Numerical Analysis

Abdullah Mijazi

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This app is not just a calculator; rather it generates step-by-step detailed solutions of problems using various known methods. It is very helpful to understand procedure of different methods as well as to find and rectify the errors in the lengthy calculations.

This app dynamically generates formula according to given problem, then put values in that formula in real time, and then calculates, so its end result would look just like somebody has written the entire calculations with pen and paper.

This app generates step-by-step detailed solutions by following methods.

1. Numeric Interpolation

a) Fixed Interval
i. Newton Forward Interpolation.
ii. Newton Backward Interpolation.
iii. Gauss Forward Interpolation.
iv. Gauss Backward Interpolation.
v. Stirling Interpolation.
vi. Bessel Interpolation.
vii. Everett Interpolation.
viii. Lagrange Interpolation.
ix. Aitken Interpolation.
x. Newton Divided Difference Interpolation.

b) Variable Interval
i. Lagrange Interpolation.
ii. Aitken Interpolation.
iii. Newton Divided Difference Interpolation.

2. Numeric Differentiation
a) Newton Forward Differentiation.
b) Newton Backward Differentiation.
c) Stirling Differentiation.
d) Bessel Differentiation.
e) Everett Differentiation.
f) Gauss Forward Differentiation.
g) Gauss Backward Differentiation.

3. Numeric Integration
a) Midpoint Rule Integration.
b) Trapezoidal Rule Integration.
c) Simpson's 1/3 Rule Integration.
d) Simpson's 3/8 Rule Integration.
e) Boole's Rule Integration.
f) Weddle's Rule Integration.
g) Romberg Rule Integration.

4. Linear System of Equations

a) Direct Methods
i. Cramer's Rule
ii. Cramer's Alternate Rule
iii. Gaussian Elimination Rule
iv. Factorization of L&U Matrix
v. Factorization with Inverse Matrix
vi. Cholesky's Rule
vii. Tri-Diagonal Rule

b) Iterative Methods
i. Jacobi's Method
ii. Gauss-Seidel Method

Who can use this app: This app is equally useful for Students as well as for Teachers to understand the subject and to pin-point the errors in lengthy calculations.

This app has the following salient features:
1. Easy to use.
2. Cover all familiar methods.
3. Give detailed (Step by step) solutions.
4. Easy to understand solutions to problems.