// Welcome to MathStudio! Press enter on your keyboard to evaluate the expressions. Press shift and enter to create a new line.
1+2+3+4+5
4*5
6!
// Algebra
x+x+x
a*a+b+b+b+c*c*c*c
Expand((a+b)^10)
Apart((x^2)/(x^2+1)^2)
Factor(x^4+5x^2-6)
// Solving Quadratic Equations
Solve(x^2+5x+6=0)
Solve(1,5,6)
// Limits
Limit((3x-15)/sqrt(x^2-10x+25), x, 5, 1)
Limit(cos(a*x)/x^2-cos(b*x)/x^2, x, 0)
// Derivatives
D(sin(x))
D(sin(x)*cos(x^2))
D(f(x)*g(x))
D(sqrt(x)^sqrt(x), x)
// Integrals
Integrate(x^2+3x-6)
Integrate(exp(x)*sin(x))
Integrate(-3/x^2+sin(x)/(1-sin(x)))
Integrate((1+2cos(x))/(1+2sin(x)))
Integrate(1/(a*x^2+b*x), x)
// Graphing
Plot(sin(x))
Plot(sin(x),cos(x),colors=[blue,red])
Plot(sin(x^2)*x)
Plot(sin(x),lineWidth=5,lineDash=[10,5])
// Parametric Plots
ParametricPlot(cos(u),sin(u))
ParametricPlot(sin(7u), sin(8u), u=[0,2@pi,400], color=blue, numbers=0)
ParametricPlot(10sin(31u), 10cos(31u), u=[0,2@pi,48], axis=0, numbers=0, color=orange)
// Polar Plots
PolarPlot(sin(2@theta))
PolarPlot(@e^sin(@theta)-2cos(4@theta)+sin(1/24(-@pi+2@theta))^5, @theta=[0,21@pi,1000], color=magenta)
PolarPlot(2-2*sin(@theta)+sin(@theta)*sqrt(abs(cos(@theta)))/(sin(@theta)+1.4),color=red,shade=middle)
// Time Graphing
Plot(sin(x+T))
Plot(sin(x+T)*x)
Plot(sin(x+T),x*cos(T)+sin(T))
// Vector Fields
VectorPlot(-y, x)
VectorPlot(-y, cos(x+T))
// Multiple Plots
Plot(sin(x), color=blue)
// Minimum, Maximum and Zero Values
Plot(sin(x),min=1)
Plot(cos(x),sin(x),color=[blue,red],min=[0,1],max=[1,0])
// List Plots
ListPlot([1,2,3,4,5,4,3,8,6,8])
ListPlot(Random(1,10,100), lines=0, points=4, shade=0, color=red)
// Regression Analysis
LinearFit([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
LinearFitModel([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
LinearFitPlot([1,4,9,5,7,5,4,2,9], [3,4,5,7,8,10,4,7,6])
QuadraticFitPlot([7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
SinFitPlot(sin((1:50)/5)*Random(1,3,50))
// 3D Graphing
Plot3D(2cos(x)*sin(y))
Plot3D(cos(x)*y+sin(y)*x, colors=[red, yellow])
Slider(a,2,10,0.1)
Plot3D(sin(T-sqrt(x^2+y^2)), colors=[red, yellow], lines=0)
// 3D Parametric Plots
ParametricPlot3D((3+sin(v)+cos(u))*sin(2v), (3+sin(v)+cos(u))*cos(2v), sin(u)+2cos(v), u=[0, 2@pi, 40], v=[0, 2@pi, 80], lines=0, name=Toroid)
// Sliders
Slider(n, 1..50)
Slider(n, 1..100)
Slider(a, 1, 10, 0.1)
Slider(a, 1, 10, .1)
Slider([a,b],1,10,0.1)
// Scripting
one = 1
one^2 + two^2 + three^2
cube(x) = x^3
data = @[29, 29]
// Lists
1:100
[1,2,3]*[4,5,6]
// Matrices
[[1,2],[3,4]]*[[5,6],[7,8]]
Inverse([[1,5,6], [2,4,5], [1,1,7]])
Inverse([[a,b], [c,d]])
Identity(5)
// Units
2@feet+24@inches
2@miles+4@kilometers
(40@miles/@hour)*3@hours
@megabytes -> @bytes
50@fahrenheit -> @celsius
2@hours -> @s
5@years -> @days
@inches -> @nanometers
@tbsp -> @tsp
@kilogram -> @pound
4@miles -> @inches