طرق عددية

MODULE DESCRIPTION FORM

نموذج وصف المادة الدراسية

Module Information معلومات المادة الدراسية
Module Title	Numerical Methods				Module Delivery
Module Type	S				Theory Lecture Lab Tutorial Practical Seminar
Module Code	GPPE310
ECTS Credits	4.0
SWL (hr/sem)	100
Module Level		3	Semester of Delivery				6
Administering Department		GPPE	College	OGEC
Module Leader	Dr Maytham Khalid Gatea		e-mail	Maytham.Khalid@buog.edu.iq
Module Leader’s Acad. Title		Lecturer	Module Leader’s Qualification				Ph.D.
Module Tutor	None		e-mail	N/A
Peer Reviewer Name		None	e-mail	N/A
Scientific Committee Approval Date		14/06/2023	Version Number			1.0

Relation with other Modules

العلاقة مع المواد الدراسية الأخرى

Prerequisite module

Semester

Five

Co-requisites module

Semester

Module Aims, Learning Outcomes and Indicative Contents

أهداف المادة الدراسية ونتائج التعلم والمحتويات الإرشادية

Module Objectives

أهداف المادة الدراسية

To develop a good knowledge of the numerical analysis concept.
To learn the solution methods numerical solution of algebraic equations (roots of equations).
To learn the solution methods for the numerical solution of a set of algebraic equations.
To understand and application of the Taylor Series.
To understand numerical differentiation (Finite Differences Calculus).
Excellent understanding of the numerical integration concept.
To learn the methods of numerical solution of ordinary differential equations.
To understand the technique of curve fitting.
The explanation and understanding of the several available methods of interpolation and extrapolation.

Module Learning Outcomes

مخرجات التعلم للمادة الدراسية

Analyze a problem and identify the computing requirements appropriate for its solution.
The students should be familiarized with the ways of solving complicated mathematical problems numerically.
The students can understand the work way of numerical software to solve and analyze different mathematical problems.
The students will be able to analyze and solve several errors and approximations in numerical methods.
The students will be able to apply several methods to solve the Equations in One Variable.
The students will be able to apply several methods to solve simultaneous equations.
The students will be able to apply several methods to solve Curve Fitting and Interpolation questions and their related techniques.

Indicative Contents

المحتويات الإرشادية

Indicative content includes the following:

Part A: (18 hrs.)

Introduction to Numerical Methods:

Errors in numerical computations.
Error calculation.

Numerical Solution of Algebraic Equations (Roots of equations):

Single and multiple roots.
Accuracy in root determination.
Solution of algebraic equations (determining roots of equations):
1. Bisection Method.
2. Fixed point Method.
3. Newton-Raphson Method.
4. Modified Newton Method.

Numerical Solution of Set of Algebraic Equations:

Iterative methods.
Solution of Set of linear algebraic equations:
1. Jacobi iteration.
2. Gauss-Seidel iteration.

Solution of a Set of nonlinear algebraic equations:

Taylor Series:

Maclaurin series
Taylor series

Order of error
Error in truncated Taylor series.

Part B: (24 hrs.)

Numerical Differentiation (Finite Difference Calculus):

Forward and backward differences.
Central differences.

Numerical Integration:

Trapezoidal rule
Simpson's rule
Romberg integration

Numerical Solution of Ordinary Differential Equations:

Solution of initial value problems.
1. Solution of 1st order ODEs
1- Euler's method
Second order Runge-Kutta method
Fourth-order Runge-Kutta method

Solution of a set of 1^st-order ODEs.
Solution of second-order ODEs

Solution of boundary value problems

Curve Fitting:

Least-squares criterion (linear regression)
Statistical definitions
Non-polynomial models

Interpolation and Extrapolation:

Interpolation with equally spaced data

Gregory-Newton forward interpolation formula
Lagrange interpolation polynomial

Interpolation with unequally spaced data

Learning and Teaching Strategies

استراتيجيات التعلم والتعليم

Strategies

The numerical analysis course will be theoretical lectures and various exercises. Moreover, it will conduct several tools and methods, for example, textbooks, videos and if applicable engineering software. Moreover, the theoretical lecture will adopt several methods, for instance, a projector, whiteboard and educational videos.

