Contents
Preface 03-04
Introduction 07-11
Chapter-1 Addition and Subtraction 12-24
1. Addition - Completing the whole
2. Addition from left to right
3. Addition of list of numbers - Shudh method
4. Subtraction - Base method
5. Subtraction - Completing the whole
6. Subtraction from left to right
Chapter-2
Digit Sums,
Casting out 9s,
9-Check Method 25-28
Chapter-3 11-Check method 29-31
Chapter-4 Special Multiplication methods 32-52
1. Base Method
2. Sub Base Method
3. Vinculum
4. Multiplication of complimentary numbers
5. Multiplication by numbers consisting of all 9s
6. Multiplication by 11
7. Multiplication by two-digit numbers from right to left
8. Multiplication by three and four-digit numbers from right to left.
Chapter-5 Squaring and square Roots 53-57
Squaring
1. Squaring numbers ending in 5
2. Squaring Decimals and Fraction
3. Squaring Numbers Near 50
4. Squaring numbers near a Base and Sub Base
5. General method of Squaring - from left to right
6. Number splitting to simplify Squaring Calculation
7. Algebraic Squaring
Square Roots
1. Reverse squaring to find Square Root of Numbers ending in 25
2. Square root of perfect squares
3. General method of Square Roots
Chapter-6 Division 58-64
1. Special methods of Division
2. Straight Division
Contents
Chapter 1
Multiplying by 11 and 11 quickly
Chapter 2
A quick method to multiply by 9's
Chapter 3
This trick shows how you can square numbers between 1 & 19 with ease
Chapter 4
Subtract double-digit numbers with speed
Chapter 5
Subtract from numbers such as 1000, 2000, 3000 and more quickly
Chapter 6
the difference of two squares
Chapter 7
An Elegant method of sqauring numbers ending in 5
Chapter 8
Multiplication when all the digitis before the last digit are the same
the last digitis add up to 10 - This is an extension of the previous method
Chapter 9
Use Duplexes to find squares of any two-digit numbers
Chapter 10
Use Duplexes to the square of any 3-digit number
Chapter 11
Remember Pi to 6 and 18 decimal places
Chapter 12
Kilometes and Miles
Chapter 13
Divisibility by 9 & 11
Chapter 14
method of Multiplying and Dividing by 10, 100 and 1000
Chapter 15
A smart rule for Multiplying 2 x 2 digits
Working with Base 100 and Base 50 multiplication
Chapter 16
Multiplying any number by 12 - a shortcut method
Chapter 17
Multiplying any number by 12 - a shortcut method
Chapter 18
Quick way of dividing by 2, 4 and 8
Chapter 19
A smart way to divide by 9
Chapter 20
Dividing by 11
Chapter 21
Converting recurring decimals into fractions
Chapter 22
Estimating
Chapter 23
Working out significant Figures (s.f.)
Chapter 24
Standard Index Form
Chapter 25
Multiplication revisited
Chapter 26
general approach to 3 x 3 multiplication
Chapter 27
Add subtract fractions quickly
Chapter 28
Adding and subtracting mixed numbers
Chapter 29
Multiplying fractions
Chapter 30
Division of fractions
Chapter 31
Converting a mixed number to a fraction
Chapter 32
Multiplying mixed numbers together
Chapter 33
Dividing mixed numbers together
Chapter 34
Finding the nth term of common sequences
Chapter 35
Sqaure roots
Chapter 36
Cube and cube roots
Chapter 37
proportions and Rations
Chapter 38
Positive and negative numbers
Adding and subtracting
Chapter 39
Multiplying positive and negative numbers
Chapter 40
Rules concerning operation of numbers
Chapter 41
Solve simultaneous equations with ease
Chapter 42
Trigonometry
Chapter 43
Basic Statistics
Chapter 44
Quickly work out percentages
Chapter 45
Multiplying out brackets
Chapter 46
using Duplexes to work out the aquare of a two term algebraic expression
Chapter 47
Factorising quadratic expressions
