طرق عددية

MODULE DESCRIPTION FORM

نموذج وصف المادة الدراسية

Module Information معلومات المادة الدراسية
Module Title	Numerical Methods				Module Delivery
Module Type	C				☒ Theory ☒ Lecture ☒ Lab ☐ Tutorial ☐ Practical ☐ Seminar
Module Code	BOG1154
ECTS Credits	5
SWL (hr/sem)	125
Module Level		UGx11 UGIII	Semester of Delivery				Five
Administering Department		Oil and Gas Engineering	College	Oil and Gas Engineering
Module Leader			e-mail
Module Leader’s Acad. Title			Module Leader’s Qualification
Module Tutor			e-mail
Peer Reviewer Name			e-mail
Scientific Committee Approval Date			Version Number			1.0

Relation with other Modules

العلاقة مع المواد الدراسية الأخرى

Prerequisite module

Semester

Co-requisites module

Semester

Module Aims, Learning Outcomes and Indicative Contents

أهداف المادة الدراسية ونتائج التعلم والمحتويات الإرشادية

Module Objectives

أهداف المادة الدراسية

To teach numerical techniques for solving non-linear equations.

Module Learning Outcomes

مخرجات التعلم للمادة الدراسية

After studying this course, the learners will be able to: -

1. Understand the basics of elementary function and their applications.

2. Describe the difference between numerical and analytical methods

and solutions.

3. Identify main sources of errors and take steps to eliminate or reduce

the impact of errors

4. Apply numerical methods to solve petroleum engineering problems.

Indicative Contents

المحتويات الإرشادية

1. Approximation and Errors

a. Accuracy,

b. Truncation,

c. Taylor series and bracketing methods

2. Linear Equations

a. Gauss elimination,

b. Eigen Values.

3. Non-Linear Equations

a. Bisection method,

b. iteration,

c. secant method,

d. Newton-Raphson method,

e. System of Nonlinear Equations and,

f. Convergence etc

4. Numerical Differentiation and Integration

a. Accuracy of derivatives,

b. Newton-Cotes Integration Formulae,

c. Integration for multiple and improper integrals.

5. Interpolation and Curve Fitting Methods

a. Binary Search,

b. approximation,

c. Lagrange polynomials,

d. Inverse type,

e. Least Squares and,

f. Orthogonal Polynomials including rational and spline function.

Learning and Teaching Strategies

استراتيجيات التعلم والتعليم

Strategies

The main strategy for delivering this module is to foster active student engagement in exercises and promote the development of critical thinking skills. This will be accomplished through interactive classes, engaging tutorials, and the incorporation of hands-on experiments and sampling activities that captivate the students' interest. By employing these approaches, students will have the opportunity to apply their knowledge and enhance their understanding of the course material.

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

125

Module Evaluation تقييم المادة الدراسية
As		Time/Number	Weight (Marks)	Week Due	Relevant Learning Outcome
Formative assessment	Quizzes		10% (10)	5 and 10	LO #1, #2 and #10, #11
	Assignments		10% (10)	2 and 12	LO #3, #4 and #6, #7
	Projects / Lab.		10% (10)	Continuous	All
	Report		10% (10)	13	LO #5, #8 and #10
Summative assessment	Midterm Exam	1hr	10% (10)	7	LO #1 - #7
Summative assessment	Final Exam	2hr	50% (50)	16	All
Total assessment			100% (100 Marks)

Delivery Plan (Weekly Syllabus) المنهاج الاسبوعي النظري
Week	Material Covered
Week 1	Week 1: Approximation and Errors: Accuracy, Truncation
Week 2	Week 2: Approximation and Errors: Taylor series and bracketing methods
Week 3	Week 3: Linear Equations: Gauss elimination
Week 4	Week 4: Linear Equations: Eigen Values
Week 5	Week 5: Non-Linear Equations: Bisection method
Week 6	Week 6: Non-Linear Equations: Iteration
Week 7	Week 7: Mid-Semester Exam
Week 8	Week 8: Non-Linear Equations: Secant method
Week 9	Week 9: Non-Linear Equations: Newton-Raphson method
Week 10	Week 10: Non-Linear Equations: System of Nonlinear Equations, Convergence
Week 11	Week 11: Numerical Differentiation and Integration: Accuracy of derivatives
Week 12	Week 12: Numerical Differentiation and Integration: Newton-Cotes Integration Formulae
Week 13	Week 13: Numerical Differentiation and Integration: Integration for multiple and improper integrals
Week 14	Week 14: Interpolation and Curve Fitting Methods: Binary Search, Approximation
Week 15	Week 15: Interpolation and Curve Fitting Methods: Lagrange polynomials, Inverse type, Least Squares, Orthogonal Polynomials (including rational and spline function)
Week 16	Preparatory week before the final Exam

Delivery Plan (Weekly Lab. Syllabus)

المنهاج الاسبوعي للمختبر

Week

Material Covered

Week 1-14

Lab part of the course will include Mathematica 11, or Matlab 2016. The

introductory programming with course work related to the course outline

shall be carried out.

Learning and Teaching Resources مصادر التعلم والتدريس
	Text	Available in the Library?
Required Texts
Recommended Texts	a. C. Woodford, C. Phillips. “Numerical Methods with Worked Examples: Matlab Edition”, Springer Science and Business Media b. Steven T. Karris. “Numerical Analysis Using MATLAB and Excel”, Orchard Publications c. Steven C. Chapra, Raymond P. Canale. “Numerical methods for engineers”, McGraw-Hill Higher Education d. Timothy Sauer. “Numerical analysis”, Pearson Education e. Stephen Wolfram. “An elementary introduction to the wolfram language”, Wolfram Media, Incorporated.
Websites

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 required but credit awarded
Fail Group (0 – 49)	F – Fail	راسب	(0-44)	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

C

BOG1154

5

125