as ''Strike one!'' for the baseball bat). Very similar to the popular Living Books computer games, this 10-by-11-inch book is more portable than a home computer. Stories in this set include Lil's Loose Tooth, Richard Scarry's Best Word Book Ever, and Winnie the Pooh in A Sweet Good Morning. The set also includes a paper piano keyboard and map and human anatomy games. Gail Hudson Batteries: 4 AA batteries required. Barron's Math Workbook for the Sat I (Barron's Math Workbook for the Sat I, 2nd Ed) Visit Our Sites: Buy Law Books Top Quality Wrist Watches

79. Scientific Activities: Mathematics theory, several aspects of probability, and some applications of statistics, linear and nonlinear ordinary and partial differential equations, harmonic analysis http://www.weizmann.ac.il/acadsec/Scientific_Activities/current/Mathematics.html

Mathematics Gideon Schechtman, Head The William Petschek Chair of Mathematics Algebraic geometry: Study was continued on integration on p-adic analytic spaces. It was shown that every smooth p-adic analytic space can be provided with an algebra of locally analytic functions which includes all analytic ones, satisfies the uniqueness property, and contains local primitives of all closed one-forms with coefficients in the algebra. It was also shown that this algebra contains a full set of local solutions of any unipotent differential equation and, as a consequence, one constructs the parallel transport of the local solutions along a path. Automorphic forms: First, work was continued on the boundedness in vertical strips of L-functions that appear in constant terms of Eisenstein series; one question studied was whether the boundedness is really a product of complex function theory. Second, topics were explored about how Riemann's zeta function, and its generalizations, depends on Riemann's original ideas. Banach spaces: The geometry of finite and infinite dimensional normed spaces and maps between them is investigated, particularly the classification of Banach spaces under Lipschitz and uniform homeomorphisms, and under Lipschitz and uniform quotient maps. Some new tight isomorphic embedding results, particularly for finite dimensional subspaces of Lp, were obtained.

80. Graduate Study In Differential Equations And Applied Mathematics These activities usually involve significant interaction with one or nonlinear analysis, functional analysis, probability, differential equations, graph theory http://www.math.uiuc.edu/GraduateProgram/researchmath/graddiffeq.html

Graduate Study in Differential Equations and Applied Mathematics Introduction The name "Applied Mathematics" covers a wide range of mathematical studies overlapping with many areas of mathematics. Dynamical Systems Dynamics is the study of processes that evolve in time. A differentiable dynamical system arises as the differentiable action of a Lie group on a manifold. Here a Lie group C acts on a manifold X as a homomorphism of C into the group of diffeomorphisms of X. In case C = R , the real numbers, the map R x X -> X induced by this action is called a flow. Differentiable flows define vector fields (as ordinary differential equations). Conversely, solutions of an ordinary differential equation may generate a (global) flow. In the study of dynamical systems as flows, one uses the qualitative theory of differential equations and differential topology. Discrete dynamical systems arise when C = Z, the integers. Here the iterates of a diffeomorphism of X define the orbit of a point x in X and one studies the orbit structure. Problems of research interest to the faculty here at Illinois include the study of particular dynamical systems which arise in control theory, celestial mechanics and nonlinear phenomena in physics. The study of differential equations by dynamical systems methods holds particular interest.

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