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The Islamic University of GazaFaculty of Engineering
Numerical Analysis
ECIV 3306
Introduction
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Introduction
• Consider the following equations.
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Numerical Methods - Definitions
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Numerical Methods
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Analytical vs. Numerical methods
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Analytical vs. Numerical methods
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Mathematician and Engineer
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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.
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Course Contents
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The Islamic University of GazaFaculty of Engineering
Civil Engineering Department
Numerical Analysis
ECIV 3306
Chapter 1
Mathematical Modeling
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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
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Mathematical Modeling
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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)
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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.
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Complex Mathematical Model
Example: Newton’s Second Law
Where:
c = drag coefficient (kg/s) ,
v = falling velocity (m/s)
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Complex Mathematical Model
At rest: (v = 0 at t = 0), Calculus can be used to solve the equation
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Analytical solution to Newton's Second Law
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Analytical solution to Newton's Second Law
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Analytical solution to Newton's Second Law
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Numerical Solution to Newton's Second Law
Numerical solution: approximates the exact solution by arithmetic operations.
Suppose
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Numerical Solution to Newton's Second Law
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Numerical Solution to Newton's Second Law
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Comparison between Analytical vs. Numerical Solution