TABLE OF CONTENTS MATHEMATICS Machinery's Handbook, 31st Edition
REAL NUMBERS AND THEIR OPERATIONS 3 Real Numbers 3 Properties of Real Numbers 3 Integers (Signed Numbers) 4 Order of Operations 5 Fractions and Mixed Numbers 6 Adding and Subtracting 7 Multiplying 8 Dividing 8 Decimal Numbers 9 Ratio and Proportion 10 Percentage 11 Powers and Roots 11 Properties of Exponents 12 Scientific Notation 13 Factorial Notation 13 Permutation 13 Combination 13 24 Definitions 24 EvaluatingAlgebraic Expressions 24 Combining Like Terms 25 Solving an Equation for an Unknown 26 Rearrangement and Transposition of Terms in Formulas 27 Algebraic Operations 27 Properties of Monomials and Exponents 27 Properties of Radicals 28 Polynomials 28 Operations on Polynomials 29 Factoring Polynomials 31 Equation Solving 31 System of Linear Equations 32 Second-Degree (Quadratic) Equation 34 Completing the Square 34 Using the Quadratic Formula 34 Cubic Equation 35 Functions 35 Graphs of Functions 36 Logarithms 36 Meaning 36 Properties 37 Common Prime Factorization of Numbers ALGEBRA
ALGEBRA
(Continued) 37
Natural
38 38
Using Calculators to Solve Logarithms Solving an Equation Using Logarithms
39 Arithmetic Sequence 39 Geometric Sequence GEOMETRY 42 Analytic Geometry 42
Rectangular Coordinate System Slope of a Line Lines and Line Segments Equation Forms of a Line
42 43 44 49 51 54 55 57
Circle Ellipse
Four-Arc Oval Approximating an Ellipse
Sphere Parabola
58 Hyperbola 59 Complex Numbers 59 61 Pure Geometry 61 71 Area and Volume 71 59 66
Imaginary Number Forms of a Complex Number Propositions of Geometry Geometric Constructions Prismoidal Formula Pappus-Guldinus Rules Finding Area of a Surface of Revolution Area of Irregular Plane Figure Areas Enclosed by Cycloidal Curves Contents of Cylindrical Tanks at Different Levels
71 72 72 73 73
75 Dimensions of Plane Figures 81 Polygons 83 Segments of a Circle 84 Segments of a Circle for Radius = 1 86 Diameters of Circles and Sides of Squares of Equal Area 87 Diagonals of Squares and Hexagons 88 Volumes of Solids
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