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.
- Error bound for root finding may be fixed or automatically calculated
- Trignometric arguments may be specified in degrees, radians or gradians
- Curves may be plotted as lines or as points
- Grid spacing may be fixed or automatically calculated
- Functions may be retained (where valid) between modules
- Splash screen may be disabled
- Axes for 3D plots may be automatically scaled fit the screen
- Image colours may be inverted when copying the graph window to clipboard
- The range for 2D plots may be automatically fitted
- The integrand can be redrawn after each step of integration
- Faster stepping to accelerate plotting during numerical approximations
- Variable initial grids resolution for surfaces
- Up to 10 user defined functions
- User defined functions may be hidden from, but still useable by, students
- Individual modules may be disabled
- Online help may be disabled
- Plotting colours througout are configurable
- 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
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Expressions supported
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- 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
- 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
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Graphing functions of one variable
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- 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
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Graphing functions of two variables
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- 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
- 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
- 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
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Finding roots of equations
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- Multi-level zoom with unzoom facility
- Right click to evaluate function
- Multiple Methods:
- Bisection
- Regula-Falsi
- Secant
- Muller
- Newton-Raphson
- Fixed point (contraction map)
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Parametric curves in two dimensions
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- 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
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Parametric curves in three dimensions
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- 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
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First order differential equations
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- 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
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First order differential equations
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- 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
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Dynamical systems of two dependent equations
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- 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
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Dynamical systems of three dependent equations
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- 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
- 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