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Course Description form
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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Numerical Analysis I
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Math 421
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3
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-
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-
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3
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Pre-requisites
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Math 331
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Brief contents, to be posted in university site and documents(4-5 lines):
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In this course the students will study: numerical solution of nonlinear equation using (bisection, fixed point, Newton method), Interpolation and polynomial approximation (Lagrange, Newton’s formulas). Numerical differentiation (first and higher derivatives). Numerical integration (Trapezoidal, Simpson’s and Gaussian quadrature).
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Faculties and departments requiring this course (if any):
Faculty of Science/ Department of Mathematics.
Objectives: Prefer In points
1- The students will learn how to solve nonlinear equations
2- The students will learn how to interpolate using different formulas.
3- The students will learn how to approximate derivatives.
4- To teach the students how to approximate difficult integrals.
Contents: Prefer In points
1- Numerical solution of nonlinear equations
2- Interpolation and polynomial approximation
3- Numerical Differentiation
4- Numerical integration
Course Outcomes:
A- Knowledge:
(Specific facts and knowledge of concepts, theories, formula etc.)
Students will know how to solve nonlinear equations, how to interpolate, how to differentiate and integrate functions numerically.
B-Cognitive Skills:
(Thinking, problem solving )
Concentration , Perception, applications and evaluation.
C- Interpersonal skills and responsibilities:
(group participation, leadership, personal responsibility , ethic and moral behavior, capacity for self directed learning)
Interpersonal skills are all behaviours and feelings that exist within all of us that influence our interactions with others. Healthy interpersonal skills reduce stress, reduce conflict, improve communication, enhance intimacy, increase understanding and promote joy.
D- Analysis and communication:
(communication, mathematical and IT skills)
Communication skills are the most important when we talk about winning the hearts. We may improve interpersonal skills with students by using technical skills too, i.e. ability to work with latest teaching aids like computers, multimedia or other technical equipments.
Assessment methods for the above elements:
These skills are assessed through coursework and written examinations.
Text book: Only one
Numerical Analysis (8th edition)
Richard Burden & J Douglas Faires
Thomson Brooks/ Cole
Supplementary references
Numerical Mathematics and Computing (5th edition)
Ward Cheny & David Kincaid
Thomson Brooks/ Cole
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Time table for distributing Theoretical course contents
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Remarks
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Experiment
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weak
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Introduction and Bisection method
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1
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Fixed point method
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2
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Newton’s method
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3
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Secant method
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4
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Interpolation ( Lagrange polynomial)
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5
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Divided Differences and Newton’s formulas
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6
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Forward and backward differences
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7
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Newton’s formulas for equally spaced points
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8
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Numerical differentiation
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9
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Numerical integration (trapezoidal rule)
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10
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Simpson’s rule
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11
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Gaussian quadrature (two and three points)
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12
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Gaussian quadrature on [a,b]
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13
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How to use Maple in numerical analysis.
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14
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Revision
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15
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Final exam.
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