The document discusses numerical methods and their applications. It provides definitions of numerical methods as procedures for solving problems with computable error estimates. Some common numerical methods are listed, including bisection, Newton-Raphson, iteration, and interpolation methods. Applications mentioned include root finding, profit/loss calculation, multidimensional root finding, and simulations. An example is given of using numerical methods for image deblurring. The document also discusses computational modeling, algorithm development and implementation, and limitations of computers in solving mathematical problems.

1. Daffodil Internatioal University

2. Name :
Omar Sharif
Designation :
Lecturer
Department
Department of Natural Sciences
Faculty
Faculty of Science and Information Technology
E-mail
omarsharif.ns@diu.edu.bd

3. Application of Numerical Methods AND MY
ACHIVEMENT

4. What is Numerical Method ?
A numerical method is a complete and definite set of
procedures for the solution of a problem, together with
computable error estimates. The study and
implementation of such methods is the province
of numerical analysis. "numerical methods."

5. Types of Numerical Methods
 1 .Bisection method
 2. Newton Rapshon method (Newton’s Iteration
method)
 3. Iteration method
 4. Newton’s forward interpolation formula
 5. Newton’s backward interpolation formula
 6. Gauss Seidel Method
 7. CURVE FITTING

6. Applications
 Usually used in computer science for root algorithm.
 It is used to determine profit and loss in the company.
 Used for Multidimensional root finding.
 Solving practical technical problems using scientific and
mathematical tools
 Network Simulation
 Train and Traffic signal
 Weather prediction
 Build up a algorithm

7. Numerical Method in
PHOTOGRAPHY :

8. Maths and crime: Deblurring a
number plate
A short crime story
• Rana robs a bank
• Escapes in a getaway car
• Pursued by police

9. SOLUTION
 Find a model of the blurring process
 Blurring function g
Original image
 f
• Blurring formula
• Inverting the formula we can get rid the blur
• BUT need to know the blurring function g
ydygyxfxh   2
)()()(

10. 
2/)/( 222
dxgdexhdeef xixiyi



Inversion formula
h(x) f(x)
An example of Image
Processing

11. Scientific computing
 Design and analysis of algorithms for
numerically solving mathematical problems in
science and engineering
 Considers the effect of approximations and
performs error analysis
 modern simulations of engineering
applications

12. Computational problems:
attack strategy
 Develop mathematical model (usually requires a combination of math skills
and some a priori knowledge of the system)
 Come up with numerical algorithm (numerical analysis skills)
 Implement the algorithm (software skills)
 Run, debug, test the software
 Visualize the results
 Interpret and validate the results
Mathematical modeling

13. Computational problems:
well-posedness
 The problem is well-posed, if
(a) solution exists
(b) it is unique
(c) it depends continuously on problem data
Simplification strategies:
Infinite finite
Nonlinear linear
High-order low-order

14. What computers can’t do
 Solve (by reasoning) general mathematical
problems  they can only repetitively apply
arithmetic primitives to input.
 Solve problems exactly.
 Represent all numbers. Only a finite subset of the
numbers between 0 and 1 can be represented.

15. MY ACHIVEMENT