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Syllabus ( MATH 310 )


   Basic information
Course title: Numerical Analysis I
Course code: MATH 310
Lecturer: Assoc. Prof. Dr. Hülya ÖZTÜRK
ECTS credits: 6
GTU credits: 4 (3+2+0)
Year, Semester: 3, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: yok
Professional practice: No
Purpose of the course: Students who can successfully complete this course are equipped with the skills to analyze various aspects, such as the solutions of equations in one variable,numerical differentiation, linear algebra and to draw appropriate conclusions in practical applications.
   Learning outcomes Up

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

  1. They obtain a wide knowledge numerical solutions of equations in one variable, numerical differentiation and approximating the eigenvalues of the matrices.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Adapt to a fast-changing technological environment, improving their knowledge and abilities constantly.
    4. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
  2. The can use the programing language Matlab efficiently in order to compute the numerical solutions and/or approximations.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Adapt to a fast-changing technological environment, improving their knowledge and abilities constantly.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. They can use the theoratical results in various applications.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Adapt to a fast-changing technological environment, improving their knowledge and abilities constantly.
    3. Using technology as an efficient tool to understand mathematics and apply it.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
   Contents Up
Week 1: Review of Calculus
Taylor Polynomials and Series
Matlab Application
Week 2: Solutions of Equations in One Variable
The Bisection method, Fixed-Point iteration
Matlab Application
Week 3: Newton’s Method
The Secant Method
Matlab Application
Week 4: The Method of False Position
Error Analysis for Iterative Methods
Matlab Application
Week 5: Direct Methods for Solving Linear Systems
Linear Systems of Equations
Matlab Application
Week 6: Linear Algebra and Matrix Inversion
Matrix Factorization
Matlab Application
Week 7: Special Types of Matrices
Iterative Techniques in Matrix Algebra
Matlab Application
Week 8: Midterm exam and solutions
Week 9: Norms of Vectors and Matrices
Eigenvalues and Eigenvectors
Matlab Application
Week 10: The Jacobi and Gauss-Siedel Iterative Techniques
Matlab Application
Week 11: Interpolation and the Lagrange Polynomial
Divided Differences Method
Matlab Application
Week 12: Hermite Interpolation
Matlab Application
Week 13: Spline Interpolation
Lineer and Quadratic Spline Interpolation
Matlab Application
Week 14: Cubic Spline Interpolation
Matlab Application
Week 15*: -
Week 16*: Final Exam
Textbooks and materials: Richard L. Burden, John Dougles, Numerical Analysis
Ward Cheney, David Kincaid, Numerical Mathematics and Computing
Endre Süli, David F. Mayers, An Introduction to Numerical Analysis
Recommended readings: Richard L. Burden, John Dougles, Numerical Analysis
Ward Cheney, David Kincaid, Numerical Mathematics and Computing
Endre Süli, David F. Mayers, An Introduction to Numerical Analysis
  * 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: 16 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: 6 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 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)
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