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
 MATH 403To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives The second part of twotier course aims to discuss methods for numerical integration or quadrature based on finding function approximation to a set of data points, using interpolation and least squares modeling. It also covers the approximate solution of ordinary differential equations, boundary value problems and partial differential equations by computational methods.
Learning Outcomes The students who succeeded in this course;
  • will be able to define Numerical Integration.
  • will be able to calculate Numerical Solution of Ordinary Differential Equations.
  • will be able to calculate Numerical Solution of HigherOrder Equations, Systems.
  • will be able to calculate Solution of Boundary Value Problems.
  • will be able to solve Nonlinear BVP's by using Finite Difference Methods.
  • will be able to solve Variational problems.
  • will be able to understand Ritz and Galerkin Method.
  • will be able to solve Numerical Solution of Partial Differential Equations and analyze stability.
Course Description In this course numerical integration and their errors, numerical solution of ordinary differential equations (Picard, Euler, RungeKutta methods), numerical solution of boundaryvalue problems for ordinary differential equations, integrointerpolation method, numerical method for system of linearalgebraic equations with tridiagonal matrix, variational problems, Ritz and Galerkin methods will be discussed.

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Numerical Integration: Trapezoid Rule, Composite Trapezoid Rule. Simpson’s Rule. Elementary Numerical Analysis (Third edition) by Kendall Atkinson, Weimin Han, John Wiley and Sons, Inc.
2 Composite Simpson’s Rule. Gaussian Numerical Integration (Quadrature), Weighted Gaussian Quadrature. Elementary Numerical Analysis (Third edition) by Kendall Atkinson, Weimin Han, John Wiley and Sons, Inc.
3 Numerical Differentiation: Finite Difference Formulas Numerical Analysis  by Timothy Sauer, 2006, Pearson –Addison Wesley.
4 Rounding Error, Extrapolation Elementary Numerical Analysis (Third edition) by Kendall Atkinson, Weimin Han, John Wiley and Sons, Inc.
5 Solutions of Systems of Equations by Iterative Methods: Jacobi Method Numerical Analysis  by Timothy Sauer, 2006, Pearson –Addison Wesley.
6 Gauss-Seidel Method and SOR Numerical Analysis  by Timothy Sauer, 2006, Pearson –Addison Wesley.
7 Convergence of Iterative Methods, Nonlinear Systems of Equations Numerical Analysis  by Timothy Sauer, 2006, Pearson –Addison Wesley.
8 Midterm
9 Least Squares and the Normal Equations: Inconsistent System of Equations Numerical Analysis  by Timothy Sauer, 2006, Pearson –Addison Wesley.
10 Fitting models to data, conditioning of least squares Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
11 Eigenvalue and Singular Values: Power Iteration Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
12 Convergence of Power Iteration, Inverse Power Iteration, Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
13 Numerical Solutions of Higher Order Equations, Systems Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
14 Finite Difference Methods for Linear BVPs Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
15 Finite Difference Methods for Nonlinear BVPs Applied Numerical Analysis Using Matlab (Second Edition) by Laurene V.Fausett, 2008, PearsonPrentice Hall.
16 Review of the semester
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials http://tandon-books.com/Mathematics/MA4423%20-%20Introductory%20Numerial%20Analysis/(MA4423)%20Sauer%20-%20Numerical%20Analysis%202e.pdf http//ins.sjtu.edu.cn/people/mtang/textbook.pdf

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
10
Presentation / Jury
Project
2
20
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
5
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
2
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
5
Presentation / Jury
Project
2
20
Seminar / Workshop
Oral Exam
Midterms
1
20
Final Exams
1
30
    Total
180

 

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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