21. Bifurcations, Phase Lines, And Elementary Differential Equations next Introduction (Next Section) Bifurcations, Equilibria, and Phase Lines Modern Topics in differential equations Courses. Robert L. Devaney. http://math.bu.edu/DYSYS/ode-bif/ode-bif.html

Introduction (Next Section) Bifurcations, Equilibria, and Phase Lines: Modern Topics in Differential Equations Courses Robert L. Devaney Introduction Qualitative approach to autonomous equations. The phase line and the graph of the vector field. ... An application: harvesting Robert L. Devaney May 6, 1995

22. Fast Marching Methods And Level Set Methods: J.A. Sethian Tracking moving interfaces in computational geometry, materials sciences, robotics, image processing, and fluid mechanics; numerical techniques based on partial differential equations. http://www.math.berkeley.edu/~sethian

FAST MARCHING METHODS AND LEVEL SET METHODS J.A. SETHIAN Dept. of Mathematics, Univ. of California, Berkeley, California 94720 E-mail: sethian@math.berkeley.edu Click here if you would like a smaller typeface version of this page Fast Marching Methods and Level Set Methods are numerical techniques which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The techniques have a wide range of applications, including problems in fluid mechanics, combustion, manufacturing of computer chips, computer animation, image processing, structure of snowflakes, and the shape of soap bubbles. These are two fundamentally different approaches to the problem of tracking moving interfaces, yet they share a common theory and numerical methodology. This web page serves as both an introductory and advanced resource for these ideas, with the goal of providing an intuitive understanding of the techniques the history, evolution, and application of these methods technical details and reference material.

23. Numerical Mathematics. Features programs that will find solutions for functions, equations, differential equations, regression, approximation, interpolation, linear algebra, integration, maxima and minima, and 3D graphing. Includes free download demonstrations and general explanation of methods used. http://www.numericalmathematics.com/

numerical mathematics free downloads software freeware download free math advanced numerical mathematics mathematical program derivatives equations calculus linear algebra differential equations integration matrix integral interpolation approximation roots maxima minima functions optimization multiple integrals quadrature nonlinear multivariable functions solutions plotting Fourier multivariate functions graphics matrices analysis numerical mathematics free downloads software freeware download free math advanced numerical math mathematical program derivatives equations calculus linear algebra differential equations integration matrix integral interpolation approximation roots maxima minima functions optimization multiple integrals quadrature nonlinear multivariable functions solutions plotting Fourier multivariate functions graphics matrices analysis Numerical Mathematics is the branch of mathematics that develops, analyzes, and applies methods to compute with finite precision numbers. Numerical mathematics is a vast field, but my hope is that I can make a

24. SOS Mathematics Differential Equations SOS Mathematics differential equations College students who have a firm calculus background can use this site to learn about differential equations. Six main sections explain low and high order http://rdre1.inktomi.com/click?u=http://www.sosmath.com/diffeq/diffeq.html&y

25. S.O.S. Math - Differential Equations Modeling via differential equations First Order differential equations Linear equations; Separable equations; Qualitative Technique Slope Fields; http://www.sosmath.com/diffeq/diffeq.html

S.O.S. Homepage Algebra Trigonometry Calculus ... CyberBoard Search our site! S.O.S. Math on CD Sale! Only $19.95. Works for PCs, Macs and Linux. Tell a Friend about S.O.S. Books We Like Math Sites on the WWW S.O.S. Math Awards ... Modeling via Differential Equations First Order Differential Equations Linear Equations Separable Equations Qualitative Technique: Slope Fields Equilibria and the Phase Line ... Euler-Cauchy Equations Series Solutions Introduction Derivatives and Index Shifting First Examples Airy's Equation ... Hermite's Equation Higher Order Linear Equations Introduction and Basic Results Homogeneous Linear Equations with Constant Coefficients Non-Homogeneous Linear Equations Method of Undetermined Coefficients ... Method of Variation of Parameters Laplace Transform Basic Definitions and Results Application to Differential Equations Impulse Functions: Dirac Function Convolution Product ... Application of Fourier Series to Differential Equations APPENDIX Tables Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA users online during the last hour

26. S.O.S. Mathematics - CyberExam SOS Mathematics CyberExam differential equations. in differential equations. The exams will be organized by topics Content of the test, Sample Tests. http://www.sosmath.com/cyberexam/diffeq/diffeq.html