Student Workload (SWL)

الحمل الدراسي للطالب محسوب لـ ١٥ اسبوعا

Structured SWL (h/sem)

الحمل الدراسي المنتظم للطالب خلال الفصل

Structured SWL (h/w)

الحمل الدراسي المنتظم للطالب أسبوعيا

Unstructured SWL (h/sem)

الحمل الدراسي غير المنتظم للطالب خلال الفصل

Unstructured SWL (h/w)

الحمل الدراسي غير المنتظم للطالب أسبوعيا

Total SWL (h/sem)

الحمل الدراسي الكلي للطالب خلال الفصل

100

Module Evaluation تقييم المادة الدراسية
As		Time/Number	Weight (Marks)	Week Due	Relevant Learning Outcome
Formative Assessment	Quizzes	2 / 30 min	5% (5)	5	LO #1, #2, #3, and #4
				10	LO #5, #6 and #7
	Assignments	2	5% (5)	3	LO #1, #2, #3, and #4
				12	LO #5, #6 and #7
Summative Assessment	Midterm Exam	2hr	30% (30)	7	LO #1 - #4
	Final Exam	3hr	60% (60)	15	All
Total assessment			100% (100 Marks)
Delivery Plan (Weekly Syllabus) المنهاج الاسبوعي النظري
Week	Material Covered
Week 1	Introduction – Numerical methods, Errors in numerical computations, Error calculation. Numerical Solution of Algebraic Equations (Roots of Equations).
Week 2	Solution of algebraic equations (determining roots of equations): Bisection Method
Week 3	Solution of algebraic equations (determining roots of equations): Fixed point Method Newton-Raphson Method Modified Newton Method
Week 4	Numerical Solution of Set of Algebraic Equations – Introduction. Solution of Set of linear algebraic equations: Jacobi iteration Gauss-Seidel iteration
Week 5	Solution of Set of nonlinear algebraic equations.
Week 6	Taylor Series.
Week 7	Mid-Exam
Week 8	Numerical Differentiation (Finite Difference Calculus) – Introduction and Forward and backward differences.
Week 9	Numerical Differentiation (Finite Difference Calculus) – Central differences and Examples.
Week 10	Numerical Integration – Introduction, Trapezoidal rule, and Simpson's rule
Week 11	Numerical Integration – Romberg integration and Examples.
Week 12	Numerical Solution of Ordinary Differential Equations – Introduction and Solution of initial value problems (1^stOrder ODEs, set of 1^stOrder ODEs, and second order ODEs).
Week 13	Numerical Solution of Ordinary Differential Equations – Solution of boundary value problems and Examples.
Week 14	Curve Fitting.
Week 15	Interpolation and Extrapolation.

Learning and Teaching Resources مصادر التعلم والتدريس
	Text	Available in the Library?
Required Texts	Numerical Methods in Engineering Practice, by A. W. Al-Khafaji and J. R. Tooley.	Yes
Recommended Texts	Numerical Methods, by R. W. Hornbeck. Numerical Methods Using MATLAB, by J. H. Mathew and K. D. Fink. Numerical Analysis, by R. L. Burden and J. D. Faires.	Available online

Grading Scheme مخطط الدرجات
Group	Grade	التقدير	Marks %	Definition
Success Group (50 - 100)	A - Excellent	امتياز	90 - 100	Outstanding Performance
	B - Very Good	جيد جدا	80 - 89	Above average with some errors
	C - Good	جيد	70 - 79	Sound work with notable errors
	D - Satisfactory	متوسط	60 - 69	Fair but with major shortcomings
	E - Sufficient	مقبول	50 - 59	Work meets minimum criteria
Fail Group (0 – 49)	FX – Fail	راسب (قيد المعالجة)	(45-49)	More work is required but credit awarded
Fail Group (0 – 49)	F – Fail	راسب	(0-44)	A considerable amount of work required

Note: Marks Decimal places above or below 0.5 will be rounded to the higher or lower full mark (for example a mark of 54.5 will be rounded to 55, whereas a mark of 54.4 will be rounded to 54. The University has a policy NOT to condone "near-pass fails" so the only adjustment to marks awarded by the original marker(s) will be the automatic rounding outlined above.

طرق عددية

Numerical Methods

S

GPPE310

4.0

100