math-254 numerical methods · 2021. 1. 19. · chapter 4 approximating functions (7 lectures)...

Math-254

Numerical Methods

Recommended Textbook: IntroductIon to numerIcal analysIs usIng matlaB author: dr. rIzwan Butt reference textBook: Numerical Analysis (Seventh Edition)

authors: rIchard l. Burden and J. douglas faIres Pdf slIdes of the course: httPs://fac.ksu.edu.sa/maBdelwahed/course/308640

Topics for the Course

chaPter 1 numBer systems and error (1 lecture) chaPter 2 solutIons of nonlInear equatIons (13 lectures) chaPter 3 systems of lInear equatIons (13 lectures) chaPter 4 aPProxImatIng functIons (7 lectures) chaPter 5 dIfferentIatIon and IntegratIon (7 lectures) chaPter 6 ordInary dIfferentIal equatIons (4 lectures)

Numerical Methods

Graphical Methods

Exact Solution Approximate Solution

Analytical Methods

1- Numerical analysis can be defined as the development and implementation of techniques to find numerical solutions to mathematical problems. 2- It is an increasingly important link between pure mathematics and its application in science and technology. 3- With the accessibility of computers, it is possible now to get rapid and accurate solutions to many complex problems that give difficulties to the mathematician, engineer and scientist. 4. Frequently, numerical analysis is called the mathematics of scientific computing.

Need finite number of steps.

No need for initial approximation.

Good for small problems.

Chance of getting exact information about problems.

Need infinite number of steps.

Need for initial approximation.

Good for large problems.

No chance of getting exact information about problems.

Iterative Methods

Direct Methods

1- In our lectures, practical justification of the methods is presented through computer examples through the use of MATLAB. 2- In recent years, the number of MATLAB users has dramatically increased. 3- The surge of popularity in MATLAB is related to the increasing popularity of UNIX and computer graphics. 4- To what extend numerical computations in the future will be programmed in MATLAB is uncertain.