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Titlebook: Numerical Methods and Modelling for Engineering; Richard Khoury,Douglas Wilhelm Harder Textbook 2016 Springer Nature Switzerland AG 2016 B

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Differentiation,. and its complement operation, ., allow engineers to measure and quantify change. Measuring change is essential in engineering practice, which often deals with systems that are changing in some way, by moving, growing, filling up, decaying, discharging, or otherwise increasing or decreasing in some way.
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978-3-319-79331-3Springer Nature Switzerland AG 2016
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Taylor Series, line mentioned in the first intuitive example is actually the tangent (or first derivative) of the curve, it should come as no surprise that this Taylor series will make heavy use of derivatives of the functions being modelled.
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