Precalculus and Computer Programming

The material in this book prepares the reader for calculus. All the topics of precalculus are covered. A good way to learn math is to study the computer programs that do the math in this book. The reader will learn how to write these programs using Excel with VBA, which is readily available in the Microsoft Office program.

The exponential, logarithmic, and trigonometric functions are defined. Because they are not algebraic, electronic calculators compute them using approximation methods. The reader is introduced to the use of Taylor series to compute them.

One discussion in the book is about the base e exponential function. It’s the only exponential function whose slope is equal to the function itself. This leads to a calculus formula that applies when the rate of change of a variable is directly proportional to the response of the variable. This calculus formula is applied to a spring-mass-damper system. This yields a polynomial, and shows how zeros of this polynomial affect response of the mass.

Another discussion shows how computing the determinant of a matrix yields the zeros of a polynomial. This discussion leads to a computer program that finds all the zeros of a general polynomial. This program is listed, explained, and demonstrated. The program can find all the zeros of a fourteenth order Butterworth polynomial.

Francis D. Hauser, PhD, is a dynamic systems analyst of the motions and control of aerospace and marine vehicles. He is also a university lecturer in graduate and undergraduate courses on optimization theory, Newtonian mechanics, linear algebra, Fourier analysis, and conventional, modern, and space-vehicle control.

Previous Books: Excel with VBA for Engineers and Mathematicians, Eigenvalues and Eigenvectors, and The Golden Ratio: The Facts and the Myths.

The idea to write these books came when the author discovered that Excel with VBA can be used to write computer programs capable of doing a complete autopilot stability analysis on a large flexible launch vehicle, and also of factoring polynomials like the fourteenth-order Butterworth. These programs are listed in the books. They run on a laptop and now on a tablet with Windows 10.