1. S.O.S. Math - Differential Equations First Order differential equations. Linear Equations Separable Equations Qualitative Technique Slope Fields Equilibria and the Phase Line 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

2. Pauls Online Notes : Differential Equations Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes” they http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

MPBodyInit('DE_files') Paul's Online Math Notes Online Notes / Differential Equations You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material. Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book Chapter , and/or the Section link provided below. For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it. E-Book Basic Concepts Differential Equations (Math 3301) Here are my online notes for my differential equations course that I teach here at Lamar University.  Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations.  I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes.

3. MIT OpenCourseWare | Mathematics | 18.03 Differential Equations, Spring 2006 | H Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/CourseHome/

skip to content Home Courses Donate ... Mathematics Differential Equations 18.03 Differential Equations Spring 2006 Linear Phase Portraits Mathlet from the d'Arbeloff Interactive Math Project. (Image courtesy of Hu Hohn and Prof. Haynes Miller.) Course Highlights This course includes lecture notes assignments , and a full set of video lectures Course Description Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams. Special Features Complete video lectures Technical Requirements Special software is required to use some of the files in this course: .rm , and .jar Staff Instructors: Prof. Arthur Mattuck

4. SpringerLink Home - Main www.springerlink.com/openurl. asp?genre=journal issn=00122661 - Similar pages differential equations WelcomeThe Interactive differential equations (IDE) website is specifically designed for students taking a differential equations course. http://www.springerlink.com/openurl.asp?genre=journal&issn=0012-2661

5. Ordinary Differential Equation -- From Wolfram MathWorld Simple theories exist for firstorder (integrating factor) and second-order (Sturm-Liouville theory) ordinary differential equations, and arbitrary ODEs http://mathworld.wolfram.com/OrdinaryDifferentialEquation.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Ordinary Differential Equation An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives . An ODE of order is an equation of the form where is a function of is the first derivative with respect to , and is the th derivative with respect to Many ordinary differential equations can be solved exactly in Mathematica using DSolve eqn y x ], and numerically using NDSolve eqn y x xmin xmax An ODE of order 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 th-order ODE has 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 coefficients can be solved when they are of certain factorable forms. Integral transforms such as the

6. Math Forum: Differential Equations The best Internet resources for differential equations classroom materials, software, Internet projects, and public forums for discussion. http://mathforum.org/differential/differential.html

Differential Equations Back to Math by Subject Math by Subject K12 Topics algebra arithmetic calculus discrete math geometry pre-calculus prob/stat Advanced Topics analysis calculus diff. equations game theory discrete math geometry (coll.) geometry (adv.) linear algebra modern algebra num. analysis Internet Resources for Differential Equations See also the Math Forum's Internet Mathematics Library: Differential Equations. Classroom materials for teachers and students Selected differential equations Internet resources for the classroom including activities and interactive resources. Software for differential equations Publicly available software and publishers online. Internet projects Activities for students and lovers of differential equations. Public forums Mailing lists and newsgroups sponsored by the Forum and others where mathematicians, teachers, and students trade ideas about differential equations. Home The Math Library Quick Reference Search ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Drexel School of Education

7. Differential Equations Calculator differential equations Calculator. Main Page Calculus Calculus, 3Dimensional differential equations Enter equations here http://www.compute.uwlax.edu/diff_eq/

Differential Equations Calculator Main Page Calculus Calculus, 3-Dimensional Differential Equations ... Expert Two ODE Single ODE Matrix for 2x2 system Enter equations here: Initial Conditions: Plot Range: (USE * FOR MULTIPLICATION!) Independant Variable = Min x: Max x: Min y: Max y: Lines Arrows None Number of field points: If you have comments or questions about this page, please email Dr. Robert H. Hoar or Matt Bedalov

8. Differential Equations This equation would be described as a second order, linear differential equation with constant coefficients. It is second order because of the highest order http://hyperphysics.phy-astr.gsu.edu/Hbase/diff.html