S.O.S. Mathematics - CyberExam Differential Equations This page is a place for students and educators to check out sample tests, midterm exams, final exams, quizzes, projects, etc... in Differential Equations The exams will be organized by topics: Content of the test Sample Tests Higher Order Diff. Eq., Laplace Transform Exam Qualitative Analysis of Systems, Linear Systems, Nonlinear Systems Exam Linear Equations, Separable Equations, Population Dynamics Exam Qualitative Analysis of Systems, Euler's Method, Nonlinear Systems Exam Back to CyberExam S.O.S. MATH: Home Page Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard 6/14/97. Last update: 6/27/97 Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA users online during the last hour

27. Yuri Safarov's Home Page King's College of London. Online book covers eigenvalues in partial differential equations. Other publications cover basic, real and Fourier analysis. In pdf format. http://www.mth.kcl.ac.uk/~ysafarov/

Professor Yuri Safarov Department of Mathematics Strand, London WC2R 2LS United Kingdom Telephone: Fax: E-mail: ysafarov@mth.kcl.ac.uk Book Preprints Lectures ... LMS Durham Symposium 1996 (photo) Updated 30 October 2003

28. DIE page numbers. 2 J. Norris, S. Smith, and CH Zang, ``Ordinary differential equations, Publisher, New York, 1976. Submission of http://www.aftabi.com/DIE/die.html

Differential and Integral Equations Editorial Board Volume 16 (2003) Volume 15 (2002) Volume 14 (2001) Volume 13 (2000) Volume 12 (1999) Volume 11 (1998) Volume 10 (1997) Volume 9 (1996) Volume 8 (1995) Volume 7 (1994) Volume 6 (1993) Volume 5 (1992) Volume 4 (1991) Volume 3 (1990) Volume 2 (1989) Volume 1 (1988) Khayyam Publishing, P.O. Box 429, Athens, Ohio 45701, USA Phone (740) 592-6136 email: khayyam@aftabi.com Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas. Instructions to Authors: Manuscripts should be typed on one side of 8.5 X 11 inch (21.5 X 28 cm) paper, double-spaced (including references), with wide margins. The author's name should be typed on the line below the title, and the affiliation and address should follow on the next line. Place any footnotes to the title at the bottom of page 1. Each paper requires a brief abstract not exceeding 150 words summarizing the techniques and main conclusions. AMS subject classifications must accompany all articles. They must be placed at the bottom of page 1 before any other footnotes. Each paper requires a separate page containing an abbreviated version of the title for the running head no more than 40 characters long, and the name and mailing address of the author to whom proofs should be sent. Equations should be centered with the number of the equation placed in parentheses at the right margin. Each figure is to be drafted in high contrast on a separate piece of white paper in a form suitable for photographic reproduction and reduction.

29. DIE Advances in differential equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on http://www.aftabi.com/ADE/ade.html

Advances in Differential Equations Editorial Board Volume 8 (2003) Volume 7 (2002) Volume 6 (2001) Volume 5 (2000) Volume 4 (1999) Volume 3 (1998) Volume 2 (1997) Volume 1 (1996) Khayyam Publishing, P.O. Box 429, Athens, Ohio 45701, USA Phone (740) 592-6136 email: khayyam@aftabi.com Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely , and of interest to a substantial number of mathematicians working in this area. Instructions to Authors: Manuscripts should be typed on one side of 8.5 X 11 inch (21.5 X 28 cm) paper, double-spaced (including references), with wide margins. The author's name should be typed on the line below the title, and the affiliation and address should follow on the next line. Place any footnotes to the title at the bottom of page 1. Each paper requires a brief abstract not exceeding 150 words summarizing the techniques and main conclusions. AMS subject classifications must accompany all articles. They must be placed at the bottom of page 1 before any other footnotes. Each paper requires a separate page containing an abbreviated version of the title for the running head no more than 40 characters long, and the name and mailing address of the author to whom proofs should be sent. Equations should be centered with the number of the equation placed in parentheses at the right margin. Each figure is to be drafted in high contrast on a separate piece of white paper in a form suitable for photographic reproduction and reduction.

30. S.O.S. Math Contains tutorials covering algebra, geometry, calculus, differential equations, matrices, and complex variables. Reviews the most important results, techniques and formulas. Presented in worksheet format and require active participation. Includes practice quizzes and forum board. http://www.sosmath.com/

Algebra Trigonometry Calculus Differential Equations ... CyberBoard Search our site! S.O.S. Math on CD Sale! Only $19.95. Works for PCs, Macs and Linux. Tell a Friend about S.O.S. Books We Like Math Sites on the WWW S.O.S. Math Awards ... Privacy Concerns? var version = 1.0; var version = 1.1; var version = 1.2; var version = 1.3; S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations! The perfect study site for high school, college students and adult learners. Get help to do your homework, refresh your memory, prepare for a test, .... Browse our more than 2,500 Math pages filled with short and easy-to-understand explanations - from simplifying fractions to the cubic formula , from the quadratic equation to Fourier series , from the sine function to systems of differential equations - this is the one stop site for your math needs. You want more? Check out our CyberExams to prepare for a test, or ask a question on our popular CyberBoard ! You can buy a personal copy of our site on CD, or browse our recommended book list Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

