1 / 23

The Islamic University of Gaza Faculty of Engineering Numerical Analysis ECIV 3306

The Islamic University of Gaza Faculty of Engineering Numerical Analysis ECIV 3306 . Introduction. Introduction. Consider the following equations. Numerical Methods - Definitions. Numerical Methods. Analytical vs. Numerical methods. Analytical vs. Numerical methods.

pravat
Download Presentation

The Islamic University of Gaza Faculty of Engineering Numerical Analysis ECIV 3306

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Islamic University of Gaza Faculty of Engineering Numerical Analysis ECIV 3306 Introduction

  2. Introduction • Consider the following equations.

  3. Numerical Methods - Definitions

  4. Numerical Methods

  5. Analytical vs. Numerical methods

  6. Analytical vs. Numerical methods

  7. Mathematician and Engineer

  8. Reasons to study numerical Analysis • Powerful problem solving techniques and can be used to handle large systems of equations • It enables you to intelligently use the commercial software packages as well as designing your own algorithm. • Numerical Methods are efficient vehicles in learning to use computers • It Reinforce your understanding of mathematics; where it reduces higher mathematics to basic arithmetic operation.

  9. Course Contents

  10. The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 1 Mathematical Modeling

  11. Chapter 1: Mathematical Modeling Mathematical Model • A formulation or equation that expresses the essential features of a physical system or process in mathematical terms. • Generally, it can be represented as a functional relationship of the form

  12. Mathematical Modeling

  13. Simple Mathematical Model Example: Newton’s Second Law (The time rate of change of momentum of a body is equal to the resultant force acting on it) • a = acceleration (m/s2) ….the dependent variable • m = mass of the object (kg) ….the parameter representing a property of the system. • f = force acting on the body (N)

  14. Typical characteristics of Math. model • It describes a natural process or system in mathematical way • It represents the idealization and simplification of reality. • It yields reproducible results, and can be used for predictive purpose.

  15. Complex Mathematical Model Example: Newton’s Second Law Where: c = drag coefficient (kg/s), v = falling velocity (m/s)

  16. Complex Mathematical Model At rest: (v = 0 at t = 0), Calculus can be used to solve the equation

  17. Analytical solution to Newton's Second Law .

  18. Analytical solution to Newton's Second Law

  19. Analytical solution to Newton's Second Law

  20. Numerical Solution to Newton's Second Law • Numerical solution: approximates the exact solution by arithmetic operations. • Suppose 

  21. Numerical Solution to Newton's Second Law .

  22. Numerical Solution to Newton's Second Law .

  23. Comparison between Analytical vs. Numerical Solution

More Related