Chapter 48
The formula method of solving quadratic equations
Chapter 49
Manipulating Indices/Exponents with ease
Chapter 50
Recurring percantage change
Contents
Content
Foreword by Mathematician Kenneth R. Williams Vii
1. Inter Base Conversion Method 1
Multiplication / Division by 10n 13
Multiplication / Division by factor of 10n 15
Square of number ending with 5n 18
Splitting Principle 20
2. Monodigit Number 25
3. Faster division by 10n − 1 or monodigit number 49
4. Vertically Crosswise Multiplication Method 54
5. Global Number System 66
6. Ripple operator 82
7. Derivation of Trachtenberg Formulae to Multiply any Number with 3-12 89
8. Square of number close to 10n having tens digit as x=7, 8 or 9 97
9. Square, Square Root and Cube of Specific Number 98
10. Recursive Square Method 102
11. Sliding Ruler Multiplication Method
( Unification of Vertically Crosswise and Trachtenberg Multiplication Method ) 105
12. Duplex square made easy 114
13. Squaring and cubing of any number 117
14. Osculation based divisibility Test 121
15. Divisibility by 10n ± 1 and Its Application 129
16. Remainder Corollary 139
17. VJ’s Universal Divisibility Test 144
18. Divisibility Chart 160
19. Nth power of two digit number made easy 161
20. Novel Approach for Multinomial Expansion 171
21. Computing mth Root of n digit number 178
22. Magical Game 183
23. Calendar calculation made easy 204
24. Why 0.999...... =1 ? 209
25. Common Balance Puzzle 211
26. Shift Add Representation and its Application 214
27. VJ’s Multiplication Method 219
28. Arithmetic Checking 229
Remainder computation 230
Algebraic Simplification 234
29. Modified Quine-McCluskey Method
( For engineering student ) 235
30. VJ’s Matrix (Rectangular) Method
( One line method to compute nth root any number ) 243
31. Vedic Division Method 270
32. Golden Lemma and Golden Pattern 278
33. Fun with Recurring Decimal 308
34. Principle behind Proportionately Sutra 335
Global Number System (Slides) 339
Bibliography 380
Course Content for the Teacher Training Course - TTC
Though the course does not aim to teach teaching, it includes advice on teaching, and two teaching projects are part of the course.
The main aim is to present mathematics as a structured, but easy and unified subject. That is to say: the mathematical content is Vedic Maths.
We start at the beginning with basic addition, subtraction, multiplication and division. Various simple and natural devices are introduced that make calculations very easy.
We concentrate on mental maths as well as written work, and various checking devices are used.
In addition to the basic general methods we have special methods in the Vedic system, which enable very tough problems to be solved with ease. This gives confidence as well as creating a sense of fun in maths work.
In addition to the basic operations we cover:
Fractions
Divisibility
Algebra
Solving equations
Squaring; square roots
Transformations
Coordinate geometry
Quadratic equations
Recurring decimals
The Vedic Numerical Code
Etc.
Various historical aspects are also included in the course.
Vedic Mathematics Teacher's Manual 2 - Advanced Level
Detailed course content is:
1. HOLISTIC MATHS
Course overview, history of our number system. 10-point circle, completing 10s, addition. Mental addition from left to right
2. COMPLETING THE WHOLE
Early history of VM. Looking for 10s in addition, including adding columns
Using addition and subtraction together
3. DOUBLING AND HALVING
Number splitting: doubling and repeated doubling. Maths teaching. Halving and repeated halving
4. CREATIVE MATHS
Improvising and extending the multiplication tables
