Math Websites of the week

Each week during the semester, we will introduce one or more websites which will be useful and
fun for your Math 112 course.

Week 1Here are some weblinks which calculate integrals
                Riemann Sums  http://mss.math.vanderbilt.edu/~pscrooke/MSS/rs.html
                   (Left, right-endpoint sums, midpoint rule)
                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)
               All these webpages are parts of a 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

               An alternate link for antiderivative is The Integrator  http://integrals.wolfram.com/
                 All links above are engined by Mathmatica, a commercial software.
                 Another set of Java Applets is based on Maple, see MapleNet - Tutorial Applets
                http://maplenet.maplesoft.com/maplets/
                (they seem slow and hard to load, but give better results)

               A story of Richard Feynmann and Logarithm http://faculty.rmwc.edu/tmichalik/feynman.htm
               or here http://www.craigr.com/books/surely.htm

Week 2Volume of solid of revolution

         Visualization of solid of revolution (disk and washer method)
         http://archives.math.utk.edu/visual.calculus/5/volumes.5/index.html
        Maple code for animation of solid of revolution
            http://www.jcu.edu/math/ictcm99/animations/Solid.html
        Visualization of solid of revolution (cylindrical shell method)
            http://archives.math.utk.edu/visual.calculus/5/volumes.6/index.html
Week 3:   Visualization of Work http://archives.math.utk.edu/visual.calculus/5/work.1/index.html
               Visualization of Average Value of a Function
                http://archives.math.utk.edu/visual.calculus/5/average.1/index.html

                Tutorial for Calculus
              Calculus Tutorial from Harvey Mudd College  http://www.math.hmc.edu/calculus/tutorials/
              Karl's Calculus Tutor http://www.karlscalculus.org/calculus.html
              Visual Calculus http://archives.math.utk.edu/visual.calculus/
              Calculus on the Web http://www.math.temple.edu/~cow/

              Webpage which calculates partial fraction of a rational function
                http://mss.math.vanderbilt.edu/~pscrooke/MSS/partialfract.html
              Webpage which factors a polynomial
                http://mss.math.vanderbilt.edu/~pscrooke/MSS/factorpoly.html

Week 4: Career for a mathematics concentrator
                Why should I study math? I http://www.maa.org/careers/index.html
                Why should I study math? II http://www.ams.org/careers/archived.html
              Mathematics That Counts  http://www.siam.org/siamnews/mtc/mtc.htm

                More information available at http://www.ams.org/careers/
                                                        http://www.math.wm.edu/~klsmit/career.html

Week 5 Improper Integral Tutorial
                   http://archives.math.utk.edu/visual.calculus/4/improper.2/index.html
             Visualization of Arc Length
              http://archives.math.utk.edu/visual.calculus/5/arclength.1/index.html
 

Week 6:   Visualization of center of mass
                  http://archives.math.utk.edu/visual.calculus/5/work.2/index.html
                 Information about Gabriel's horn or Torricelli's Trumpet (infinite surface area, and finite enclosed volume)
                  http://mathworld.wolfram.com/GabrielsHorn.html
              http://curvebank.calstatela.edu/torricelli/torricelli.htm
                Koch's snowflake (infinite arc length, and finite enclosed area)
                   http://scidiv.bcc.ctc.edu/Math/Snowflake.html
                   http://www.ecu.edu/si/cd/interactivate/activities/koch/

Week 7: Spring Break

Week 8Malthus' Essay on population "An Essay on the Principle of Population"
                   http://www.ac.wwu.edu/~stephan/malthus/malthus.0.html
                Dfield program online Java version http://math.rice.edu/~dfield/dfpp.html
                Interactive Differential Equations http://www.aw.com/ide/index.html
              Millennium Prize Problems http://www.claymath.org/Millennium_Prize_Problems/

Week 9: 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

Week 10: Orthogonal Trajectories http://www.aw.com/ide/Media/JavaTools/orthotrj.html
               Solve a Linear Equation http://mss.math.vanderbilt.edu/~pscrooke/MSS/linode.html

Week 11: Fibonacci Numbers and the Golden Section http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
             Calculating and Graphing Sequences http://mss.math.vanderbilt.edu/~pscrooke/MSS/sequence.html

Week 12: Calculating a series http://mss.math.vanderbilt.edu/~pscrooke/MSS/sum.html


Created by Junping Shi, January 15th, 2003, updated April 1st, 2003
Any comments? send to shij@math.wm.edu