Optimization

Minimize or maximize a function:

maximize x(1-x)e^x

Minimize or maximize a function of several variables:

maximize 5 + 3x - 4y - x^2 + x y - y^2

Minimize or maximize a function subject to a constraint:

maximize e^x sin y on x^2+y^2=1

Numerical Analysis

Find a root of an equation using Newton's method:

using Newton's method solve x cos x = 0

Use numerical methods to find roots of numbers:

find root of 2 with bisection method

Approximate an integral using a specified numerical method:

5 interval trapezoidal rule integrate sinx cosx on [0,4]

Solve an ODE using a numerical method:

use Euler method y' = -2 x^3 y, y(1) = 5, from 1 to 10

Dynamical Systems

Analyze the logistic map:

logistic map r=3.569935

Analyze the Lotka–Volterra predator‐prey model:

predator-prey model

Fractals

Plot fractals given by dynamical systems:

Julia set -0.40+0.65i

Mandelbrot set

Packing & Covering of Objects

Estimate the number of objects required to fill a container:

How many baseballs fit in a Boeing 747?

Estimate the number of objects required to cover a specified area:

pennies to cover 2 square miles

Estimate the number of objects required to circle another object:

How many grains of rice would it take to stretch around the moon?

Game Theory

Get information about a mathematical game:

battle of the sexes

chicken game

tic-tac-toe game

rock-scissors-paper game