COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Numerical Analysis I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 403
Fall
3
0
3
7
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. And also they should develop some experience in the implementation of numerical methods by using a computer.
Learning Outcomes The students who succeeded in this course;
  • will be able to define Errors, Big O Notation, Stability and Condition Number, Taylor's Theorem.
  • will be able to solve Nonlinear Equations.
  • will be able to solve Linear Systems.
  • will be able to calculate Interpolating and Polynomial Approximation.
  • will be able to use least squares method.
Course Description In this course the solution of linear and nonlinear systems will be discussed\nnumerically. Several interpolation methods will be given. Least squares will be discussed.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Errors, Big O Notation, Stability and Condition Number, Taylor's Theorem. Lecture notes
2 The Solution of Nonlinear Equations: Bisection Method, Fixed Point Iteration, Numerical Analysis by Timothy Sauer, 2006, Pearson Section : 1.1, 1.2
3 Newton-Rapson Method, Secant Method. Numerical Analysis by Timothy Sauer, 2006, Pearson Section 1.4, 1.5
4 The Solution of Linear Systems: Solving Triangular System, Gauss Elimination and Pivoting. Numerical Analysis by Timothy Sauer, 2006, Pearson Section 2.1
5 LU Factorization Numerical Analysis by Timothy Sauer, 2006, Pearson Section 2.2
6 Sources of Error. Numerical Analysis by Timothy Sauer, 2006, Pearson Section 2.3
7 Iterative Methods: Jacobi Method, Gauss Seidel Method and SOR Numerical Analysis by Timothy Sauer, 2006, Pearson Section 2.5
8 Midterm Exam
9 Interpolation: Lagrange Interpolation Numerical Analysis by Timothy Sauer, 2006, Pearson Section 3.1
10 Newton’s Divided Differences, Interpolation error Numerical Analysis by Timothy Sauer, 2006, Pearson Section 3.1, 3.2
11 Chebyshev Interpolation Numerical Analysis by Timothy Sauer, 2006, Pearson Section 3.4
12 Least Squares and the normal equation Numerical Analysis by Timothy Sauer, 2006, Pearson Section 4.1
13 A survey of Models, QR Factorization Numerical Analysis by Timothy Sauer, 2006, Pearson Section 4.2, 4.3
14 Nonlinear Least Squares Numerical Analysis by Timothy Sauer, 2006, Pearson Section 4.4
15 Review of the semester
16 Review of the semester
Course Notes/Textbooks

Numerical Analysis  by  Timothy Sauer,

2006, Pearson

Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
30
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
40
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
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
3
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
4
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
20
Final Exams
1
25
    Total
161

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

X
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

X
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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