Differential Equations A differential equation is an equation which contains the derivatives of a variable, such as the equation Here x is the variable and the derivatives are with respect to a second variable t. The letters a, b, c and d are taken to be constants here. This equation would be described as a second order linear differential equation with constant coefficients. It is second order because of the highest order derivative present, linear because none of the derivatives are raised to a power, and the multipliers of the derivatives are constant. If x were the position of an object and t the time, then the first derivative is the velocity , the second the acceleration , and this would be an equation describing the motion of the object. As shown, this is also said to be a non-homogeneous equation, and in solving physical problems, one must also consider the homogeneous equation. Index HyperPhysics HyperMath Differential equations ... Go Back First Order Homogeneous DE A first order homogeneous differential equation involves only the first derivative of a function and the function itself, with constants only as multipliers. The equation is of the form

9. Differential Equations Notes Postscript notes on various topics in differential equations by Bruce Ikenaga. http://marauder.millersville.edu/~bikenaga/diffeq/deqnote.html

Differential Equations Notes These are links to PostScript files containing notes for various topics in differential equations. How do I view/print the notes? How may I use/distribute the notes? How did you write them? intro.ps (464K, 4 pages): Introduction to differential equations. 1stord.ps (382,730 bytes, 9 pages): First-order linear equations. sepvar.ps (91K, 4 pages): Separation of variables. exist.ps (92K, 2 pages): Existence and uniqueness for first-order equations. onetank.ps (29K, 2 pages): Tank problems. logistic.ps (66K, 2 pages): Logistic growth. exact.ps (44K, 4 pages): Exact equations and integrating factors. homogen.ps (50K, 5 pages): Homogeneous equations. bern-ric.ps (40K, 3 pages): Bernoulli equations and Riccati equations. miscsol.ps (47K, 5 pages): Review of elementary solution methods. constco.ps (69K, 6 pages): Linear equations with constant coefficients. indep.ps (66K, 6 pages): Linear independence and the Wronskian. redord.ps (44K, 4 pages): Reduction of order. undet.ps (65K, 7 pages):

10. BU Differential Equations Project Teaching differential equations With a Dynamical Systems Viewpoint By Paul Blanchard. College Mathematics Journal, Volume 25, no. 5, November, 1994, pp. http://math.bu.edu/odes/

The Boston University Ordinary Differential Equations Project Project Directors: Paul Blanchard Robert L. Devaney Glen R. Hall e-mail: odes@math.bu.edu This project, originally funded by two grants from the National Science Foundation, promotes the use of ideas from the modern theory of dynamical systems in the traditional sophomore-level course in differential equations. Qualitative, analytic, and numerical approaches are stressed throughout the course. We have written a textbook published by Brooks/Cole that supports our approach, and occasionally we conduct workshops at various sites around the country. Please note: Our publisher is Brooks/Cole Publishing Co., a division of Thomson Learning. To contact Brooks/Cole for faculty support, call 800-423-0563 ( ISBN numbers and information about ancillaries Available at this site: Upcoming Workshops and Talks None currently scheduled. About the text Table of Contents Faculty Support and Ancillary Material How to obtain instructor's manual, student solutions manual, desk copies, etc. Spanish Edition Who are we?

11. MathPages: Calculus And Differential Equations Kevin Brown s compilation of postings including many topics in differential equations. http://www.mathpages.com/home/icalculu.htm

Calculus and Differential Equations The Laplace Equation and Harmonic Functions Fractional Calculus Analytic Functions, The Magnus Effect, and Wings Fourier Transforms and Uncertainty ... Math Pages Main Menu

12. MathHelp Notebook On Differential Equations If you feel confident with differential equations already, then feel free to skip to the exit quiz at the end. It is very important that you practise using http://www.ucl.ac.uk/Mathematics/geomath/level2/deqn/MHde.html

13. Difference Equations To Differential Equations By Dan Sloughter. Published in PS/PDF with applets under GPL. http://math.furman.edu/~dcs/book/

