ENGINEERING PROJECT

The MATLAB system consists of these main parts:

This part of MATLAB is the set of tools and facilities that help to use and become more productive with MATLAB functions and files. Many of these tools are graphical user interfaces. It includes:

• The MATLAB desktop and Command Window,
  
• An editor and debugger,
• A code analyzer,
  
• Browsers for viewing help,
• The workspace,
  
• Folders.

Mathematical Function Library.[6]

This library is a vast collection of computational algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

The Language.[6]

The MATLAB language is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick programs you do not intend to reuse. You can also do "programming in the large" to create complex application programs intended for reuse.

Graphics.[6]

MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well as annotating and printing these graphs. It includes high-level functions for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It also includes low-level functions that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your MATLAB applications.

External Interfaces.[6]

The external interfaces library allows you to write C and Fortran programs that interact with MATLAB. It includes facilities for calling routines from MATLAB (dynamic linking), for calling MATLAB as a computational engine, and for reading and writing MAT-files.

History of Laplace transform

1) MARQUIS PIERRE-SIMON DE LAPLACE (1749-1827)[5]

The laplace Transform is named after the great French mathematician and astronor Laplace, who first presented the transform and its applications to differential equations in a paper published in 1779. Laplace developed the foundations of potential theory and made important contributions to special functions, probability theory, astronomy and celestial mechanics.

In his Exposition du systeme du monde (1796), Laplace formulated a nebular hypothesisof cosmic origin and tried to explain the universe as a pure mechanism. In his Traite de mecanique celeste ( celestial mechanic), which completed the work of Newton, Laplace used mathematics and physics to subject the solar system and all heavenly bodies to the laws of motion and the principle of gravitation. Newton had been unable to explain the irregularities of some heavenly bodies.

Laplace presented a copy of mecanique celeste to Napoleon, who, after reading the book, took laplace to task for not including God in his scheme: "You have written this huge book on the system of the world without once mentioning the author of universe." "Sire," Laplace retorted, " I had no need of that hypothesis." Napoleon was not amused, and when he reported this reply to another great mathematician-astronomer, Louis de Lagrange, the latter remarked, "Ah, but that is a fine hypothesis. Its explained so many things."

Napoleon, following his policy of honouring and promoting scientists, made Laplace the minister of the interior.


2) OLIVER HEAVISIDE (1850- 1925)[5]

Although Laplace published his transform method to solve differential equations in 1779, the method did not catch on until a century later. It was rediscovered indepandently in a rather awkward form by an eccentric British engineer, Oliver Heaviside, one of the tragic figures in the history of science and engineering. Heaviside was (for example) :

• The first to find the solution to the distortionless transmission line.
• The innovator of lowpass filter.
• The first to write Maxwell's equation in modern form.
• The codiscoverer of rate energy transfer by an electromagnetic field.
• An important contributor to the developement of vector analysis. In fact, he essentially created the subject indepandently of Gibbs.
• The first to theorize (along with Kennelly of Harvard) that a conductiing layer (the Kennelly-Heaviside layer) of atmosphere exists, which allows radio waves to follow earth's curvature instead of travelling off into space in a straight line.

below is the laplace transform table.