Vedic Math Teachers Manual, Volume 3, Advanced

India: Motilal Banarsidass. 2005. F First Edition. H Hardcover. New. Contents:PREFACE LESSON 1 LEFT TO RIGHT CALCULATIONS 1.1 INTRODUCTION 1.2 ADDITION 1.3 MULTIPLICATION Advantages OF LEFT TO RIGHT CALCULATION 1.4 WRITING LEFT TO RIGHT SUMS 1.5 SUBTRACTION 1.6 DIGIT SUMS 1.7 CHECKING DEVICES CHECKING SUBTRACTION SUMS 1.8 ALL FROM 9 AND THE LAST FROM 10 1.8a SUBTRACTION FROM A BASE 1.8b BAR NUMBERS ADVANTAGES OF BAR NUMBERS 1.8c GENERAL SUBTRACTION LESSON 2 SPECIAL METHODS 2.1 MULTIPLICATION NEAR A BASE 2.1a Numbers just below the base 2.1.b Above the base 2.1c Above and below 2.1d Proportionately 2.1e With different bases 2.2 MENTAL CALCULATIONS 2.3 SPECIAL NUMBERS 2.3a Repeating numbers 2.3b Proportionately 2.3c Disguises 2.4 DIVISION BY NINE 2.4a Adding Digits 2.4b A Short Cut 2.4c Dividing by 8 2.4d Algebraic Division 2.4e Dividing by 11, 12 etc. LESSON 3 RECURRING DECIMALS 3.1 DENOMINATOR ENDING IN 9 3.2 A SHORT CUT 3.3 PROPORTIONATELY 3.4 LONGER NUMERATORS 3.5 DENOMINATORS ENDING IN 8, 7, 6 3.6 DENOMINATORS ENDING IN 1 3.7 DENOMINATORS ENDING IN 2, 3, 4 3.8 WORKING 2, 3 ETC. FIGURES AT A TIME LESSON 4 TRIPLES 4.1 Definitions 4.2 Triples for 45°, 30° and 60° 4.3 Triple Addition 4.4 Double Angle 4.5 Variations of 3,4,5 4.6 Quadrant Angles 4.7 Rotations LESSON 5 GENERAL MULTIPLICATION 5.1 TWO-Figure Numbers Explanation/ The Digit Sum Check 5.2 Moving Multiplier 5.3 Algebraic PRODUCTS The Digit Sum Check 5.4 Three-Figure Numbers 5.5 Four-Figure Numbers 5.6 Writing Left to Right Sums 5.7 From Right to Left setting the sums out 5.8 Using Bar Numbers LESSON 6 SOLUTION OF EQUATIONS 6.1 TRANSPOSE AND APPLY 6.1a SIMPLE EQUATIONS 6.1b MORE THAN ONE X TERM 6.2 SIMULTANEOUS EQUATIONS 6.2a GENERAL SOLUTION 6.2b Special Types 6.3 QUADRATIC EQUATIONS 6.4 ONE IN RATIO THE OTHER ONE ZERO 6.5 MERGERS 6.6 WHEN THE SAMUCCAYA IS THE SAME IT IS ZERO 6.6a Samuccaya as a common factor 6.6b Samuccaya as the Product of the Independent Terms 6.6c Samuccaya as the Sum of the Denominators 6.6d Samuccaya as a Combination or Total Proof/ EXTENSION 6.6e other typeS 6.7 THE ULTIMATE AND TWICE THE PENULTIMATE 6.8 ONLY THE LAST TERMS 6.9 SUMMATION OF SERIES 6.10 FACTORISATION LESSON 7 SQUARES AND SQUARE ROOTS 7.1 Squaring 2-FIGURE NUMBERS 7.2 Algebraic Squaring 7.3 Squaring Longer Numbers 7.4 Written Calculations 7.4a Left to Right 7.4b Right to Left 7.5 Square Roots of Perfect Squares LESSON 8 APPLICATIONS OF TRIPLES 8.1 Triple Subtraction 8.2 Triple Geometry 8.3 Angle Between Two Lines 8.4 Half Angle 8.5 Coordinate Geometry 8.5a Gradients 8.5b Length of Perpendicular 8.5c Circle Problems 8.5d EQUATION OF A LINE 8.6 COMPLEX NUMBERS CONTENTS LESSON 9 DIVISIBILITY 9.1 Elementary Parts 9.2 The Ekadhika 9.3 Osculation Explanation 9.4 Testing Longer Numbers 9.5 Other Divisors 9.6 The Negative Osculator 9.7 OSCULATING WITH GROUPS OF DIGITS LESSON 10 STRAIGHT DIVISION 10.1 Single Figure on the Flag 10.2 Short Division Digression 10.3 Longer Numbers Multiplication Reversed 10.4 Decimalising the Remainder 10.5 Negative Flag Digits 10.6 Larger Divisors 10.7 ALGEBRAIC DIVISION LESSON 11 SQUARE ROOTS 11.1 Squaring 11.2 Square Root of a Perfect square 11.2a Preamble 11.2b Two-Figure Answer Reversing Squaring 11.2c Three-Figure Answer Reversing Squaring 11.3 General Square Roots 11.4 Changing the Divisor Heuristic Proof 11.5 ALGEBRAIC SQUARE ROOTS LESSON 12 TRIPLE TRIGONOMETRY 12.1 COMPOUND ANGLES 12.2 INVERSE FUNCTIONS 12.3 THE GENERAL TRIPLE 12.4 TRIGONOMETRIC EQUATIONS 12.4a SIMPLE EQUATIONS 12.4b A SPECIAL TYPE LESSON 13 COMBINED OPERATIONS 13.1 Algebraic 13.2 Arithmetic 13.2a SUMS OF PRODUCTS 13.2b ADDITION AND DIVISION 13.2c STRAIGHT DIVISION 13.2d MEAN AND MEAN DEVIATION 13.2e DIVIDING SUMS OF PRODUCTS 13,2f VARIANCE 13.3 Pythagoras’ Theorem LESSON 14 SOLUTION OF POLYNOMIAL EQUATIONS 14.1 QUADRATIC EQUATIONS 14.1a x > 1 PROOF 14.1b x 1 14.1e –1 < x < 0 14.1f x LARGE 14.2 HIGHER ORDER EQUATIONS 14.2a CUBE ROOT 14.2b CUBIC EQUATIONS A SIMPLIFICATION A CUBIC WITH 0 < x< 1 14.2c QUINTICS LESSON 15 CALCULUS METHODS 15.1 PartialF