Multiplying and Dividing by 5, 50, 25
5. A MAGIC NUMBER
Digit sums, 9-point circle, casting out nines. Digit sum puzzles and divisibility by 3, 9, 6, 15
6. CHECKING IT OUT
Checking with digit sums. Checking with first and last figures / Vedic Square
7. THE INVISIBLE NUMBER
Calculating left to right. Doubling & halving / Finger maths
8. SUBTRACTION
Recent history. Subtraction-left to right. Checking subtractions
9. EXPLAINING VEDIC MATHS
Questions on Vedic Maths. Combining/comparing fractions
10. ALL FROM 9 AND THE LAST FROM 10
Subtraction. Bar numbers
11. THE POWER OF NEGATIVE THINKING
Using bar numbers for subtraction. Number splitting
12. ANOTHER MAGIC NUMBER
Multiplication by 11. Divisibility by 11 and a ‘digit sum’ check
13. COHERENT MATHS
General multiplication and reverse. Algebraic multiplication and its reverse
14. MATHEMAGICS
Multiplying numbers near 100. Proofs
15. NUMBER PATTERNS
Using Proportion to extend base multiplication
Multiplying near base 10, and multiples of 10
16. THINK OF A NUMBER
Use of transposition in solving word puzzles. Solving equations
17. SPECIAL AND GENERAL
Some special multiplication devices
18. SPECIAL DIVISION
Dividing by 9, 8, 11 etc. Algebraic division
19. NATURAL MATHS
The Sutras. Calculating areas. Temperature conversions. Spotting the obvious
20. DEMONSTRATIONS
Advice on structuring a talk
21. GENERAL MULTIPLICATION
Extending the Vertically and Crosswise method
22. SQUARES AND ROOTS
Squaring 2-figure numbers and binomials. Square root of a perfect square
23. TRIPLES
Triple notation and addition. Rotations with triples
24. GENERAL SQUARING
The duplex, Squaring numbers of any size. Algebraic squaring
25. THE CROWNING GEM
Straight division. How to choose your remainder. Decimalizing the remainder
26. STRAIGHT DIVISION
Extending straight division to 3-figure divisors. Negative flag digits. Changing the numbers. Two figures or more on the flag
27. MASSIVE MULTIPLICATIONS
Multiplying numbers near high bases. Squaring near a base
Multiplying numbers near different bases
28. COORDINATE GEOMETRY
Equation of a line through two given points. Equation of a line through a given point and parallel or perpendicular to a given line
29. SQUARE ROOTS
The general method
30. CALCULUS
Solving quadratic equations by two methods. Comparison of some Vedic and conventional methods
31. RECURRING DECIMALS
From left to right and from right to left
32. SPECIAL NUMBERS
An easy kind of multiplication and special numbers
Their application in making recurring decimals easier
33. DIVISIBILITY
The osculation process
34. TRIPLE GEOMETRY
Triple subtraction and applications
35. LEFT TO RIGHT
Written calculations from left to right
36. COMBINING CALCULATIONS / THE VALUE OF pi
Calculating from the left. Sanskrit and Pi
Advanced Diploma Course
Course Content:
Week 1
1. Product of Three Numbers, Binomials
Numbers near a Base, General method for Three Numbers, Product of Binomials
2. Cubing, Cube Root
Cubing – near a Base, Cubing and Beyond, Cubing Binomials, Cube Rt
3. Recurring Decimals
4. Division – Part 1
Flag Division, dividing with 9s
Week 2
5. Division – Part 2
Base division’ Proportion – Direct and Inverse, Comparing Prices
6. Divisibility– Part 1
7. Divisibility– Part 2
Divisibility (right to left, left to right), Creating a Number Divisible by Given Number, Divisibility puzzles
8. Algebraic division
Two methods, dividing the remainder, series expansions.
Week 3
9. Algebraic square root - to any number of terms
10. Factorisation
Factorising – quadratics (incl 2 and 3 variables), cubics, etc., evaluating polynomials