31. Journal Of Differential Equations Journal of differential equations The Journal of differential equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to http://rdre1.inktomi.com/click?u=http://www.apnet.com/www/journal/de.htm&y=0

32. Fortran Codes Ernst Hairer's collection of code for solving DEs. http://www.unige.ch/math/folks/hairer/software.html

Fortran and Matlab Codes If you have any problems with the file transfer, please, contact Ernst.Hairer (at) math.unige.ch We hope the programs will be of use for you and your group. We appreciate, if you communicate us your experiences (bad and good) with our codes. A testset of stiff differential equations with drivers for some of our codes is also at your disposal. Geometric Integrators (Structure-Preserving Algorithms) Symplectic methods for Hamiltonian systems and symmetric methods for reversible problems show an improved qualitative and quantitative behaviour, especially for long-time integrations. For a description see: E. Hairer, C. Lubich and G. Wanner (2002): Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential equations. Springer Series in Comput. Math., vol. 31 as well as the article E. Hairer and M. Hairer (2002): GniCodes - Matlab programs for geometric numerical integration. The tar file gnicodes.tar contains a directory with the following Fortran 77 codes (for unfolding the directory use the command tar xvf gnicodes.tar

33. Delta College Differential Equations Lab Home Page Delta College differential equations Mathematica Laboratory. http://calculus.sjdccd.cc.ca.us/ODE/ODE-h.html

34. SPRINT Modular generalpurpose package written in Fortran 77 for the numerical solution of systems of differential-algebraic equations and 1D partial differential equations. It is used at Shell Research Laboratories and at several UK, Europe and North American Universities, and it forms the basis of the underlying solver in the SPRINT2D and SPRINT3D software. http://www.scs.leeds.ac.uk/cpde/SPRINT1.html

SPRINT Software (Back to the CPDE Unit Home Page) Development of the original SPRINT (Software for PRoblems IN Time) software took place from 1982 to 1988 and was primarily funded by Shell Research at Thornton. SPRINT is a modular general-purpose package written in Fortran 77 for the numerical solution of systems of differential-algebraic equations and 1D partial differential equations. It is used at Shell Research Laboratories and at several UK, Europe and North American Universities, and it forms the basis of the underlying solver in the and software. A C version also exists. The philosophy behind the software is described in , the modified Gear's method integrator in , the new adaptive theta method in , and the improved differential-algebraic integrators in and . The new spectral method used in the spatial discretisation is described in , and the new finite difference discretisation in . Complete descriptions of the software and example applications, including examples with integro-differential equations and adaptive meshes are given in and . The SPRINT package is described in detail in The majority of the original SPRINT software has been implemented inside the NAG Fortran Library , in subchapters D02N and D03P (since Mark 14). The original was extended and re-written for the NAG Library as described in

35. Partial Differential Equation -- From MathWorld (1). in general, partial differential equations are much more difficult to solve analytically than are ordinary differential equations. http://mathworld.wolfram.com/PartialDifferentialEquation.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Differential Equations Partial Differential Equations Partial Differential Equation A partial differential equation (PDE) is an equation involving functions and their partial derivatives ; for example, the wave equation in general, partial differential equations are much more difficult to solve analytically than are ordinary differential equations . They may sometimes be solved using a characteristics Green's function integral transform Lax pair ... separation of variables , orwhen all else fails (which it frequently does)numerical methods such as finite differences Fortunately, partial differential equations of second-order are often amenable to analytical solution. Such PDEs are of the form Linear second-order PDEs are then classified according to the properties of the matrix as elliptic hyperbolic , or parabolic If is a positive definite matrix , i.e.

36. Weldon's Home Page Research focused on optimization, differential algebra equations, geographic information systems, biomedicine, environment applications and fuzzy industrial scheduling. University of Colorado at Denver. Page includes biography, hobbies, curriculum vitae, and publications. http://www-math.cudenver.edu/~wlodwick/

