Linear and Nonlinear Equations in Numerical Analysis, Study notes of Mathematical Methods for Numerical Analysis and Optimization

The difference between linear and nonlinear equations in Mathematics. It provides definitions and examples of both types of equations and presents the major differences between them in a tabular form. The document also includes information on the degree of the equations and their general representations. It concludes with examples of linear and nonlinear equations and explains the difference between linear equations in one variable and two variables.

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2022/2023

Available from 01/09/2023

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NUMERICAL ANALYSIS
Numerical linear and nonlinear algebra: In Mathematics, you must have learned
about different types of equations. Here, we are going to discuss the difference
between linear and nonlinear equations. The difference between them is
described here with the help of definitions and examples.
Linear means something related to a line. All the linear equations are used to
construct a line. A non-linear equation is such which does not form a straight line.
It looks like a curve in a graph and has a variable slope value. The major difference
between linear and nonlinear equations is given here for the students to
understand it in a more natural way. The differences are provided in a tabular
form with examples.
What is the difference between Linear and Nonlinear Equations?
Linear Equations Non-Linear Equations
It forms a straight line or represents the
equation for the straight line
It does not form a straight line but
forms a curve.
It has only one degree. Or we can also
define it as an equation having the
maximum degree 1
A nonlinear equation has the degree
as 2 or more than 2, but not less than
2.
All these equations form a straight line in
XY plane. These lines can be extended to
any direction but in a straight form.
It forms a curve and if we increase
the value of the degree, the
curvature of the graph increases.
The general representation of linear The general representation of
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NUMERICAL ANALYSIS

Numerical linear and nonlinear algebra: In Mathematics, you must have learned about different types of equations. Here, we are going to discuss the difference between linear and nonlinear equations. The difference between them is described here with the help of definitions and examples. Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value. The major difference between linear and nonlinear equations is given here for the students to understand it in a more natural way. The differences are provided in a tabular form with examples. What is the difference between Linear and Nonlinear Equations? Linear Equations Non-Linear Equations It forms a straight line or represents the equation for the straight line It does not form a straight line but forms a curve. It has only one degree. Or we can also define it as an equation having the maximum degree 1 A nonlinear equation has the degree as 2 or more than 2, but not less than

All these equations form a straight line in XY plane. These lines can be extended to any direction but in a straight form. It forms a curve and if we increase the value of the degree, the curvature of the graph increases. The general representation of linear The general representation of

Linear Equations Non-Linear Equations equation is; y = mx +c Where x and y are the variables, m is the slope of the line and c is a constant value nonlinear equations is; ax² + by² = c Where x and y are the variables and a,b and c are the constant values Examples : 10x = 1 9y + x + 2 = 0 4y = 3x 99x + 12 = 23 y Examples: x²+y² = 1 x² + 12xy + y² = 0 x²+x+2 = 25 Note: The linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. For example, 5x + 2 = 1 is Linear equation in one variable. But 5x + 2y = 1 is a Linear equation in two variables. Let us see some examples based on these concepts. Example : Solve the linear equation 3x+9 = 2x +18. Solution: Given, 3x+9 = 2x + 18 ⇒ 3x – 2x = 18 – 9