11. Solution of equations
Simultaneous, special
12. Calculus methods - Part 1
Quadratic equations, partial fractions, derivatives of products and quotients
13. Calculus methods - Part 2
Trig functions, series expansions, integration by ‘parts’ etc.
Week 4
14. Triple Geometry
Double and Half angle triple, geometry
15. Transformations
Rotations of points, lines & curves, reflections
16. Coordinate geometry
Linear interpolation, distance of a point from a line, perp bisector
17. Trigonometry – Part 1
Compound angles, inverse functions
Week 5
18. Trigonometry – Part 2
Trig proofs, trig equations.
19. Triple Code Numbers
Grouping and Generating Triples
20. Code Numbers and Angles
Solution of Trig. Equations
21. Complex numbers
Multiplication, division, square root
Vedic Mathematics Teacher's Manual 1 - Elementary Level
Contents
PREFACE
LESSON 1 COMPLETING THE WHOLE
INTRODUCTION
THE TEN POINT CIRCLE
MULTIPLES OF TEN
DEFICIENCY FROM TEN
DEFICIENCY AND COMPLETION TOGETHER
MENTAL ADDITION
COMPLETING THE WHOLE
COLUMNS OF FIGURES
BY ADDITION AND BY SUBTRACTION
SUBTRACTING NUMBERS NEAR A BASE
LESSON 2 DOUBLING AND HALVING
DOUBLING
MULTIPLYING BY 4, 8
HALVING
SPLITTING NUMBERS
DIVIDING BY 4, 8
EXTENDING YOUR TABLES
MULTIPLYING BY 5, 50, 25
DIVIDING BY 5, 50, 25
DIVIDING BY 5
DIVIDING BY 50, 25
LESSON 3 DIGIT SUMS
ADDING DIGITS
THE NINE POINT CIRCLE
CASTING OUT NINES
DIGIT SUM PUZZLES
MORE DIGIT SUM PUZZLES
THE DIGIT SUM CHECK
MULTIPLICATION CHECK
THE VEDIC SQUARE
PATTERNS FROM THE VEDIC SQUARE
NUMBER NINE
LESSON 4 LEFT TO RIGHT
ADDITION: LEFT TO RIGHT
MULTIPLICATION: LEFT TO RIGHT
DOUBLING AND HALVING
SUBTRACTION: LEFT TO RIGHT
CHECKING SUBTRACTION SUMS
MORE SUBTRACTIONS
LESSON 5 ALL FROM 9 AND THE LAST FROM 10
ALL FROM 9 AND THE LAST FROM 10
SUBTRACTION
ADDING ZEROS
ONE LESS
ONE MORE
ONE LESS AGAIN
MONEY
LESSON 6 NUMBER SPLITTING
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
LESSON 7 BASE MULTIPLICATION
TIMES TABLES
NUMBERS JUST OVER TEN
MULTIPLICATION TABLE PATTERNS
RECURRING DECIMALS
NUMBERS CLOSE TO 100
MENTALLY
NUMBERS OVER 100
MENTAL MATHS
RUSSIAN PEASANT MULTIPLICATION
LARGER NUMBERS
NUMBERS ABOVE THE BASE
PROPORTIONATELY
ANOTHER APPLICATION OF PROPORTIONATELY
MULTIPLYING NUMBERS NEAR DIFFERENT BASES
SQUARING NUMBERS NEAR A BASE
A SUMMARY
LESSON 8 CHECKING AND DIVISIBILITY
DIGIT SUM CHECK FOR DIVISION
THE FIRST BY THE FIRST AND THE LAST BY THE LAST
THE FIRST BY THE FIRST
THE LAST BY THE LAST
DIVISIBILITY BY 4
DIVISIBILITY BY 11
REMAINDER AFTER DIVISION BY 11
ANOTHER DIGIT SUM CHECK
LESSON 9 BAR NUMBERS
REMOVING BAR NUMBERS
ALL FROM 9 AND THE LAST FROM 10
SUBTRACTION
CREATING BAR NUMBERS
USING BAR NUMBERS
LESSON 10 SPECIAL MULTIPLICATION
MULTIPLICATION BY 11
CARRIES
LONGER NUMBERS
BY ONE MORE THAN THE ONE BEFORE
MULTIPLICATION BY NINES
THE FIRST BY THE FIRST AND THE LAST BY THE LAST
USING THE AVERAGE
SPECIAL NUMBERS
REPEATING NUMBERS
PROPORTIONATELY
DISGUISES
LESSON 11 GENERAL MULTIPLICATION
REVISION
TWO-FIGURE NUMBERS
CARRIES
MOVING MULTIPLIER
EXTENSION
MULTIPLYING BINOMIALS
MULTIPLYING 3-FIGURE NUMBERS
WRITTEN CALCULATIONS
LESSON 12 SQUARING
SQUARING NUMBERS THAT END IN 5
SQUARING NUMBERS NEAR 50
GENERAL SQUARING
THE DUPLEX
NUMBER SPLITTING
ALGEBRAIC SQUARING
DIGIT SUMS OF SQUARES
SQUARE ROOTS OF PERFECT SQUARES
3 AND 4 FIGURE NUMBERS
LESSON 13 EQUATIONS
ONE-STEP EQUATIONS
TWO-STEP EQUATIONS
THREE-STEP EQUATIONS
LESSON 14 FRACTIONS
VERTICALLY AND CROSSWISE
A SIMPLIFICATION
COMPARING FRACTIONS
UNIFICATION OF OPERATIONS
LESSON 15 SPECIAL DIVISION
DIVISION BY 9
LONGER NUMBERS
CARRIES
A SHORT CUT
DIVISION BY 8 ETC.
DIVISION BY 99, 98 ETC.
