81. Multivariable Calculus Review quizzes for calculus, differential equations, linear algebra and other advanced math fields. http://www.math.ucla.edu/~ronmiech/

Pic 20 Java Applets Calculus 131A Problems ... Sample Final 31A Questions or comments? Send them to rjm@math.ucla.edu

82. Research In Differential Equations At Rice University differential equations. Faculty. F. Reese Harvey; Several complex variables,partial differential equations, differential geometry. http://math.rice.edu/People/diffeq.html

Differential Equations Faculty Robin Forman ; Relationships between topology and analysis, with an emphasis on ideas from mathematical physics. Robert Hardt ; Geometric measure theory, partial differential equations, continuum mechanics. F. Reese Harvey ; Several complex variables, partial differential equations, differential geometry. Frank Jones ; Partial differential equations, real analysis. John C. Polking ; Partial differential equations, several complex variables. Stephen Semmes ; Harmonic analysis, complex variables, partial differential equations, differential geometry. The Department People Graduate Study Links

83. Sturm A biography of the Mathematican who worked on differential equations and created the form now call SturmLiouville equations. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Sturm.html

Born: 22 Sept 1803 in Geneva, Switzerland Died: 18 Dec 1855 in Paris, France Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Sturm came from a Protestant family and, in order to learn German, he attended the local Lutheran church where sermons were preached in that language. When Sturm was sixteen years old his father died and he changed tack in his academic studies, leaving the humanities and taking up the study of mathematics. He was taught mathematics at Geneva Academy by Simon Lhuilier in 1821 and immediately Lhuilier recognised the mathematical genius in Sturm. However, Lhuilier was over seventy years of age and close to retiring at this time so it was his successor Jean-Jacques Schaub who inspired Sturm. Schaub did more than teach Sturm mathematics for he supported him financially at the Academy. Sturm's family had been left in considerable financial difficulties on the death of his father so the financial assistance allowed Sturm to continue with his education. Gergonne 's In Paris he was introduced into the scientific circles by the family. Sturm wrote to his friend Colladon (see [1]):-

84. Online And Private Math, Physics, Engineering, English Tutor In Redwood City & S Offers online and local private tutoring for elementary school to college level students. Subjects include algebra, geometry, trigonometry, precalculus, calculus, differential equations, electrical engineering, and elementary physics. Private tutoring is available in Redwood City, California area. Page includes contact information. http://www.askatutor.net/

Welcome to Ask A Tutor Net Online and Private Tutors - Elementary School Through College Level Students Welcome Knowledge Excellence Empowerment Our Service Online Tutoring Private Tutoring Test Preparation ... Become a Private Tutor in your Area Download Example Problems (coming soon) Our Service As online and private tutors for elementary school to college level students, we, at Ask A Tutor dot Net , perform quality tutoring in mathematics, elementary physics, electrical engineering, and/or English courses. We accept students on a single or reoccurring basis. What Students and Parents are Saying Subjects Tutored Math English Sciences Engineering Basic Math Composition Elementary Physics Circuits and Devices Algebra Grammar Biology Statics Pre Algebra Mechanics General Sciences Geometry Spelling Trigonometry Outlining Pre Calculus Sentences Calculus I, II, III Technical Writing Differential Equations Linear Algebra Finite Math Online Tutoring manrao@askatutor.net

85. (Germany) Universität Erlangen-Nürnberg DIME Project Data Local Iterative Methods for the Efficient Solution of Partial differential equations. People, publications, software. http://wwwbode.cs.tum.edu/Par/arch/cache/

86. The 2002 UAB International Conference On Differential Equations And Mathematical Birmingham, Alabama, USA; 2630 March 2002.Category Science Math differential equations Events Past Events...... The 2002 UAB International Conference on differential equations andMathematical Physics Birmingham, Alabama March 2630, 2002. Talks http://www.math.uab.edu/uab02/

The 2002 UAB International Conference on Differential Equations and Mathematical Physics Birmingham, Alabama March 26-30, 2002 Talks of 25 minutes in length in all areas of differential equations and mathematical physics are invited. An online registration form is available here (the deadline is March 1, 2002). Please visit this site for updates, or send us an email if you have any questions. Click here to put yourself on the mailing list (registering automatically puts you on the mailing list). Program Plenary Speakers M. Aizenman, Princeton University J. Glimm, SUNY at Stony Brook S. Jitomirskaya, UC Irvine A. Laptev, KTH, Stockholm J. Lebowitz, Rutgers University E. Lieb, Princeton University T.-P. Liu, Stanford University and Academia Sinica (Taiwan) C.-A. Pillet, Univ. de Toulon, CPT-CNRS/FRUMAM R. Weder, UNAM, Mexico City General Sessions General sessions will be open for registered participants. Click here to access our online registration form (the deadline is March 1, 2002). Focus Sessions Talks in the Focus Sessions are by invitation of the organizers (listed in parentheses). Conservation Laws (G.-Q. Chen, Northwestern University)

