FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 404 | Course Introduction and Application Information
| Course Name |
Numerical Analysis II
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 404
|
Fall/Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
First Cycle
|
|||||
| Mode of Delivery | Online | |||||
| Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecture / Presentation | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | The aim of this course is to use numerical methods to solve linear system of equations, nonlinear equations, evaluate integrals and find eigenvalues. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | In this course the solution of linear systems of equations will be discussed using direct and iterative methods. Numerical integration and differentiation techniques and finding eigenvalues numerically will be discussed. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Matrix algebra | M. Tezer, C. Bozkaya , "Numerical Analysis", (METU, 2018). Section 2.2 |
| 2 | The LU Factorization, Sources of Error | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2 |
| 3 | The PA = LU Factorization | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2 |
| 4 | Iterative Methods: Jacobi Method | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2 |
| 5 | Gauss–Seidel Method and SOR, Convergence of iterative methods | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2 |
| 6 | Methods for symmetric positive-definite matrices | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2, |
| 7 | Nonlinear Systems of Equations | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 2 |
| 8 | Midterm | |
| 9 | Numerical Differentiation: Finite difference formulas | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 5 |
| 10 | Rounding error, Extrapolation | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 5 |
| 11 | Newton–Cotes Formulas for Numerical Integration: Trapezoid Rule, Simpson’s Rule | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 5 |
| 12 | Composite Newton–Cotes formulas Open Newton–Cotes Methods, Gaussian Quadrature | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 5 |
| 13 | Eigenvalues and Singular values: Power Iteration Methods | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 12 |
| 14 | QR Algorithm | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) Chapter 12 |
| 15 | Semester Review | |
| 16 | Final Exam |
| Course Notes/Textbooks | Timothy Sauer, Numerical Analysis, 2nd edition, (Pearson, 2012) ISBN-13: 978-0-321-78367-7 |
| Suggested Readings/Materials | M. Tezer, C. Bozkaya , "Numerical Analysis", (METU, 2018). ISBN13: 9789754293777 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques |
6
|
24
|
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
26
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
6
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
6
|
6
|
36
|
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
20
|
20
|
| Final Exam |
1
|
34
|
34
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
|||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
|||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
X | ||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
|||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
|||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
|||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
|||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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