Introduction to GNUPlot for Mathematical Visualization

What is GNUPlot?

GNUPlot is a command-line-driven graphing utility for Linux (and other OSes) that enables dynamic visualization of mathematical functions, datasets, and 3D surfaces. It supports:

2D/3D plotting
Multiple functions on the same graph
Script automation
Export to PNG, PDF, SVG, etc.

Starting GNUPlot

Launch GNUPlot in your Linux terminal:

gnuplot

Clearing the Screen

To clear the GNUPlot console (not the plot window):

!clear # Linux/macOS
!cls # Windows

Basic Example: Plotting a Function

Plot a simple quadratic equation:

reset # Clears all previous settings
plot x**2 + 3*x - 5 title "Quadratic Function"

Handling Multiple Operations

GNUPlot executes commands sequentially. To avoid clashes when plotting multiple calculus operations:

Explicit Parentheses: Always group operations.
```
plot (sin(x)/x) * exp(-x**2)
```

Temporary Variables: Use set for complex expressions.

set dummy t
parametric = "plot sin(t),cos(t)"
eval parametric

Reset Between Plots: Prevent variable/function collisions.
```
reset
plot integral(sin(x)*exp(x))
```

Key Notes

Clashing Operations: Functions like sum, integral, and derivative may conflict if not properly scoped. Use reset between unrelated plots.
Persistent Variables: Defined variables (e.g., a=5) remain active until manually unset or reset.
Thread Safety: GNUPlot is single-threaded; concurrent instances require separate sessions.

Advanced Example: Multiple Calculus Operations

reset
f(x) = sin(x) / x
set title "Function and its Derivative"
plot f(x) title "f(x)", \
     (f(x+0.01) - f(x))/0.01 title "Numerical Derivative"

Output Options

To save plots without displaying them:

set terminal png
set output "plot.png"
replot # Repeats the last plot command
!feh plot.png # View in Linux (requires feh)

Conclusion

GNUPlot provides powerful mathematical visualization while requiring careful handling of operational scope. Always use reset when switching between unrelated tasks.