Course
Bharatiya Ganit Shastra for Students of Mathematics & Physics department
1.ARITHMETIC
1. History of Bharatiya Mathematics & Fundamentals of Vaidik Ganit
- Bharatiya Ganit Shashtra
- Concepts of complements – with respect to 10, 100, 1000
- Sum of the complements – 10, 100 & 1000
- Additive & Subtractive Digital Root – Casting out multiples of 9s & 11s
2. Vinculum, Number Formation, Addition & Subtraction (Arithmetic & Algebraic)
- Vinculum – Normal form to Vinculum & Vice versa
- Addition – Dot Method, Complement Method, Vinculum Method
- Subtraction – Complement Method, Vinculum Method
3. Multiplication – Vertically Crosswise, Base & Sub-Base Rule
- Conventional Multiplication Rule
- Vertically Crosswise – 2 x 2, 3 x 2, 3 x 3, 4 x 4
- Base – Above base, Below base & Mixed Base - 10, 100, 1000 etc
- Sub-Base – Above sub-base, Below sub-base & Mixed sub-base - 20, 30, 200 etc
4. Divisibility (Connection in between Multiplication & Division) & Primes
- Divisility rules – Osculator Rule
5. Division - Using Dhwajaank Rule - Horizontal method
- Division by single digit
- Division by two digit
- Division by three digit
6. Indices – Squares, Cubes
- Square – Using Base Method & Duplex Method
- Cube – Using Base Method & Triplex Method
7. Radicals – Sq. Roots, Cube Roots (of perfect squares and cube numbers ONLY)
- Square Root – Viloknam
- Cube Root – Viloknam
8.Inverse of numbers and Percentage Values
- Inverse of numbers
- Percentage conversion and its applications
9. Inverse of numbers and Percentage Values
- Inverse of numbers
- Percentage conversion and its applications
10. Combined Operations
- Product of three two-digit numbers simultaneously
- Sum of Products
11. Magic Square by Vedic Rules
- Introduction
- Magic Square Odd: 3x3, 5x5
- Magic Square Even: 4x4
2.ALGEBRA
1. Polynomials
- Multiplication and Division of Polynomials
- Quick factorisation of polynomials till degree3
- Equations in one variable upto degree 3
- H.C.F
2. Quadratic Equation
- Quadratic equations in single variable
- Roots of Quadratic Equation
- Relation between roots and coefficients of Quadratic Equation and Application
- Solution of Quadratic equations
- Simultaneous quadratic equations of 3 variables
- Kuttaka : Aryabhata, Brahmgupta, Bhasakaracharaya, solution of Indeterminate Equation of form ax + c = by
- Varga Prakriti - Brahmgupta-Bhasakrachaya equation, Chakrabal method to solve the equation, Dx^2 + k = y^2
3.Determinants and Matrices
- Definitions,differences, Properties of a determinant
- Expansion of a determinant by swami ji's method upto 3 or 4 order
- Expansion of a determinant using properties
- Expansion of a determinant with one or two very large elements
- Simultaneous linear equations upto order 3--Consistency and Solution
3.TRIGONOMETRY
1. Baudhayan Triples
- Formation of Triples
- Finding the no. of triangles with Integral sides when one side/hypotenuse is given
2. Trigonometric Ratios
- Unit Circle and the general Triple
- Degree,Radians and Gradians
- Baudhayan Triples of Some Standard Angles
- Allied angles with X and Y axes respectively
- Arc length and Area of a Sector in a Circle
3.Compound Angles
- Sum and Difference of Triples
- Multiple and Sub-multiples of angles
- Heights and Distances
- Two-Dimenional and Three -Dimensional Problems using Triples
4.CO-ORDINATE GEOMETRY
1. Co-ordinates
- Images(Water and Mirror) and in some important Lines.
- Distance Formula(Vedic Version) and Use of Anurupyen
- Area of a triangle (Shortcut)
- Division of a line segment ( Internal and External)
- Centroid,Incentre,Circumcentre in a triangle
2. Straight Line
- Slope of a Line
- Vedic Equation of a Straight Line( one equation for five conventional equations)
- Parallel and Perpendicular Lines
- Symmetric equation of a St. Line using a Baudhayan Triple & it's wide use
- Angle between two Lines using Triples
- Rotation of a point about another point
- Equation of a line making a certain angle with a given line
3.Circle
- Definition, Formation of its Equation
- Quick formation of a circle through three given points
- Checking whether points are Concyclic or not
- Tangents and Normals
5.CALCULUS
1. Derivatives
- Derivative of a Product ( by vertically cross-wise)
- Derivative of a Quotient
2. Integration
- Integration by Parts ( Quick method)
- Partial Fractions (Quick Formation)
- Formation of Series for a function using Calculus
6.STATISTICS
1. Baudhayan Triples
- Division of Addition
- Mean and Mean Deviation, Dividing Sum of Products/squares
- Variance
