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Mechanical engineering principles began to be formalized the late 18th century, but the field did not truly come into its own as a discipline until 1847 with the founding of the Institution of Mechanical Engineers. The practice of mechanical engineering involves the design of mechanical systems, such as power and energy systems, aircraft and aerospace products, weapon systems, pumps, engines, compressors and physically operating machinery of all types. Mechanical engineers are college-educated professionals with a thorough grounding in math, physics and engineering principles.
Mechanical engineers need to be comfortable with math. According to WeUseMath.org, mathematics is the language of physical science and engineering. All subfields of mechanical engineering involve the use of math, and many require a thorough understanding of advanced math including trigonometry and calculus. The ability to understand and solve differential equations and the ability to use math in statistics is particularly important for mechanical engineers.
Physics is the study of the natural laws of the universe, and knowledge of physics is essential for a mechanical engineer. Mechanical engineers have to understand and apply the principles of physics in virtually all aspects of their work -- how much force is required to overcome gravity or friction or the properties of coherent light such as lasers, for example.
Working as a mechanical engineer obviously involves the application of basic engineering principles. Every mechanical engineer needs to be familiar with basic mechanical principles, methods for determining the strength of materials, fluid mechanics, statics and dynamics, thermodynamics, hydraulics, material fatigue, properties of lubricating oils, cylindrical gear units, shaft couplings and vibration and control theory.
Mechanical engineers also need to be familiar with statistical methods. Almost all projects are designed and modeled first before beginning to construct a prototype, and the use of statistics is involved in every step of this process. Statistics is particularly important in determining the strength of materials or calculating the reliability or expected working life of a mechanical device.