What Newt can do

Below is a (hopefully) complete list of Newt's functionality. Newt has pretty much stablised over the last year, but there's always room for improvement, especially in the area of useability.



Configuration Top


Miscellaneous Top

  • Context sensitive online help
  • Intelligent function parser supports implicit multiplication
  • Operators have correct precedence
  • Numeric constants can be entered as full (numeric) expressions
  • Constants pi and e available
  • Iterative calculations support run, pause, and stepping
  • Multi-level zoom with unzoom facility
  • Range of curves in 2D may be fitted to ensure the curve is visible
  • Interactive rotation of 3D axes
  • Copy to Windows clipboard as a bitmap (with invert option)
  • Built-in special functions:
    • Bessel functions
    • Blancmange
    • Taylor series
    • Fourier summations
    • Heaviside Step function
    • Frac, Floor and Ceil
    • Function composition

Expressions supported Top

  • Standard functions
    • sqrt
    • abs (absolute value, may also use || brackets)
    • log (base 10 logarithm)
    • ln (natural logarithm)
    • exp(f(x)) (Exponentiation, may also be written as e^f(x))
  • Trigonometric functions
    • sin
    • cos
    • tan
    • cosec
    • sec
    • cot
    • arcsin
    • arccos
    • arctan
    • arccot
  • Hyperbolic function
    • sinh
    • cosh
    • tanh
  • Special Functions
    • step(f(x),g(x)) (0 if f(x) > g(x), 1 if f(x) <= g(x))
    • frac(f(x)) (fractional part of x)
    • floor(f(x)) (largest integer < x)
    • ceil(f(x)) (largest integer > x)
    • jb(n,f(x)) (Bessel functions of the first kind, order n, 0 <= n <= 20)
    • yb(n,f(x)) (Bessel functions of the second kind, order n, 0 <= n <= 20)
    • bn(n,f(x)) (Blancmange function of f(x) of order n, 0 <= n <= 20)
    • fc(f(x),g(x)) (Composition, i.e. g(f(x)))
    • tp(n,f(x),g(x)) (Taylor polynomial of order n, for g(x), about f(x))
    • fs(n,f(n),f(x,n)) (Fourier series of order n, with coeff f(n), and summation term of f(x,n))
    • f1(x)...f9(x) (User defined functions)
  • The terms pi and e may be used as such where:
    • pi = 3.1415926536
    • e = 2.7182818285
  • In modules that accept stepped constants, a, b and c may be used
  • Scientific notation is not accepted, so
    • 2e5 = 2*e*5
    • 2e-5 = 2*e - 5
  • Implicit multiplication, and function composition, are accepted, so
    • pisinx = pi*sin(x)
    • 2.5sinx = 2.5*sin(x)
    • xsinx = x*sin(x)
    • sinxcosx = sin(x*cos(x)) (NB!)
    • xx = x^2
    • xxx = x^3 ... etc
  • Round brackets () may be used to alter order of evaluation
  • Absolute value brackets ||, however, if nesting is required use abs()
  • Will accept successive unary minus signs
    --x, ---x, etc...
  • Will accept negated exponents without brackets
    e.g. e^-x
  • Numeric values are converted as follows:
    • 2..5 = 2.0
    • 2.1.5 = 2.1
    • In general everything after the second . is discarded
  • User defined functions may be used in compositions
  • Will accept nested arguments without brackets
    • sincosx = sin(cos(x))
    • f1cosx = f1(cos(x))
    • f1x = f1(x)
  • User functions may not result in infinite recursion
  • Constant fields will accept any valid expression as long as it evaluates to a constant

Graphing functions of one variable Top

  • Functions stored in a menu for replotting, editing or removal
  • Multi-level zoom with unzoom facility
  • Right click to evaluate function
  • Plot up to nine functions simultaneously
  • Up to three stepped constants for families of graphs

Graphing functions of two variables Top

  • Interactive rotation of axes
  • Grid may be refined for a smoother plot
  • Contour plotting (level lines)
  • Turn shading and constant lines on and off
  • Zoom out

Differentiation Top

  • Approximate the slope at a point in successive steps
  • Numerically approximate derivative curve
  • Plot actual derivative to compare
  • Multi-level zoom with unzoom facility
  • Right click to evaluate function

Integration Top

  • Plot area picture
  • Plot area curve (antiderivative) numerically
  • Plot actual integral to compare
  • Multi-level zoom with unzoom facility
  • Right click to evaluate function
  • Multiple Methods:
    • Left integration
    • Right integration
    • Middle integration
    • Random integration
    • Trapezium rule
    • Simpson's rule
    • 4th order Newton-Cotes

Finding roots of equations Top

  • Multi-level zoom with unzoom facility
  • Right click to evaluate function
  • Multiple Methods:
    • Bisection
    • Regula-Falsi
    • Secant
    • Muller
    • Newton-Raphson
    • Fixed point (contraction map)

Parametric curves in two dimensions Top

  • Multi-level zoom with unzoom facility
  • Variable step count for t for smoother plots
  • Variable domain for t
  • Domain and range may be fitted (with the correct aspect ratio)
  • Stepped constants to plot families of curves

Parametric curves in three dimensions Top

  • Multi-level zoom with unzoom facility
  • Variable step count for t for smoother plots
  • Variable domain for t
  • Interactive rotation of 3D axes
  • Stepped contants to plot families of curves

First order differential equations Top

  • Multi-level zoom with unzoom facility
  • Right click to plot an initial value curve at a point
  • Plot variable resolution slope fields
  • Set value for h (step size)
  • Set run speed for plotting
  • Multiple Methods:
    • Euler
    • Euler with predictor
    • 2nd order Runge-Kutta
    • 4th order Runge-Kutta

First order differential equations Top

  • Multi-level zoom with unzoom facility
  • Right click to plot an initial value curve at a point
  • Plot variable resolution slope fields
  • Set value for h (step size)
  • Set run speed for plotting
  • Multiple Methods:
    • Euler
    • Euler with predictor
    • 2nd order Runge-Kutta
    • 4th order Runge-Kutta

Dynamical systems of two dependent equations Top

  • Multi-level zoom with unzoom facility
  • Right click to plot an initial value curve at a point
  • Right click and drag to refine an area
  • Variable step count
  • Variable step size
  • Plot phase portraits and dependent graphs (x and y against t)
  • Directional arrows on curves
  • Repeated plots in different colours

Dynamical systems of three dependent equations Top

  • Zoom out
  • Set step count
  • Set step size for finer or coarser plots
  • Phase portraits
  • Plot solutions to initial value problems (IVPs)
  • Specify a sub-volume for the 3D grid
  • Interactive rotation of 3D axes
  • Directional arrows on curves
  • Overlay initial value problem curves and phase portraits

Printing facilities Top

  • Full colour and black and white printing
  • Specify a title for the plot
  • Describe the plot in a footnote
  • Arbitrary number of labels on the graph