Course Title: Numerical Analysis (1) Course Code: MTH3402-4
Program: BSc. in Mathematics Department: Mathematics
College: Jamoum University College
Institution: Umm Al-Qura University
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Table of Contents
A. Course Identification ... 3
6. Mode of Instruction (mark all that apply) ... 3
B. Course Objectives and Learning Outcomes ... 3
1. Course Description ... 3
2. Course Main Objective ... 3
3. Course Learning Outcomes ... 4
C. Course Content ... 4
D. Teaching and Assessment ... 5
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods ... 5
2. Assessment Tasks for Students ... 5
E. Student Academic Counseling and Support ... 6
F. Learning Resources and Facilities ... 6
1.Learning Resources ... 6
2. Facilities Required ... 6
G. Course Quality Evaluation ... 6
H. Specification Approval Data ... 7
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A. Course Identification
1. Credit hours:
2. Course type
a. University College Department ✔ Others
b. Required ✔ Elective
3. Level/year at which this course is offered: Eighth level/fourth year 4. Pre-requisites for this course (if any):
Ordinary Differential Equations (4042502-4)
5. Co-requisites for this course (if any):
None
6. Mode of Instruction (mark all that apply)
No Mode of Instruction Contact Hours Percentage
1 Traditional classroom Four
hours/week %100
2 Blended 0 0
3 E-learning 0 0
4 Distance learning 0 0
5 Other 0 0
7. Contact Hours (based on academic semester)
No Activity Contact Hours
1 Lecture 40
2 Laboratory/Studio 0
3 Tutorial 0
4 Others (specify) 0
Total 40
B. Course Objectives and Learning Outcomes
1. Course Description
Numerical analysis is the branch of Mathematics that is concerned with the theoretical
foundations of numerical algorithms for the solution of problems arising in different scientific applications. The subject addresses a variety of questions ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations, with particular emphasis on the stability, accuracy, efficiency and reliability of numerical algorithms. The purpose of this course is to provide an elementary introduction into this active and exciting field, and is aimed to students in their third year of the Bachelor program in Mathematics.
2. Course Main Objective
The primary objective of the course is to develop the basic understanding of numerical algorithms and improve skills to implement these algorithms with different programming languages e.g., MATLAB.
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3. Course Learning Outcomes
CLOs Aligned
PLOs 1 Knowledge and Understanding: by the end of this course, the
student is expected to be able to 1.1 Describe different algorithms
1.2 Recall the importance of numerical interpolation
1.3 Recognize different iterative methods (Jacobi –Gauss Seidel) 1.4 List ''again'' the values and eigenvectors of a symmetric matrix
2 Skills: by the end of this course, the student is expected to be able to 2.1 Discuss robustness and relative performance of different algorithms 2.2 Apply interpolation methods for solving mathematical problems
numerically
2.3 Calculate the errors and the rates of convergence
2.4 Develop numerical algorithms for the solution of algebraic eigenvalue problems
3 Values: by the end of this course, the student is expected to be able to
3.1 Evaluate different tools used in ordinary differential equations course 3.2 Recognize the relationship between different areas of mathematics and
the connections between mathematics and other disciplines.
C. Course Content
No List of Topics Contact
Hours 1
Introduction:
• Definitions of numerical errors e.g., rounding and chopping errors.
• Discussion of major sources of errors in numerical analysis. 3
2
Solution of algebraic equations:
• The Bisection algorithm and its coding.
• Newton-Raphson algorithm and its coding.
• Properties of the fixed-point algorithm.
6
3
Solution of linear equations:
• The Concept of Gaussian elimination and Gauss Jordan methods.
• The LU factorization of matrices.
• The Cholesky factorization Iterative methods
• Revise the different matrix norms.
• Jacobi iteration algorithm.
• Gauss-Seidel algorithm.
12
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Numerical Interpolation:
• Polynomial interpolation.
• Introduction to Lagrange interpolating polynomial. 7
5
• Interpolation based on Lagrange interpolating polynomial.
• Newton interpolation method using divided differences.
5 Numerical Differentiation. 5
6 Numerical Integration 5
7 General Revision. 2
Total 40
D. Teaching and Assessment
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods
Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and Understanding
1.1 Describe different algorithms. Lecture and Tutorials Exams, Quizzes 1.2 Recall the importance of numerical
interpolation
Lecture and Tutorials Exams, Quizzes 1.3 Recognize different iterative methods
(Jacobi –Gauss Seidel)
Lecture and Tutorials Exams, Quizzes
1.4
Apply interpolation methods for
Solving mathematical problems numerically
Lecture and Tutorials Exams, Quizzes
2.0 Skills
2.1 Discuss robustness and relative performance of different algorithms
Lecture/ Individual or group work
Exams, Quizzes 2.2 Apply interpolation methods for
solving mathematical problems numerically
Lecture/ Individual or group work
Exams, Quizzes
2.3 Develop numerical algorithms for the solution of the algebraic problems
Lecture/ Individual or group work
Exams, Quizzes
3.0 Values
3.1 Evaluate different tools used in ordinary differential equations course
Lecture/ Individual or group work
Exams, Quizzes 3.2 Recognize the relationship between
different areas of mathematics and the connection between mathematics and other disciplines
Lecture/ Individual or group work
Exams, Quizzes
2. Assessment Tasks for Students
# Assessment task* Week Due Percentage of Total
Assessment Score
1 Midterm Exam 6th %25
2 Quizes and homeworks During semester %25
3 Final exam End of semester %50
*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)
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E. Student Academic Counseling and Support
Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice:
• Office hours (scheduled 3hrs \ week ).
• Contact with students by e-mail, and e-learning facilities.
F. Learning Resources and Facilities
1.Learning ResourcesRequired Textbooks
- Numerical Analysis. 9th ed. R.L. Burden and J.D. Faires: Edition Brooks / cole: -73563-538-0-978 .2011136
- An Introduction to Numerical Analysis. Endre Süli, David F.
Mayers Cambridge : -0521810264 -2003 .0521007941 Essential References
Materials
Numerical Analysis. 9th ed. R.L. Burden and J.D. Faires: Edition Brooks / cole: -73563-538-0-978 .2011136
Electronic Materials None Other Learning
Materials None
2. Facilities Required
Item Resources
Accommodation
(Classrooms, laboratories, demonstration rooms/labs, etc.)
Large classrooms that can accommodate more than 30 students
Technology Resources
(AV, data show, Smart Board, software, etc.)
Data Show, Smart Board Other Resources
(Specify, e.g. if specific laboratory equipment is required, list requirements or
attach a list)
None
G. Course Quality Evaluation
Evaluation
Areas/Issues Evaluators Evaluation Methods
Effectiveness of teaching and assessment
Students Direct
Quality of learning resources Students Direct Extent of achievement of
course learning outcomes
Faculty Member Direct
Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)
Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)
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H. Specification Approval Data
Council / Committee Council of the Mathematics Department
Reference No.
Date