Difference Equations to Differential Equations An introduction to calculus Each section of the text is in Portable Document Format (PDF). PDF viewers are available here and here A PostScript version may be found here (the old homepage). A mirror for this site is available here Difference Equations to Differential Equations was written with the help of Tex DVIPS xdvi PDFTeX ... Acrobat Reader ® and Mathematica A companion multi-variable calculus text, The Calculus of Functions of Several Variables , is available here For an alternative introduction to calculus, see Yet Another Calculus Text Answers for selected problems are available here Send e-mail to Dan Sloughter to report any errors. Chapter 1: Sequences, limits, and difference equations Calculus: areas and tangents Applet: Area of a circle Applet: Tangent line for a parabola Sequences The sum of a sequence Difference equations ... Nonlinear difference equations Chapter 2: Functions and their properties Functions and their graphs Trigonometric functions Applet: Square wave approximation Applet: Sound wave approximation Limits and the notion of continuity Continuous functions Some consequences of continuity Chapter 3: Best affine approximations Best affine approximations Applet: Affine approximations Best affine approximations, derivatives, and rates of change

14. Journal Of Differential Equations - Elsevier The Journal of differential equations is concerned with the theory and the application of differential equations. The articles published are addressed not http://www.elsevier.com/locate/jde

Home Site map Elsevier websites Alerts ... Journal of Differential Equations Journal information Product description Editorial board Audience Abstracting/indexing ... Special issues and supplements Subscription information Bibliographic and ordering information Conditions of sale Dispatch dates Journal-related information Contact the publisher Impact factor Most downloaded articles Other journals in same subject area ... Select your view JOURNAL OF DIFFERENTIAL EQUATIONS Editors-in-Chief: S.-N. Chow, J.K. Hale, J. Mallet-Paret, K. Mischaikow See editorial board for all editors information Online Submission Description The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: ISSN: 0022-0396 Imprint: ACADEMIC PRESS Subscriptions for the year 2008, Volumes 244-245, 24 issues Institutional online access: ScienceDirect eSelect For purchase of online access to this journal on ScienceDirect.

15. Modules For Differential Equations SecondOrder Linear Homogeneous differential equations with Constant Coefficients Spring Motion Forced Spring Systems, I Matrix Operations 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 ... The van der Pol System Return to CCP Homepage Return to CCP Materials modules at math.duke.edu

16. Differential Equations differential equations, a translation of Differentsial nye uravneniya, is devoted exclusively to differential equations and the associated integral http://www.maik.ru/cgi-perl/journal.pl?lang=eng&name=difeq&page=main

17. Project Links | Differential Equations Index This module on lake pollution is about using differential equations to model lake pollution. To model lake pollution can be complicated, because there are 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).

18. Differential Equations - Ordinary Differential Equations Journals, Books & Onlin differential equations Dynamical Systems Diff. Equations. differential equations, a translation of Differentsial nye Uravneniya is devoted exclusively http://www.springer.com/west/home/math?SGWID=4-10042-70-35524520-0

19. Differential Equations differential equations provide the medium for the interaction between mathematics (especially calculus) and various branches of science and engineering. http://www.physics.upenn.edu/courses/gladney/mathphys/java/sect2/subsubsection2_

Back to Contents! Next: The Growth of Populations Up: Describing How Things Change Previous: Derivatives at Work Differential Equations Simulation of photons from a laser interacting with atoms The rate for synthesis of ammonia from nitrogen and hydrogen can be determined from the solution of differential equations Differential equations provide the medium for the interaction between mathematics (especially calculus) and various branches of science and engineering. The physicist, chemist, biologist, engineer, or social scientist models a process with a differential equation and then turns the equation over to the mathematician who tries to provide a solution which results in a complete description of the original process. Differential equations come in all levels of complexity and even today there is active mathematical research in differential equations. In this section, we will look at a couple of the simplest, yet most important, differential equations. Radioactive decay: Over a given time interval, each atom in a sample of a radioactive element has the same (usually fairly or extremely small) chance for disintegration as any other. Thus, if we have a quantity

20. Electronic Journal Of Differential Equations Full text available in DVI, PDF, PS and TeX formats. Searchable index. http://ejde.math.txstate.edu/

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