// 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