87. Horwitz, Alan Professor of mathematics at the Delaware County Campus of Penn State University in Media, PA. His research interests polynomial interpolation, numerical integration, algebraic differential equations, means, and ratios of polynomials with real zeros. http://www.math.psu.edu/horwitz/

88. FemLego Finite Element simulations using symbolic computing. Presented are a set of Maple procedures and Fortran subroutines that can be used to build complete Fortran simulation codes for partial differential equations, with the entire problem definition done in Maple. Examples and Downloads available. http://www.mech.kth.se/~gustava/femLego

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89. Department Of Scientific Computing (Director: Prof. Dr. Peter Zinterhof) Department of Scientific Computing. Research areas cover high dimensional number theoretic numerics, image and video processing, parallel processing, automated theorem proving and artificial intelligence, foundations of abstract signal processing, computer science and society, theoretical physics, integral and differential equations, and neural networks. http://www.cosy.sbg.ac.at/sc/

News Home Department Info Faculty and Staff Research and Projects Information for Students ... secure connection Welcome to the Department of Scientific Computing URL: http://www.cosy.sbg.ac.at:80/sc/index.html - last modified: Tuesday, 18-Mar-2003 10:17:28 CET webmaster contact:

90. Math Unit III: More On The Derivative And Differential Equations Exact definition of derivation and calculating the relationship of derivatives of related functions. http://dept.physics.upenn.edu/courses/gladney/mathphys/subsection3_1_1.html

Back to Contents! Next: Force Revisited Up: CONSERVING EQUATIONS Previous: CONSERVING EQUATIONS Math Unit III: More on the derivative and differential equations In the last unit, we discussed how mathematicians and scientists deal with quantities that change in ways other than linearly. The key idea turns out to be the rate of change of the quantity. The lowbrow way to measure the rate of change is to compute the average rate of change over a small interval. The high-class way to talk about change is to try to compute the derivative , or instantaneous rate of change In real-world situations, when one deals with measured data, it is often the case that the data has been measured only for certain specific values of the independent variable. Then, one can only compute average rates of change between the data points. But in mathematics, when one deals with abstractly-defined functions, it is possible to compute derivatives. Often, mathematical models are developed using derivatives, predictions are made based upon these mathematical models, and then experimental results are compared to the predictions to see how well the models reflect reality. 1. Review and extensions

91. Arieh Iserles University of Cambridge. Research interests in numerical ordinary differential equations; also functional equations, approximation theory, special functions, numerical partial differential equations, nonlinear algebraic equations and nonlinear dynamical systems. http://www.damtp.cam.ac.uk/user/na/people/Arieh/

92. Midwest Partial Differential Equations Seminar Spring 2001 Midwest PDE at Indiana University; 78 April 2001.Category Science Math differential equations Events Past Events......Midwest Partial differential equations Seminar, a semiannual meetingon recent developments in partial differential equations. http://www.math.uic.edu/~lewis/midwpde/

Midwest Partial Differential Equations Seminar The Midwest Partial Differential Equations Seminar Home Page has moved to http://www.math.uic.edu/midwpde/index.htm The Midwest Partial Differential Equations Seminar is partially funded by a grant from the National Science Foundation. Last modified Wednesday, December 10, 1997 10:19:36 AM, by jlewis@uic.edu

93. A Matlab Differentiation Matrix Suite Functions for solving differential equations by the spectral collocation (a.k.a. pseudospectral) method. http://ucs.orst.edu/~weidemaj/differ.html

A Matlab Differentiation Matrix Suite This is a software suite designed for MATLAB 5 consisting of seventeen functions for solving differential equations by the spectral collocation (a.k.a. pseudospectral) method. It includes functions for computing differentiation matrices of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. It also includes FFT-based routines for Fourier, Chebyshev and sinc differentiation. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. In the accompanying paper it is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability. Paper Download the compressed version of the paper (paper.ps.gz, gzipped PostScript 0.4MB), or the uncompressed version (paper.ps, PostScript 1.2MB). Functions We have made every effort to test these functions. However, NO GUARANTEES are made about their validity. Please contact us at

94. Interactive Differential Equations http://www.aw.com/ide/

95. Linear Methods Textbook suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations by Evans M. Harrell II and James V. Herod. HTML, RTF and PDF with Maple and Mathematica worksheets. http://www.mathphysics.com/pde/

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96. Modules For Differential Equations Numerical Solutions of differential equations, World Class Sprints, SecondOrderLinear Homogeneous differential equations with Constant Coefficients, http://www.math.duke.edu/education/ccp/materials/diffeq/

