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 roots of an equation using Newton's method

using Newton's method solve x cos x = 0

use numerical methods to find the 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]

Dynamical Systems

analyze the logistic map

logistic map r=3.569935

analyze the Lotka–Volterra predator‐prey model

predator-prey model

Control Systems

analyze a transfer function model

transfer function (s^2-3)/(-s^3-s+1)

analyze a state space model

state {{0,1,0},{0,0,1},{1/5,-1,0}}, input {{0},{0},{1}}, output {{-3,0,1}}

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