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37. Ordinary Differential Equation -- From MathWorld order (integrating factor) and secondorder (Sturm-Liouville theory) ordinary differential equations, and arbitrary ODEs with linear constant coefficients can http://mathworld.wolfram.com/OrdinaryDifferentialEquation.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Differential Equations Ordinary Differential Equations Ordinary Differential Equation An ordinary differential equation (frequently called an "ODE" or a "diffy Q") is an equality involving a function and its derivatives . An ODE of order n is an equation of the form where y is a function of x is the first derivative with respect to x , and is the n th derivative with respect to x An ODE of order n is said to be linear if it is of the form A linear ODE where is said to be homogeneous . Confusingly, an ODE of the form is also sometimes called "homogeneous." In general, an n th-order ODE has n linearly independent solutions. Furthermore, any linear combination of linearly independent functions solutions is also a solution. Simple theories exist for first-order integrating factor ) and second-order Sturm-Liouville theory ) ordinary differential equations, and arbitrary ODEs with linear constant

38. Solving DDEs With MATLAB Deals with the solution of delay differential equations with constant delays http://www.runet.edu/~thompson/webddes/

Solving DDEs with MATLAB L.F. Shampine Mathematics Department Southern Methodist University Dallas, TX 75275 lshampin@mail.smu.edu S. Thompson Radford University Radford, VA 24142 thompson@radford.edu As of MATLAB 6.5 (Release 13), is part of the official MATLAB release. The MathWorks web side provides documentation for the solver , as well as a tutorial on solving delay differential equations in MATLAB. For the convenience of people who are using an earlier release of MATLAB, below we provide the preliminary (and no longer maintained) version of dde23 as well as auxiliary functions for use with MATLAB prior to R13. We urge you to use the official version first included in R13 but as a temporary measure, the version below can be used with earlier releases. The information on this page deals with the solution of delay differential equations (DDEs) with constant delays using MATLAB . Included are a tutorial on using the MATLAB dde23 solver to solve DDES, a manuscript containing technical details for the solver, and a manuscript dealing with the event location procedures used in dde23. In addition, the necessary M-files for the solver as well as the M-files for the problems discussed in the tutorial are available. Please contact one of the authors if you experience any difficulties with the material on this page or if you have any questions, comments, or suggestions regarding the information on this page.

39. [math/9808130] Homological Methods In Equations Of Mathematical Physics These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and selfcontained exposition of the cohomological theories naturally related to partial differential equations. http://arxiv.org/abs/math.DG/9808130

Mathematics, abstract math.DG/9808130 From: Alexander Verbovetsky [ view email ] Date ( ): Mon, 31 Aug 1998 09:57:31 GMT (107kb) Date (revised v2): Mon, 21 Dec 1998 17:07:11 GMT (107kb) Homological Methods in Equations of Mathematical Physics Authors: Joseph Krasil'shchik Alexander Verbovetsky Comments: 150 pages, AmS-LaTeX 1.2 (based on LaTeX 2e), needs to run through LaTeX four times, no figures, Lectures given in August 1998 at the International Summer School in Levoca, Slovakia. Revised version 2 (Mon, 21 Dec 1998): misprints corrected, Definition 4.3 on page 70 changed Report-no: DIPS 7/98 Subj-class: Differential Geometry; Analysis of PDEs; Mathematical Physics; Exactly Solvable and Integrable Systems These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invariants of differential equations are discussed. The lectures contain necessary introductory material on the geometric theory of differential equations and homological algebra. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

40. Ciprian Tudor Laboratoire de Probabilites et Modeles Aleatoires, Universit© de Paris VI. Research interests Anticipating Stochastic Calculus; Fractional Brownian Motion; Mathematical Finance; Weak Convergence; Stochastic differential equations. http://pageperso.aol.fr/cipriantudor/

Accueil Loisirs et Sorties Divers - Passions BIENVENUE! WELCOME! BINE ATI VENIT! Page web de CIPRIAN A. TUDOR Laboratoire de Probabilites et Modeles Aleatoires Universite de Paris VI 4, place Jussieu 75252 Paris Cedex 05 France Email: tudor@ccr.jussieu.fr Phone: +33144277043 Fax: +33144277223 Research Interests: Anticipating Stochastic Calculus Fractional Brownian Motion Mathematical Finance Weak Convergence Stochastic Differential Equations Publications and accepted papers (with Samy Tindel and Frederi Viens Sharp Gaussian regularity on the circle and ... application to the fractional stochastic heat equation ", 2003, to appear in Journal of Functional Analysis. Martingale type stochastic calculus for anticipating integral processes to appear in Bernoulli. (with Frederi Viens Brownian sheet Electronic Journal of Probability, 2003 (8), paper 14, pag. 1-31. (with Xavier Bardina and Maria Jolis) " Weak convergence to the fractional Brownian sheet and other ... two-parameter Gaussian processes Statistics and Probability Letters, 2003, 65(4), pg. 317-329 (with Samy Tindel and Frederi Viens Stochastic evolution equations with fractional Brownian motion Probability Theory Related Fields, 2003, 127, pag.

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