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The concept of flying has taken root only within the past 120 years or so, when the Wright brothers were credited for the first controlled manned flight in 1903 at Kitty Hawk, NC.  It has since grown into a full-fledged system of transportation, some marveling over the direction it has taken in providing routine flights around the world in luxury airliners.

The development of commercial aviation has occasionally pointed to a concern regarding the safety of large jetliners carrying numerous passengers.  It has experienced numerous trials incurring devastation from ice, wind, volcanic ash, and birds.  Although the absolute design of today's aircraft may still be less than one-hundred percent settled, statistically it is ten times safer than taking a train, and nineteen times safer than driving a car.

The design and development of aircraft involve many branches of engineering and applied science.  It is primarily composed of an airframe, various flight systems, and a powerplant.  The airframe may be a designed of aluminum alloys, titanium, and composites as a means to reduce weight.  Major studies involving mathematical models are used to determine flight loads on an aircraft which in turn provide information for yet another mathematical study of determining the internal loads, or stresses.  Further stress analysis is then incorporated to determine all the remaining pathways of forces until every remaining structural member, bolt, and rivet has been accounted for.

Mathematical modeling is a term used in trade, derived from a complex field of numerical methods. Numerical methods, or numerical analysis, has its origins since the days of Gauss and Newton. It has progressed through the efforts of mathematicians and engineers into workable and impressive mathematical modeling techniques, one of these which is called the Finite Element Method. During the process of carrying out this method, calculations in the thousands are made using a math-based microprocessor, or modern day computer.

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