Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
6MATH382NUMERİCAL ANALYSİS II3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The course aims to introduce approximation theory techniques such as higher order interpolation schemes, as well as regression and least square methods. Introduce ordinary differential equations (ODEs) and Partial Differential equations (PDEs), and some numerical methods for solving. In addition, introduce system of nonlinear equations and the related methods. Furthermore, an introduction to eigenvalue problems and optimization method will be presented.
Course Content APPROXIMATION THEORY: Hermite Interpolation, Spline Interpolation.
SYSTEMS OF NONLINEAR EQUATIONS: Fixed Points for Functions of Several Variables, Newton's Method.
CURVE FITTING: Least-Squares Regression, Linear Regression, Polynomial Regression, Multiple Linear Regression.
ORDINARY DIFFERENTIAL EQUATIONS: Euler’s Method, Improvements of Euler’s Method, Runge-Kutta Methods, Systems of Equations, Multistep Methods.
PARTIAL DIFFERENTIAL EQUATIONS: Elliptic Partial Differential Equations, Parabolic Partial Differential Equations, Hyperbolic Partial Differential Equations, Finite Difference: Elliptic Equations, Finite Difference: Parabolic Equations.
APPROXIMATING EIGENVALUES: Linear Algebra and Eigenvalues, The Power Method.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Nasser AGHAZADEH nasseraghazadeh@iyte.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021.
Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 30
Quizzes 0 % 0
Homeworks 5 % 30
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
8
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 42 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 36 36
Exams and Exam Preparations 1 6 6
Total Work Load   Number of ECTS Credits 3 84

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand the numerical methods for the basic problems of numerical analysis
2 Ability to solve ODEs, eigenvalue problems, Hermite and spline interpolation
3 To understand the general concepts of curve-fitting with computer implementations
4 To understand the possibilities and the limitations of the different methods
5 Ability to implement basic numerical methods on computer


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 APPROXIMATION THEORY: Hermite polynomials Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Section 3.4
2 APPROXIMATION THEORY: Spline interpolation Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Section 18.6. Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Section 3.4.
3 CURVE FITTING: Least-Squares Regression, Linear Regression Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 17
4 CURVE FITTING: Polynomial Regression, Multiple Linear Regression Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 17
5 SYSTEMS OF NONLINEAR EQUATIONS: Fixed Points for Functions of Several Variables, Newton's Method Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Chapter 10
6 ORDINARY DIFFERENTIAL EQUATIONS: Euler’s Method, Improvements of Euler’s Method Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 25
7 ORDINARY DIFFERENTIAL EQUATIONS: Runge-Kutta Methods, Systems of Equations Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 25
8 ORDINARY DIFFERENTIAL EQUATIONS: Multistep Methods Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 25
9 PARTIAL DIFFERENTIAL EQUATIONS: Elliptic Partial Differential Equations, Parabolic Partial Differential Equations, Hyperbolic Partial Differential Equations, Finite Difference for Elliptic Equations Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Chapter 12. Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 8E, McGraw-Hill Education, 2021. Chapter 29-30.
10 PARTIAL DIFFERENTIAL EQUATIONS: Finite Difference for Parabolic Equations Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Chapter 12.
11 APPROXIMATING EIGENVALUES: Linear Algebra and Eigenvalues Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Chapter 9.
12 APPROXIMATING EIGENVALUES: The Power Method Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10E, Cengage Learning, 2016. Chapter 9.
13 OPTIMIZATION:
14 OPTIMIZATION:


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4 1 1 2
C2 4 4 3 2
C3 4 4 4 2
C4 4 4 2
C5 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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