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 
 
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;

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. 
 Core Courses  
Major Area Courses  X  
Supportive Courses  
Media and Managment Skills Courses  
Transferable Skill Courses 
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  GaussSeidel 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://tandonbooks.com/Mathematics/MA4423%20%20Introductory%20Numerial%20Analysis/(MA4423)%20Sauer%20%20Numerical%20Analysis%202e.pdf http//ins.sjtu.edu.cn/people/mtang/textbook.pdf 
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 EndofSemester Activities on the Final Grade  1  40 
Total 
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 
#  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 uptodate, 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