10

ex: The Function That Equals Its Own Derivative

The natural exponential function is identical with its derivative. This is the source of all the properties of the exponential function and the basic reason for its importance in applications.—RICHARD COURANT AND HERBERT ROBBINS, What Is Mathematics? (1941)

When Newton and Leibniz developed their new calculus, they applied it primarily to algebraic curves, curves whose equations are polynomials or ratios of polynomials. (A polynomial is an expression of the form anxn + an−1xn−1 + … + a1x + a0; the constants ai are the coefficients, and n, the degree of the polynomial, is a non-negative integer. For example, 5x3 + x2 − 2x + 1 is a polynomial of degree 3.) The simplicity of these equations, and ...

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