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

Slides:



Advertisements
Similar presentations
Truncation Errors and Taylor Series
Advertisements

Approximations and Errors
Special Matrices and Gauss-Siedel
ECIV 301 Programming & Graphics Numerical Methods for Engineers.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 4 Programming and Software EXCEL and MathCAD.
Least Square Regression
CVEN Computer Applications in Engineering and Construction Dr. Jun Zhang.
Least Square Regression
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 17 Least Square Regression.
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 3 Approximations and Errors.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 2 Mathematical Modeling and Engineering Problem Solving.
ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 3 Programming and Software.
Numerical Solutions of Ordinary Differential Equations
Numerical Methods for Engineering MECN 3500
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 11.
Bracketing Methods Chapter 5 The Islamic University of Gaza
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 1 Mathematical Modeling.
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Mathematical Modeling and Engineering Problem solving.
Chapter 3 Math Vocabulary
Newton’s second law of motion
Numerical Methods Intro to Numerical Methods &
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 21 Newton-Cotes Integration Formula.
Chapter 1 Computing Tools Analytic and Algorithmic Solutions Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Newton’s Second Law of Motion
Math 3120 Differential Equations with Boundary Value Problems
Mathematical Modeling and Engineering Problem Solving
Equation of Motion for a Particle Sect nd Law (time independent mass): F = (dp/dt) = [d(mv)/dt] = m(dv/dt) = ma = m(d 2 r/dt 2 ) = m r (1) A 2.
CSE 3802 / ECE 3431 Numerical Methods in Scientific Computation
Newton’s 2 nd Law of Motion. 2 nd Law Defined The acceleration of an object depends on the mass of the object and the amount of force applied The acceleration.
 Law 1: › Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.  Law 2 : › The.
Laws of Motion Forces: chapter st Law An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an.
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Introduction Course Outline.
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 7 Roots of Polynomials.
ES 240: Scientific and Engineering Computation. Chapter 1 Chapter 1: Mathematical Modeling, Numerical Methods and Problem Solving Uchechukwu Ofoegbu Temple.
Part 1 Chapter 1 Mathematical Modeling, Numerical Methods, and Problem Solving PowerPoints organized by Dr. Michael R. Gustafson II, Duke University and.
Accelerated Motion. Newton’s Second Law of Motion (Law of Force)- Net force acting on an object causes the object to accelerate in the direction of the.
Part 1 Chapter 1 Mathematical Modeling, Numerical Methods, and Problem Solving PowerPoints organized by Dr. Michael R. Gustafson II, Duke University and.
Newton’s second law. Acceleration(m /s 2 ) Mass (kg) The acceleration of an object equals the net force divided by the mass. Net force (N) Newton’s second.
NEWTON’S 2 ND LAW OF MOTION By: Per.7. WHAT IS IT? Newton's second law Of Motion Newton's second law Of Motion can be formally stated as follows: The.
Newton’s Second Law of Motion. 2 nd Law of Motion  The net (total) force of an object is equal to the product of its acceleration and its mass.  Force.
Newton’s 2 nd Law Chapter 6. An object accelerates when a net force acts on it.
Today: (Ch. 3) Tomorrow: (Ch. 4) Apparent weight Friction Free Fall Air Drag and Terminal Velocity Forces and Motion in Two and Three Dimensions.
Fall 2011 PHYS 172: Modern Mechanics Lecture 7 – Speed of Sound in a Solid, Buoyancy Read 4.9 – 4.13.
Modeling First Order Systems in Simulink And Analyzing Step, Pulse and Ramp Responses SOEN385 Control Systems and Applications.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 1.
9/2/2015PHY 711 Fall Lecture 41 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 4: Chapter 2 – Physics.
Traffic Simulation L2 – Introduction to simulation Ing. Ondřej Přibyl, Ph.D.
Solving Engineering Problems
Introduction.
244-1: INTRODUCTION TO PROGRAMMING
1.3 ARITHMETIC OPERATIONS WITH SCALARS
Newton’s second law In this lesson, students learn to apply Newton's second law to calculate forces from motion, and motion from forces. The lesson includes.
Chapter 1.
CE 102 Statics Chapter 1 Introduction.
Introduction.
Newton’s Laws Of Motion
Which one would be easier to accelerate by pushing?
Mathematical Modeling, Numerical Methods, and Problem Solving
Action and Reaction.
Introduction.
Introduction.
MOMENTUM (p) is defined as the product of the mass and velocity -is based on Newton’s 2nd Law F = m a F = m Δv t F t = m Δv IMPULSE MOMENTUM.
Least Square Regression
ARRAY DIVISION Identity matrix Islamic University of Gaza
Mathematical Model.
General Principles 4/10/2019.
USING ARRAYS IN MATLAB BUILT-IN MATH FUNCTIONS
Newton’s Laws of Motion
Introduction.
Presentation transcript:

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

Consider the following equations.

Numerical Methods - Definitions

Numerical Methods

Analytical vs. Numerical methods

Mathematician and Engineer

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.

Course Contents

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

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

Mathematical Modeling

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/s 2 ) ….the dependent variable m = mass of the object (kg) ….the parameter representing a property of the system. f = force acting on the body (N)

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.

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

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

Analytical solution to Newton's Second Law.

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

Numerical Solution to Newton's Second Law.

.

Comparison between Analytical vs. Numerical Solution