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Engineering Mathematics by C. Vijayakumari, P. Sivaramakrishna Das

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4

Applications of Differential Calculus

4.1 CURVATURE IN CARTESIAN COORDINATES

4.1.0 Introduction

To characterize a curve completely we have seen various aspects of the curve such as increasing and decreasing nature, maximum and minimum points, concavity and convexity, symmetry and special points such as points of inflexion etc. Another aspect to characterize the shape of a curve is the degree of its bending or curvature.

In many practical problems we are concerned with the bending of a curve at different points or the bending of two curves such as rail tracks. The concept of curvature is considered while laying rail tracks and designing highways. The curvature at a point is a numerical measure of the rate of bending of a curve.

4.1.1 Measure ...

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