Readers wishing to renew and extend their acquaintance with a variety of branches of mathematics will find this volume a practical companion. Geared toward those who already possess some familiarity with its subjects, the easy-to-follow explanations and straightforward tone make this book highly accessible. The contents are arranged logically and in order of difficulty: fractions, decimals, square and cube root, the metric system, algebra, quadratic and cubic equations, graphs, and the calculus are among the topics. Explanations of mathematical principles are followed by worked examples, and the book includes a convenient selection of tables that cover the trigonometrical functions and logarithms necessary for completing some of the examples.
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BEFORE we can use figures to arrive at correct results we must possess certain tools in the form of the standard symbols. These symbols are used all over the world and it is very necessary to memorise them, because they are, in effect, the shorthand of calculation. Here they are :
+ Plus, or add.
β Minus, or subtract.
Γ Multiply by.
Γ· Divide by.
/ Divide by (Solidus).
= Is equal to.
its always equal to. Identical with.
,
, or
Approximately equal to.
.. Therefore.
Since, because.
( Single bracket.
{ Double bracket, or brace.
[ Square bracket.
~ Difference of.
< Less than.
> Greater than.
Equal to, or less than.
Equal to, or greater than.
Not less than.
Not greater than.
β Varies as.
β Infinity.
Parallel with.
β₯ Perpendicular to.
β Vinculum or bar drawn over a group of algebraic terms (but the use of brackets is preferable).
Β± Plus or minus, i.e. either plus or minus, according to circumstances.
| + Codified plus sign, indicates that direction is taken into account as well as addition, as in obtaining the vector sum of two forces.
V Sign of vector subtraction.
The symbols Β°, β², and β³ are used to denote a degree, a minute, and a second respectively in the sexagesimal system of measurement, in which a right angle is divided into ninety equal parts called degrees, and each degree is divided into sixty equal parts called minutes, and each minute is divided into sixty equal parts called seconds.
Ξ£ Sigma, the sum, or βsummation of the products of.β
Ο Pi, the ratio of circumference to diameter, also 180Β° in circular measure.
ΞΈ Theta, any angle from the horizontal.
Ο Phi, any angle from the vertical.
Circle, or station point. Ξ Triangle, or trig station.
β Square root. The
sign is known as a radical.
Cube root.
Fourth root.
means factorial 5, or continued product up to 5=1 Γ 2 Γ 3 Γ 4 Γ 5. The factorial sign is sometimes written thus : ! Hence 5 ! means the continued product up to 5, and is the same as
.
II n=continued product of numbers up to n=1 Γ 2 Γ 3 ... n.
a, b, c used for known quantities ; x, y, z for unknown quantities. n is used in place of any whole number.
A full stop (.) is sometimes used instead of the multiplication sign.
Parallelogram.
Square.
Circumference.
Ξ΄ Sign of differentiation.
β Unequal to.
: Is to.
:: As ; so is (ratio)
Not parallel.
β Angle
Right angle.
Semi-circle.
Quadrant.
Arc.
(), [], { } Vincula.
is the sign of integration between limits o and x.
The symbol
means βthe area beneath the curve whose ordinate is y, from x=a to x=b.β
sin3
means the summation of the cubes of the sines of the angles 0 to 90.
The sign + (plus) or β (minus) has a higher separating power in a formula than Γ (multiplication) ; therefore parts connected by Γ may be multiplied out before passing beyond the other signs. Remember that plus times plus = +, plus times minus= β, minus times minus = +.
ROMAN NUMERALS
It will be observed that IV=4, means 1 short of 5 ; in the same way IX=9, means 1 short of 10 ; XL=40, means 10 short of 50 ; XC=90, means 10 short of 100 ; so for 1814 we have MDCCCXIV, and for 1953 we have MCMLIII.
OTHER MATHEMATICAL TERMS
Acnode. β A point outside a curve whose co-ordinate satisfies the equation of the curve ; a conjugate point.
Addend. β A quantity or number which is to be united in one sum with another quantity or number. This latter quantity is called the augend.
Adfected. β Containing different powers of an unknown quantity.
Aliquant. β Contained in another number but wi...
Table of contents
Title Page
Copyright Page
PREFACE
Table of Contents
CHAPTER I - MATHEMATICAL TERMS AND SIGNS
CHAPTER II - FRACTIONS
CHAPTER III - CONTINUED FRACTIONS: APPROXIMATIONS
CHAPTER IV - DECIMALS
CHAPTER V - DUODECIMALS
CHAPTER VI - SQUARE ROOT AND CUBE ROOT
CHAPTER VII - SOME SHORT CUTS
CHAPTER VIII - LOGARITHMS
CHAPTER IX - THE METRIC SYSTEM
CHAPTER X - PROGRESSION : ARITHMETICAL, GEOMETRICAL, AND HARMONICAL
CHAPTER XI - AVERAGES β RATIO AND PROPORTION β PERCENTAGES
CHAPTER XII - INTEREST β DISCOUNT β PRESENT VALUE β ANNUITIES
CHAPTER XIII - ALGEBRA
CHAPTER XIV - SIMPLE EQUATIONS
CHAPTER XV - SIMULTANEOUS EQUATIONS
CHAPTER XVI - PERMUTATIONS AND COMBINATIONS
CHAPTER XVII - THE BINOMIAL THEOREM
CHAPTER XVIII - ALGEBRAIC FACTORS
CHAPTER XIX - INDICES
CHAPTER XX - ALGEBRAIC FRACTIONS, H.C.F., AND L.C.M.
CHAPTER XXI - QUADRATIC AND CUBIC EQUATIONS
CHAPTER XXII - GRAPHS
CHAPTER XXIII - MENSURATION β TRIGONOMETRY
CHAPTER XXIV - AREAS OF CIRCLE, TRIANGLES, AND QUADRILATERALS
CHAPTER XXV - VOLUME β WEIGHT β MASS β DENSITY β SOLIDS
CHAPTER XXVI - THE INFINITESIMAL CALCULUS : DIFFERENTIATION
