The Handbook of Essential Mathematics

For Pubic Release: Distribution Unlimited

The Air Force Research Laboratory

The Handbook of Essential Mathematics

Formulas, Processes, and Tables Plus Applications in Personal Finance

X

Y

Y XY

Y2

X

X2

XY

(X + Y)2=X2 + 2XY + Y2

Compilation and Explanations: John C. Sparks Editors: Donald D. Gregory and Vincent R. Miller

For Pubic Release: Distribution Unlimited

The Handbook of Essential Mathematics

Air Force Publication 2006 For Public Release: Distribution Unlimited

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Forward

Wright-Patterson Air Force Base (WPAFB) has enjoyed a lengthy and distinguished history of serving the Greater-Dayton community in a variety of ways. One of these ways is through the WPAFB Educational Outreach (EO) Program, for which the Air Force Research Laboratory (AFRL) is a proud and continuous supporter, providing both technical expertise (from over 2000 practicing scientists and engineers) and ongoing resources for the various programs sponsored by the WPAFB Educational Outreach. The mission of the WPAFB EO program is

To form learning partnerships with the K-12 educational community in order to increase student awareness and excitement in all fields of math, science, aviation, and aerospace; ultimately developing our nation's future scientific and technical workforce.

In support of this mission, the WPAFB EO aspires to be the best one-stop resource for encouragement and enhancement of K-12 science, math and technology education throughout the United States Air Force. It is in this spirit that AFRL offers The Handbook of Essential Mathematics, a compendium of mathematical formulas and other useful technical information that will well serve both students and teachers alike from early grades through early college. It is our sincere hope that you will use this resource to either further your own education or the education of those future scientists and engineers so vital to preserving our cherished American freedoms.

LESTER MCFAWN, SES Executive Director Air Force Research Laboratory

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Introduction

Formulas! They seem to be the bane of every beginning mathematics student who has yet to realize that formulas are about structure and relationship--and not about memorization. Granted, formulas have to be memorized; for, it is partly through memorization that we eventually become `unconsciously competent': a true master of our skill, practicing it in an almost effortless, automatic sense. In mathematics, being `unconsciously competent' means we have mastered the underlying algebraic language to the same degree that we have mastered our native tongue. Knowing formulas and understanding the reasoning behind them propels one towards the road to mathematical fluency, so essential in our modern high-tech society.

The Handbook of Essential Mathematics contains three major sections. Section I, "Formulas", contains most of the mathematical formulas that a person would expect to encounter through the second year of college regardless of major. In addition, there are formulas rarely seen in such compilations, included as a mathematical treat for the inquisitive. Section I also includes select mathematical processes, such as the process for solving a linear equation in one unknown, with a supporting examples. Section II, "Tables", includes both `pure math' tables and physical-science tables, useful in a variety of disciples ranging from physics to nursing. As in Section I, some tables are included just to nurture curiosity in a spirit of fun. In Sections I and II, each formula and table is enumerated for easy referral. Section III, "Applications in Personal Finance", is a small textbook within a book where the language of algebra is applied to that everyday financial world affecting all of us throughout our lives from birth to death. Note: The idea of combining mathematics formulas with financial applications is not original in that my father had a similar type book as a Purdue engineering student in the early 1930s.

I would like to take this opportunity to thank Mr. Al Giambrone--Chairman of the Department of Mathematics, Sinclair Community College, Dayton, Ohio--for providing requiredmemorization formula lists for 22 Sinclair mathematics courses from which the formula compilation was partially built.

John C. Sparks March 2006

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Dedication

The Handbook of Essential Mathematics is dedicated to all Air Force families

O Icarus...

I ride high...

With a whoosh to my back And no wind to my face, Folded hands In quiet rest-- Watching...O Icarus... The clouds glide by, Their fields far below Of gold-illumed snow, Pale yellow, tranquil moon To my right--

Evening sky.

And Wright...O Icarus...

Made it so-- Silvered chariot streaking On tongues of fire leaping--

And I will soon be sleeping Above your dreams...

August 2001: John C. Sparks

100th Anniversary of Powered Flight 1903--2003

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