ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 545 )


   Basic information
Course title: Numerical Analysis I
Course code: MATH 545
Lecturer: Assoc. Prof. Dr. Hülya ÖZTÜRK
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: To teach the fundamental principles of numerical analysis
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Explain the fundamental principles of numerical analysis

    Contribution to Program Outcomes

    1. Acquire scientific knowledge and work independently
    2. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
  2. Grasp applications of differential equations

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    7. Develop mathematical, communicative, problem-solving, brainstorming skills.
    8. Effectively express his/her research ideas and findings both orally and in writing
    9. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Seminar/presentation
  3. Solve differential equations numerically

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    7. Develop mathematical, communicative, problem-solving, brainstorming skills.
    8. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Numerical Solution of Initial-Value problems
Euler's Method
Week 2: Runge Kutta methods
Week 3: Predictor-Corrector methods:
Adams-Moulton
Adams-Bashforth
Milne's and Simpson's methods
Week 4: Extrapolation methods
Week 5: Adaptive techniques
Week 6: Methods for systems of equations
Week 7: Stiff Differential Equations
Week 8: Boundary-value problems for ordinary differential equations:
Linear Shooting method
Week 9: Boundary-value problems for ordinary differential equations:
Linear Shooting method
Week 10: Linear Finite Difference
Week 11: Non-linear Shooting method
Week 12: Non-linear Finite Difference
Week 13: Variational techniques
Week 14: Rayleigh-Ritz method
Week 15*: Matlab applications
Week 16*: Final exam
Textbooks and materials: Numerical Methods, Faires and Burden, 2013
Numerical Methods and Analysis, Buchanan and Turner, 1992
Recommended readings: Numerical Methods, Faires and Burden, 2013
Numerical Methods and Analysis, Buchanan and Turner, 1992
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 14 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 3 14
Practice, Recitation: 0 0
Homework: 6 10
Term project: 10 2
Term project presentation: 1 1
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 1 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
-->