Vedic Math Teachers Manual - 3 Advanced

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
14.1c 0 < x < 1
14.1d 0 < x < 1 and x² Coefficient > 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 Partial Fractions
15.2 Integration by ‘Parts’; TRUNCATING
15.3 BINOMIAL AND MACLAURIN THEOREMS
15.4 Derivatives of a Product
15.5 Derivative of A Quotient
15.6 Differential Equations – 1
15.7 Differential Equations – 2
15.8 Limits  220

LESSON 16 APPLIED MATHEMATICS

16.1 SIMPLE HARMONIC MOTION
16.2 PROJECTILES
16.3 FORCES IN EQUILIBRIUM
16.4 WORK AND MOMENT

LESSON 17 TRIGONOMETRIC FUNCTIONS

17.1 DERIVATIVES
17.2 SERIES EXPANSIONS
17.3 INVERSE TRIGONOMETRIC FUNCTIONS

17.3a DERIVATIVES
17.3b SERIES

17.4 EVALUATING TRIGONOMETRIC FUNCTIONS

17.4a COSINE
17.4b SINE
17.4c INVERSE TANGENT

LESSON 18 TRIGONOMETRIC AND TRANSCENDENTAL EQUATIONS

18.1 POLYNOMIAL EQUATIONS
18.2 TRIGONOMETRIC EQUATIONS
18.3 TRANSCENDENTAL EQUATIONS; KEPLER’S EQUATION

REFERENCES

SUTRAS AND SUB-SUTRAS

INDEX OF THE VEDIC FORMULAE  INDEX

INDEX