Introduction of Engineering Mathematics
Engineering Mathematics is concerned with the application of mathematics in a variety of disciplines in various regions such as technology, science, business and commerce. The Mathematicians of engineering are occupied in the formation, application and study of advanced mathematical techniques relevant to specific problems. Once this referred mostly to the application of mathematics to these disciplines as mechanics and fluid dynamics but presently, the engineering mathematics has supposed a much broader meaning and embraces such diverse fields as the theory of optimization, communication theory, theory of games, and numerical analysis. Certainly nowadays there is an extraordinary variety and range of applications of mathematics in industry and government, including main real-world problems such as design and medical diagnosis, materials processing, development of network management and weather prediction.
Engineering mathematics is at the core of all branches of engineering, from aerospace to electronics engineering and from mechanical engineering to computer science. In our data-rich culture the engineering mathematics fulfils an essential role. From the overflow of data collected from sounds, images and texts we require to extract significant and suitable information.
Important topics in engineering mathematics
Maclaurin's & Taylor theorem, mean value theorem, Roll's theorem, application to rates small increments approximations and errors, Polar & parametric coordinates curvature definition formula in intrinsic Cartesian and polar coordinates, radius of curvature or center of curvature, Tangents or sub tangents normal and subnormal differential / coefficient of arc length in Cartesian.
Asymptotes, envelopes, Indeterminate forms partial differentiation, evolutes, Euler's theorem application of partial differentiation in approximately and errors of Taylor's series of two variables maxima and minima of functions of one and two variables. Definite integrals and their properties Integral as the limit of a sum application to summation of series Area, length of curves volume and surface of solids of revolutions.
Beta and gamma function multiple integral, double integral and triple integral application to problem in area, volume center of gravity moment of inertia and center of pressure.
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