DIVISOR BELOW A BASE NUMBER
TWO-FIGURE ANSWERS
DIVISOR ABOVE A BASE NUMBER
LESSON 16 THE CROWNING GEM
SINGLE FIGURE ON THE FLAG
SHORT DIVISION DIGRESSION
LONGER NUMBERS
NEGATIVE FLAG DIGITS
DECIMALISING THE REMAINDER
SUTRAS AND SUB-SUTRAS
9-POINT CIRCLES
REFERENCES
INDEX OF THE VEDIC FORMULAE
INDEX
Vedic Mathematics Teacher's Manual 2 - Intermediate Level
Contents
PREFACE
LESSON 1 Basic Devices
Introduction
Digit Sums
Left to Right
Addition
Multiplication
Advantages of left to Right Calcn
Writing Left to Right Sums
Checking Devices
Subtraction
Subtraction from Left to Right
Checking Subtraction Sums
LESSON 2 MORE BASIC DEVICES
Number Splitting
Addition 14 / Subtraction
Multiplication 16 / Division
All from 9 and the Last from 10
Subtraction from a Base
Calculations Involving Money
First Extension
Second Extension
Combining the Extensions
Bar Numbers
Advantages of Bar Numbers
General Subtraction
LESSON 3 SPECIAL METHODS
Proportionately
Doubling and Halving
Extending the Multiplication Tables
Multiplying by 5, 50, 25
All from 9 and the Last from 10: Multiplication
Numbers just below 100
Geometrical Proof
Algebraic Proof
Other Bases
Numbers above the Base
One Number ABOVE and one below the Base
Proportionately
Multiplying Numbers near Different Bases
Squaring Numbers near a Base
Mental Calculations
Special methods
LESSON 4 BY ONE MORE THAN THE ONE BEFORE
Special Multiplications
Squaring Numbers that End in 5
A Variation
Multiplication Summary
Recurring Decimals
Denominator Ending in 9
Proof
A Short Cut
Proportionately
Longer Numerators
LESSON 5 AUXILIARY FRACTIONS
Auxiliary Fractions: First Type
Denominators Ending in 8, 7, 6
Auxiliary Fractions: Second Type
Denominators Ending in 1
Alternative Method
Denominators Ending in 2, 3, 4
Working 2, 3 etc. Figures at a Time
LESSON 6 VERTICALLY AND CROSSWISE
Fractions
Adding & Subtracting Fractions
Proof
A Simplification
Comparing Fractions
Multiplication and Division
General Multiplication
Revision
Multiplying 2-Figure Numbers
Explanation
Explanation of earlier special method
The Digit Sum Check
Multiplying 3-Figure Numbers
Moving Multiplier
Algebraic Multiplications
The Digit Sum Check
Three-Figure Numbers
Four-Figure Numbers
Writing Left to Right Sums
From Right to Left
setting the sums out
Using Bar Numbers
LESSON 7 SQUARES AND SQUARE ROOTS
General Squaring
Two-Figure Numbers
Number Splitting
Algebraic Squaring
Squaring Longer Numbers
Written Calculations – Left to Right
Written Calculations – Right to Left
Square Roots of Perfect Squares
LESSON 8 SPECIAL MULTIPLICATION METHODS
Special Numbers
Repeating Numbers
Proportionately
Disguises
Using the Average
PROOF
Multiplication by Nines
Multiplication by 11
Percentages
Increasing
Reducing
LESSON 9 TRIPLES
Definitions
Triples for 45°, 30° and 60°
Triple Addition
Double Angle
Variations of 3,4,5
Quadrant Angles
Rotations
LESSON 10 SPECIAL DIVISION
Division by Nine
Adding Digits
A Short Cut
Dividing by 8
Algebraic Division
Dividing by 11, 12 etc.
Larger Divisors
Divisor just Below a Base
A Simplification
Divisor just Above a Base
Proportionately
LESSON 11 STRAIGHT DIVISION
Single Figure on the Flag
Short Division Digression
Longer Numbers
Multiplication Reversed
Decimalising the Remainder
Negative Flag Digits
Larger Divisors
Algebraic Division
LESSON 12 EQUATIONS
Linear
One x Term
Two x Terms
Quadratic Equations
Simultaneous Equations
By Addition and By Subtraction
A Special Type
General Method
Another Special Type
LESSON 13 APPLICATIONS OF TRIPLES
Triple Subtraction
Triple Geometry
Angle Between Two Lines
Half Angle
Coordinate Geometry
Gradients
Circle Problems
Length of Perpendicular
LESSON 14 SQUARE ROOTS
Squaring
Square Root of a Perfect square
Preamble
Two-Figure Answer
Reversing Squaring
Three-Figure Answer
Reversing Squaring
General Square Roots
Changing the Divisor
Heuristic Proof
LESSON 15 DIVISIBILITY
Elementary Parts
The Ekadhika
Osculation
Explanation
Testing Longer Numbers
Other Divisors
The Negative Osculator
LESSON 16 COMBINED CALCULATIONS
Algebraic
Arithmetic
Pythagoras Theorem
SUTRAS AND SUB-SUTRAS
9-POINT CIRCLES
REFERENCES
INDEX OF THE VEDIC FORMULAE
INDEX
Vedic Mathematics Teacher's Manual 3 - Advanced Level
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
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 Alebraic 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
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