|
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines. Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations.Differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some continuously changing quantities (modelled by functions) and their rates of change (expressed as derivatives) is known or postulated. This is well illustrated by classical mechanics, where the motion of a body is described by its position and velocity as the time varies. Newton's Laws allow one to relate the position, velocity, acceleration and various forces acting on the body and state this relation as a differential equation for the unknown position of the body as a function of time. In many cases, this differential equation may be solved explicitly, yielding the law of motion. An example of modelling a real world problem using differential equations is determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is constant but air resistance is proportional to the ball's velocity. This means the ball's acceleration, which is the derivative of its velocity, depends on the velocity. Finding the velocity as a function of time requires solving a differential equation. Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions, functions that make the equation hold true. Only the simplest differential equations admit solutions given by explicit formulas. Many properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy. From Wikipedia under the
GNU Free Documentation License  cupe3913.on.ca admin Fri, 17 Jul 2009 16:08:45 GM PostCategoryIcon Posted in Postings, School of Engineering | PostTagIcon Tags: expire 07/27/2009. MATH-2270 Applied . Differential Equations. Unit 1 · Honduran trade unions & allies blockade highways in opposition to military coup ...  moreintelligentlife.com Emily Bobrow hu, 28 May 2009 16:50:38 GM What an exciting promise Steven Strogatz seemed to offer with "Loves Me, Loves Me Not (Do the Math". He sets out to examine love affairs "mathematically", suggesting that . equations. that summarise specific romantic.  wseas-athens-wseas.blogspot.com Malaysia Sun, 02 Aug 2009 00:48:00 GM Keywords: Nonlinear, Algebraic, . Differential. , . Equations. , Witch, Multiple-optima, Functions, Programming, Boolean extension of the file: .doc. Special (Invited) Session: Organizer of the Session: How Did you learn about congress: ... From Google Blog Search: "Differential Equations"  news.google.com Science Daily (press release) In the world's first published mathematical model of tissue transfer, mathematicians have shown that they can use differential equations to determine which ... and more » news.google.com Examiner.com Ito's lemma and so forth as well as ordinary calculus, differential equations , numerical methods, linear algebra and possibly a little computational ... news.google.com Gazeta Universytecka Rados aw C zaja: Differential Equations with Sectorial Operator, bibliogr., aneksy, 15 z literaturtoznawstwo. Nadzieje i zagro enia. ... From Google News Search: "Differential Equations" Do you have any tips for someone taking differential equations? Q. I'm taking a differential equations class over the summer and things are going by quickly. I'm not doing too well. Do you have any tips besides answering the qustions in the book? Are there any "eureka" moments that I should comprehend before I continue in my struggle? Asked by Alwaysundersiege - Thu Jun 15 01:17:51 2006 - - 4 Answers - 1 Comments A. Sorry to say but there are no eureka moments in mathematics. There is only a couple of tips that I can give you: practice and practice smart. And focus and pay attention at class. When you practice though, dont practice using just one question book. Try different ones and try different levels of difficulty. The thing about academical mathematics is that the more you are experienced with many questions, the better you become. If you encounter a question that you cant do, ask somebody who can. Pay attention to the way of solving rather than the answer itself. All the best. Love+peace Answered by cedric t - Thu Jun 15 01:24:29 2006 How do you solve differential equations of the form dv/dt=f(t)+g(v)? Q. The specific equation I'm trying to solve is: dv/dt = ae^(bt) - cv where a, b and c are positive constants. I know how to solve differential equations of the form dv/dt = f(t)g(v) but not dv/dt = f(t) + g(v). Asked by Mark R - Fri Sep 7 13:42:35 2007 - - 2 Answers - 0 Comments A. dv/dt + cv = ae^(bt) this is of the type dv/dt + P(t)v = Q(t) multiply through by e^( P(t)dt), in this case e^( cdt) = e^(ct) e^(ct).dv/dt + cv.dv/dt = ae^(bt).e^(ct) the LHS is then an exact derivative d/dt(ve^(ct)) = ae(bt + ct) integrating both sides ve^(ct) = ae(bt + ct)/(b + c) + K v = ae^(bt) / (b + c) + Ke(-ct) Answered by fred - Sat Sep 8 09:33:53 2007 I need help with differential equations?
Q. I'm having trouble with the introductory topic of differential equations. I know the calculus behind it, but I seem to be having trouble actually solving them. I think I really just need practice. Could anyone help me with learning how to solve them? Thanks in advance! Asked by Sarah G - Mon Mar 16 16:49:22 2009 - - 1 Answers - 0 Comments From Yahoo Answer Search: "Differential Equations"
See also:
|
Weak and Variational Forms of Poisson's Equation
Differential Equations in a Nutshell
The Polar Representation Theorem