Numerical Analysis (MATH381) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Analysis MATH381 Area Elective 3 0 2 4 7
Pre-requisite Course(s)
MATH 135 Mathematical Analysis I and MATH 231 Linear Algebra I
Course Language English Elective Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Problem Solving. The aim of this course is to study the concepts, the fundamental results, the methods and the techniques of the Numerical Analysis for the numerical solution of mathematical problems. In this context it aims to teach the students how to implement numerical calculations effectively, how to understand the pros and cons of different methods and how to approach a problem numerically. The students who succeeded in this course; Describe difficulties in finite-precision arithmetic in computers and list sources of possible errors in computations Find numerical solutions of nonlinear equations and systems of nonlinear equations; determine convergence conditions and the order of convergence of the methods, Find exact/approximate solutions of linear systems by direct and iterative methods; state and determine convergence properties of iterative methods; Find interpolation polynomial; perform error analysis; find Least-Squares approximations for data and functions, Perform numerical differentiation, numerical integration and error analysis; Find the eigenvalues and eigenvectors with iterative methods and state the conditions for convergence of the methods Find numerical solutions of ordinary differential equations using explicit/ implicit methods and single-step/multistep methods; determine order of convergence of the methods Computational and mathematical preliminaries, numerical solution of nonlinear equations and systems of nonlinear equations, numerical solution of systems of linear equations, direct and iterative methods, the Algebraic Eigenvalue Problem, interpolation and approximation, numerical differentiation and integration, numerical solution of ODE`s.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Mathematical preliminaries, Floating Point Arithmetic, Errors. pp. 1-7,10, 12-13, 22-25, 28-33
2 Numerical Solution of Nonlinear Equations: Bisection and Regula-Falsi Methods. Secant, Newton’s and Steffenson’s Methods. pp. 43-61, 71-83
3 Theory for One-Point Iteration Methods, Order of Convergence, Aitken’s Process. Nonlinear Systems of Equations, Jacobi, Gauss-Seidel and Newton’s Method for Nonlinear Systems. pp. 44-50, 101-107, 112-115
4 Numerical Solution of System of Lineer Equations: Direct Methods: Gaussian Elimination, Pivoting Strategies, LU Decomposition. pp. 142-145, 148-156, 166-171
5 Iterative Methods for Solving System of Lineer Equations: Jacobi, Gauss-Seidel and Successive Over Relaxation(SOR) Methods, Convergence Analysis. pp. 180-186
6 Interpolation: Interpolation Theory, Polynomial Interpolation, Lagrange Interpolation, Divided Differences, Finite Differences and Table-Based Newton Interpolation Methods. pp. 207-212, 215-220, 227-233
7 Midterm
8 Approximation: Least-Squares Approximation, Data Linearization. Numerical Differentiation: Approximating the Derivative, Numerical Differentiation Formulas, Error Analysis. pp. 258-263, 268-278 pp. 316-323, 333-336,
9 Numerical Integration: Trapezoidal and Simpson’s Rules, Newton-Cotes Integration Formulas, Error Analysis, Composite Rules for Numerical Integration, Romberg Integration, Error Analysis. pp. 346-365, 374-378
10 Eigenvalue Problem: The Power Method, Inverse Power Method, Householder’s Method and Eigenvalues of Symmetric Matrices. pp. 549-556, 574-580
11 Numerical Solution of Ordinary Differential Equations; Existence, Uniqueness and Stability Theories. pp. 424-427
12 Numerical Solution of Ordinary Differential Equations; Existence, Uniqueness and Stability Theories. pp. 424-427
13 Euler’s Method and Heun’s Method. Taylor Series Methods, Runge-Kutta Methods, Adams Method and Error Analysis, Systems of Differential Equations. pp. 429-434, 437-439, 444-446, 450-454, 464-468, 475-479
14 Euler’s Method and Heun’s Method. Taylor Series Methods, Runge-Kutta Methods, Adams Method and Error Analysis, Systems of Differential Equations. pp. 429-434, 437-439, 444-446, 450-454, 464-468, 475-479
15 General Review
16 Final Exam

Sources

Course Book 1. Numerical Methods for Mathematics Science and Engineering, J.H.Mathews, Prentice Hall, 1992, second edition. 2. Numerical Analysis, by L.W.Johnson & R.D.Riess, Addison Wesley, 1982 3. An Introduction to Numerical Analysis, by K.E.Atkinson, John Wiley and Sons, 1999 4. Numerical Analysis, by R.L.Burden&J.D.Faires, Prindle, Weber and Schmidt, 1985.

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 7 20
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 80
Final Exam/Final Jury 1 35
Toplam 10 135
 Percentage of Semester Work 65 35 100

Course Category

Core Courses X

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 5 80
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 5 80
Presentation/Seminar Prepration
Project
Report
Homework Assignments 7 5 35
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 12 24
Prepration of Final Exams/Final Jury 1 15 15