Click on a module name below to see an OVERVIEW of its contents. Modules Helper Application Tutorial Numerical Solutions of Differential Equations World Class Sprints Logistic Growth Model Harvesting Fish Harvesting: Effort and Yield Predator-Prey Models Battle of the Beetles Lotka-Volterra Predation Three-Species Food Web Second-Order Linear Homogeneous Differential Equations with Constant Coefficients Spring Motion Forced Spring Systems, I Forced Spring Systems, II Oscillation and Comparison Linear and Nonlinear Oscillators Matrix Operations Eigenvalues and Eigenvectors Trajectories of Linear Systems The Pendulum ... The van der Pol System Return to CCP Homepage Return to CCP Materials modules@math.duke.edu

97. Calculus Tutorial - Harvey Mudd College Mathematics Department Tutorials covering precalculus, calculus, multivariable calculus, linear algebra and differential equations. http://www.math.hmc.edu/calculus/

Visit the HMC Math Department! Visit the HMC Math Department!

98. Topics In Differential Equations Topics in differential equations. Contents. R4 Text Version (Worksheet)First Order differential equations (tutorials). A look at http://calclab.math.tamu.edu/docs/math308/topics.html

Topics in Differential Equations Contents Introductory Material First Order Differential Equations Applications of First Order Differential Equations Numerical Methods for First Order Differential Equations ... Notes on these worksheets Introductory Material tutorials DE quick tour for Maple A first day demo of using dsolve, odeplot, DEplot1, etc. Using Maple for DE Example of using Maple to analyze two nonlinear DEs Intro to DEs on Maple Several DEs solved and checked w/ Maple. Maple V R.3 Maple V R.4 Using dsolve to find exact solutions of many differential equations or systems of equations, with or without initial conditions.Intro to DEs on Maple. Maple V R3: Text Version Worksheet Maple V R4: Text Version Worksheet First Order Differential Equations tutorials A look at the separable DE dy x^2 = - dx 1-y^2 Solutions are found by finding the integral curves. Maple Code to determine whether or not a DE is separable. Solving y'=x^2+y^2 Three different methods of solving this: exactly, graphically, numerically. An Solving y'=sin(x) + sin(y) Example of a DE Maple cannot solve. DEplot is used to figure out what is happening.

99. Liouville The mathematician who developed SturmLiouville differential equations. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Liouville.html

Joseph Liouville Born: 24 March 1809 in Saint-Omer, France Died: 8 Sept 1882 in Paris, France Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Joseph Liouville Gergonne 's Journal he proved some geometrical results which he wrote up as papers although they were never published. Liouville entered the Ecole Polytechnique in 1825 and attended 's in session 1825-26. He also attended courses by Arago at the Ecole Polytechnique as well as a second course by Cauchy 's courses, it is clear that Cauchy must have had a strong influence on him. Liouville graduated in 1827 with de Prony and Poisson among his examiners. partial differential equations and the theory of heat. In 1831 Liouville was appointed to his first academic post, as assistant to Claude Mathieu In 1836 Liouville founded a mathematics journal . This journal, sometimes known as Journal de Liouville , did much for mathematics in France throughout the 19th century. Liouville had already gained an international reputation with papers published in Crelle 's Journal but at the same time the quality of Crelle 's Journal made him aware of deficiencies in the avenues for mathematical publications which there were in France. Certainly he was unhappy with the style of the Paris Journals for he wrote in 1836:-

100. Project Links | Differential Equations Index differential equations Modules. Full Metadata . Lake Pollution. v, This moduleon lake pollution is about using differential equations to model lake pollution. http://links.math.rpi.edu/webhtml/DEindex.html

Differential Equations Modules To find out more about what the version numbers mean, click on any of the indicators. Down to the Mechanical Oscillations Modules Boundary Value Problems for ODEs writeVersionGraphic("BoundaryValue"); v writeVersionNumber("BoundaryValue"); Introduction to boundary value problems and eigenvalue problems for ODEs in the context of buckling,heat conduction/diffusion,vibration problems. Intro to Fourier method. Authors: Richard Weinacht, George Hsiao, B. Lenhoff, Andrew Zydney, Jack R. Vinson Keywords: differential equations, heat transfer, diffusion, strength of materials, buckling, heat conduction, vibrating beam, vibrating string, BVP, eigenvalue Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ] Continuously Stirred Reactor writeVersionGraphic("CSTR"); v writeVersionNumber("CSTR"); The most important unit operation in a chemical process is generally a chemical reactor. Chemical reactions are either exothermic (release energy) or endothermic (require energy input) and therefore require that energy either be removed or added to the reactor for a constant temperature to be maintained. Exothermic reactions are the most interesting systems to study because of potential safety problems (rapid increases in temperature, sometimes called "ignition" behavior) and the possibility of exotic behavior such as multiple steady-states (for the same value of the input variable there may be several possible values of the output variable). In this module we consider a perfectly mixed, continuously stirred tank reactor (CSTR).

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