10 Applications of Differentiation and Integration
In general terms, the usefulness of calculus in elementary engineering maths lies in the
application of differentiation as a rate of change or slope of a curve and integration as an
area under a curve. These are essentially applications to very useful mathematical methods.
There are also specific applications to various disciplines of engineering, such as centroids
and moments of inertia in solid mechanics and rms values in electronic engineering.
Also, there are examples in statistics. The applications to mathematical methods are the
main subject of this chapter. Some engineering and statistics examples are covered under
Applications.
Prerequisites
It will be helpful if you know something about:- techniques of differentiation (Chapter 8
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)- techniques of integration (Chapter 9
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)- simple ideas of limits (230
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)- coordinate geometry (Chapter 7
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)- tangent and normal to a curve (230
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)- equation of a line (212
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)- inequalities (97
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)- solving algebraic equations (Chapter 2
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)- plotting graphs (91
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)Objectives
In this chapter you will find- differentiation as a gradient and a rate of change
- tangent and normal to a curve
- stationary points and points of inflection
- curve sketching
- the definite integral as the area under a curve
- volume of a solid of revolution