Numerical : Unit I

is to find the exact solutions of mathematical problems.

is a study of algorithms that use numerical approximations in solving problems.

should be accurate and precise enough for particular problems.

Rolle's Theorem

Extreme Value Theorem

Intermediate Value Theorem

nonlinear equations

system of linear equations

quadratic equations

eigen value problems

finding the root of the functions.

finding the zero of the functions.

finding the x value which f(x)=0.

No solution

Unique solution

Dual solutions

Infinite many solutions

$x_{n+1}=x_n+\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

$x_{n+1}=x_n-\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

$x_{n+1}=x_n+\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

$f'\left(x_o\right)\$ is approaching zero

$f'\left(x_o\right)\$ increases too rapidly

$x_o$ is too far from the root

$f\left(x\right)\$ is approaching zero

Secant

Normal

Chord

Tangent

3 decimal places

2 decimal places

4 decimal places

any number of decimal places will do