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
               and you will mostly use Calculus Toolkit
                    Definite Integral
                    Numerical Integration
                    (midpoint, trapezoid, and Simpson)
                        Calculate partial fraction of a rational function

Week 1Malthus' Essay on population "An Essay on the Principle of Population"
              Interactive Differential Equations
              Growth and decay:
              Logistic Growth:
              Logistic Phase Line:

              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
              MathServ DE Toolkit
              Drawing a Direction Field
                  Euler's Method
              Solve a Separable Equation
              Illustration of Euler's method:

Week 3: Saddle-Node Bifurcation Tool
             Transcritical Bifurcation Tool
             Pitchfork Bifurcation: Supercritical Tool
             Pitchfork Bifurcation: Subcritical Tool

Week 4: Solve a Linear Equation

Week 5Vector Fields Tool
              Two Dimensional Equations Tool
              Lotka-Volterra Tool
              Simple Harmonic Oscillator Tool
              Romeo and Juliet Tool

Week 6 Eigen Engine Tool
             Parameter Path Animation Tool
             Parameter Plane Input Tool
             Matrix Element Input Tool
             Four Animation Paths Tool

Week 7:

Week 8: Mass and Spring Tool
            Damped Vibrations: Energy Tool 
            Critical Damping Tool

Week 9:  Damped Forced Vibrations Tool

Week 10: Competitive Exclusion Tool
               Forced Damped Pendulum Tool
               Lorenz Equations
               Math's Wild-And-Crazy Guy (An article on Washington Post about a mathematician of Chaos)

Week 11: Pendulums Tool
              Hamilton's equation
              A new solution to the three body problem - and more
              How Pendulum Clocks Work
              Galileo's Pendulum Experiments

Week 12: Laplace: Definition Tool
               Laplace: Transformer Tool
               Laplace: Shifting Theorem Tool
               Laplace: Shift and Step Tool
               Laplace: Delta Function Tool

Created by Junping Shi, August 26th, 2003, updated August 21st, 2004
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