Math Websites of the week for Math 302 (Differential Equations)

Each week during the semester, we will introduce one or more websites which will be useful and
fun for your Math 302 course.

Week 0: If you need to do some calculus calculation, you will find this website helpful

               Mathematical Toolkit developed in Vanderbilt University.
               The link for the whole project is  MathServ http://math.vanderbilt.edu/mathserv/index.html
               and you will mostly use Calculus Toolkithttp://mss.math.vanderbilt.edu/~pscrooke/toolkit.html
                    Definite Integral http://mss.math.vanderbilt.edu/~pscrooke/MSS/definiteintegral.html
                    Antiderivative http://mss.math.vanderbilt.edu/~pscrooke/MSS/antiderivative.html
                    Numerical Integration http://mss.math.vanderbilt.edu/~pscrooke/MSS/numintegration.html
                    (midpoint, trapezoid, and Simpson)
                        Calculate partial fraction of a rational function
                   http://mss.math.vanderbilt.edu/~pscrooke/MSS/partialfract.html

Week 1Malthus' Essay on population "An Essay on the Principle of Population"
                   http://www.ac.wwu.edu/~stephan/malthus/malthus.0.html
              Interactive Differential Equations http://www.aw-bc.com/ide/index.html
              Growth and decay: http://www.aw-bc.com/ide/Media/JavaTools/grwthdcy.html
              Logistic Growth: http://www.aw-bc.com/ide/Media/JavaTools/poplgstc.html
              Logistic Phase Line: http://www.aw-bc.com/ide/Media/JavaTools/poplgphs.html

              Some links about population models:

A 1999 CNN article on the carrying capacity of the Earth
The U.S. Census Bureau announced new population projections on Thursday, January 13, 2000.
The International Society of Malthus (include hid original paper: Essay on the Principle of Population (1798))
Biography of Pierre François Verhuls
Boom and Bust Mathematics (an article about Verhulst's model)
The Struggle for Existence - A Classic of Mathematical Biology and Ecology by G.F. Gause (1934)
Week 2:   Dfield program online Java version http://math.rice.edu/~dfield/dfpp.html
              MathServ DE Toolkit  http://mss.math.vanderbilt.edu/~pscrooke/detoolkit.html
              Drawing a Direction Field  http://mss.math.vanderbilt.edu/~pscrooke/MSS/tangentfield.html
                  Euler's Method   http://mss.math.vanderbilt.edu/~pscrooke/MSS/euler.html
              Solve a Separable Equation  http://mss.math.vanderbilt.edu/~pscrooke/MSS/sepode.html
              Illustration of Euler's method: http://www.aw-bc.com/ide/Media/JavaTools/nmthtmst.html

Week 3: Saddle-Node Bifurcation Tool http://www.aw-bc.com/ide/Media/JavaTools/bf1dsdnd.html
             Transcritical Bifurcation Tool  http://www.aw-bc.com/ide/Media/JavaTools/bf1dtrcr.html
             Pitchfork Bifurcation: Supercritical Tool  http://www.aw-bc.com/ide/Media/JavaTools/bf1dptsp.html
             Pitchfork Bifurcation: Subcritical Tool   http://www.aw-bc.com/ide/Media/JavaTools/bf1dptsb.html
 

Week 4: Solve a Linear Equation http://mss.math.vanderbilt.edu/~pscrooke/MSS/linode.html

Week 5Vector Fields Tool http://www.aw-bc.com/ide/Media/JavaTools/vctfield.html
              Two Dimensional Equations Tool http://www.aw-bc.com/ide/Media/JavaTools/twoddfeq.html
              Lotka-Volterra Tool http://www.aw-bc.com/ide/Media/JavaTools/popltkvl.html
              Simple Harmonic Oscillator Tool http://www.aw-bc.com/ide/Media/JavaTools/smpharos.html
              Romeo and Juliet Tool http://www.aw-bc.com/ide/Media/JavaTools/romejuli.html

Week 6 Eigen Engine Tool  http://www.aw-bc.com/ide/Media/JavaTools/eignengn.html
             Parameter Path Animation Tool http://www.aw-bc.com/ide/Media/JavaTools/lnclppan.html
             Parameter Plane Input Tool http://www.aw-bc.com/ide/Media/JavaTools/lnclppln.html
             Matrix Element Input Tool http://www.aw-bc.com/ide/Media/JavaTools/lnclmtrx.html
             Four Animation Paths Tool http://www.aw-bc.com/ide/Media/JavaTools/lncl4pth.html

Week 7:

Week 8: Mass and Spring Tool
            Damped Vibrations: Energy Tool 
            Critical Damping Tool  http://www.aw-bc.com/ide/idefiles/media/JavaTools/vibecrit.html

Week 9:  Damped Forced Vibrations Tool http://www.aw-bc.com/ide/idefiles/media/JavaTools/vibefdmp.html
              

Week 10: Competitive Exclusion Tool http://www.aw-bc.com/ide/idefiles/media/JavaTools/popcmpex.html
               Forced Damped Pendulum Tool  http://www.aw-bc.com/ide/idefiles/media/JavaTools/pndfrcph.html
               Lorenz Equations http://www.aw-bc.com/ide/idefiles/navigation/toolindexes/27.htm#27
               Math's Wild-And-Crazy Guy (An article on Washington Post about a mathematician of Chaos)
               http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A15111-2003Jan5&notFound=true
 

Week 11: Pendulums Tool http://www.aw-bc.com/ide/idefiles/media/JavaTools/pndulums.html
              Hamilton's equation http://mathworld.wolfram.com/HamiltonsEquations.html
              A new solution to the three body problem - and more http://www.ams.org/featurecolumn/archive/orbits1.html
              How Pendulum Clocks Work http://home.howstuffworks.com/clock.htm
              Galileo's Pendulum Experiments http://es.rice.edu/ES/humsoc/Galileo/Student_Work/Experiment95/galileo_pendulum.html
 

Week 12: Laplace: Definition Tool http://www.aw-bc.com/ide/Media/JavaTools/lapdefin.html
               Laplace: Transformer Tool http://www.aw-bc.com/ide/Media/JavaTools/laptrans.html
               Laplace: Shifting Theorem Tool  http://www.aw-bc.com/ide/Media/JavaTools/lapshthm.html
               Laplace: Shift and Step Tool  http://www.aw-bc.com/ide/Media/JavaTools/lapshstp.html
               Laplace: Delta Function Tool  http://www.aw-bc.com/ide/Media/JavaTools/lapdelta.html


Created by Junping Shi, August 26th, 2003, updated August 21st, 2004
Any comments? send to shij@math.wm.edu