9/13/24, 9:16 Basic Numerical Methods - BCom BBA-Theory Notes
AM (Juraz)
BASIC NUMERICAL METHODS (B.COM/ BBA)
Equatio
Module I- Equations
ns
An equation is a statement of equality between two
expressions. It contains one or more derivatives.
Types of Equations
1.Linear equations
2.Exponential equations
3.Quadratic equations
4.Cubic equations
Properties of Equations
1.Any quantity can be added to both sides.
2.Any quantity can be subtracted from both sides.
3.Any quantity can be multiplied to both sides.
4.Any quantity can be divided to both sides.
5.Any function can be applied to both sides.
Linear equation
It is an equation for a straight line. The power of the
unknown in the linear equation will be 1.
Simple linear equation
Simple linear equations are first degree equation in which
one variable is unknown.
Simultaneous Equations
Simultaneous equations are a set of equations containing
multiple variables.
Quadratic equations
Quadratic equation is a polynomial equation of the second
degree. The general form is ax2+bx+c=0.
Factorization
The process of writing an expression as a product of two or
more common factor is called method of factorization.
Break Even point
A breakeven point is a point at which there is no profit,
there is no loss. Cost are equal to revenue.
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, 9/13/24, 9:16 Basic Numerical Methods - BCom BBA-Theory Notes
AM (Juraz)
Matrix
Module II- Matrices
Matrix is a rectangular arrangement of numbers or symbols
enclosed by a pair of brackets. The term matrix was first
introduced in 1850 by J J Sylvester.
Types of Matrices
1. Row matrix
A matrix which has only one row is called a row matrix or row
vector.
2. Column matrix
A matrix which has only one column is called a column
matrix or column vector.
3. Null matrix
If every element of an m x n matrix is zero, the matrix is
called zero matrix or null matrix.
4.Square matrix
If the number of rows and columns in a matrix are same,
such matrix is called square matrix or rectangular matrix.
5.Unit matrix
It is a square matrix with 1 on the principal diagonal and
zeros elsewhere. It is also called identity matrix.
6.Diagonal matrix
A square matrix in which every non- diagonal elements is
zero is called diagonal matrix
7.Scalar matrix
A diagonal matrix whose leading diagonal elements are all
equal is called diagonal scalar matrix
8.Upper triangular matrix
A matrix is known as upper triangular matrix if all the
elements below the leading diagonal are zero.
9.Lower triangular matrix
A matrix is known as lower triangular matrix if all the
elements above the leading diagonal are zero.
10. Sub matrix
The matrix obtained by deleting one or more rows or
columns or both of a matrix is called sub matrix.
about:blan 2/11
k
AM (Juraz)
BASIC NUMERICAL METHODS (B.COM/ BBA)
Equatio
Module I- Equations
ns
An equation is a statement of equality between two
expressions. It contains one or more derivatives.
Types of Equations
1.Linear equations
2.Exponential equations
3.Quadratic equations
4.Cubic equations
Properties of Equations
1.Any quantity can be added to both sides.
2.Any quantity can be subtracted from both sides.
3.Any quantity can be multiplied to both sides.
4.Any quantity can be divided to both sides.
5.Any function can be applied to both sides.
Linear equation
It is an equation for a straight line. The power of the
unknown in the linear equation will be 1.
Simple linear equation
Simple linear equations are first degree equation in which
one variable is unknown.
Simultaneous Equations
Simultaneous equations are a set of equations containing
multiple variables.
Quadratic equations
Quadratic equation is a polynomial equation of the second
degree. The general form is ax2+bx+c=0.
Factorization
The process of writing an expression as a product of two or
more common factor is called method of factorization.
Break Even point
A breakeven point is a point at which there is no profit,
there is no loss. Cost are equal to revenue.
about:blan 1/11
k
, 9/13/24, 9:16 Basic Numerical Methods - BCom BBA-Theory Notes
AM (Juraz)
Matrix
Module II- Matrices
Matrix is a rectangular arrangement of numbers or symbols
enclosed by a pair of brackets. The term matrix was first
introduced in 1850 by J J Sylvester.
Types of Matrices
1. Row matrix
A matrix which has only one row is called a row matrix or row
vector.
2. Column matrix
A matrix which has only one column is called a column
matrix or column vector.
3. Null matrix
If every element of an m x n matrix is zero, the matrix is
called zero matrix or null matrix.
4.Square matrix
If the number of rows and columns in a matrix are same,
such matrix is called square matrix or rectangular matrix.
5.Unit matrix
It is a square matrix with 1 on the principal diagonal and
zeros elsewhere. It is also called identity matrix.
6.Diagonal matrix
A square matrix in which every non- diagonal elements is
zero is called diagonal matrix
7.Scalar matrix
A diagonal matrix whose leading diagonal elements are all
equal is called diagonal scalar matrix
8.Upper triangular matrix
A matrix is known as upper triangular matrix if all the
elements below the leading diagonal are zero.
9.Lower triangular matrix
A matrix is known as lower triangular matrix if all the
elements above the leading diagonal are zero.
10. Sub matrix
The matrix obtained by deleting one or more rows or
columns or both of a matrix is called sub matrix.
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