A numerical computing environment is software in which engineers and scientists do maths on large sets of numbers with a few lines of code, and see the results as graphs. The best-known one is MATLAB, which many Indian engineering colleges teach. The name comes from "matrix laboratory". A matrix is a table of numbers. In MATLAB, nearly everything is a matrix, from a list of sensor readings to a photo.
Why use it instead of a general programming language? In many general languages, adding two lists of a million numbers needs a loop that goes through them one by one. In MATLAB, the engineer writes one line, such as c = a + b. Common tasks come ready-made: drawing a graph, solving equations, filtering a signal, or finding the frequencies in a signal. Extra sets of functions for one field, such as signal processing or control systems, are sold separately as toolboxes.
Say an engineer at a pump maker in Coimbatore is investigating a pump that vibrates too much. A vibration sensor on the pump, connected to a data recorder, takes 10,000 readings a second. She records for 5 seconds, which gives 50,000 readings, each stamped with its time. Readings stamped with the time like this are time series data. She loads the file into MATLAB with one line of code, and plots it with another. The graph shows only a dense, shaking line.
So she runs a Fourier transform, with one more line. A Fourier transform splits a signal into the frequencies it contains, as a trained ear separates a chord into its notes. The result shows two peaks. One is at 48 hertz, or 48 times a second, the speed at which the motor turns. The other is at 147 hertz. She compares this with the bearing's fault frequencies, which the bearing maker publishes. 147 hertz matches a crack in the bearing's outer ring. The bearing is replaced, and the second peak disappears. The whole analysis took about 20 lines of code.
Signals like this are often seen first on oscilloscopes and test instruments, which can export their readings for analysis. Faults in motors and bearings are exactly what factories try to catch early.
MATLAB is also the base for model-based design, where the same maths becomes the logic of a controller. Statisticians in banks and drug companies more often use statistical software, which is built for data about people and samples rather than signals.
MATLAB is sold by licence, and a licence for a company is expensive. Free alternatives exist: Python with its numerical libraries, and GNU Octave, which runs most MATLAB code. Many Indian teams use both.