In this chapter, important conceptions of mathematical analysis such as derivatives and differentials, and their mechanical and geometrical meanings, are given. Then the concept of the derivative is applied to study the free fall of a mass, linear motion at velocities near the speed of light, and applications in numerical analysis. There are important formulas for derivatives, such as Leibniz’s formula for the derivatives of products of functions. The concept of the derivative is also applied to curvature, conics, and evolvents. These topics are treated both in Cartesian and in polar coordinates. We apply these techniques to geometric objects given explicitly or implicitly, or by parametric equations in either coordinate system.
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