MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs SOCIOLOGYGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
SOCIOLOGY
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MATH3012 Numerical Analysis Fall 2 2 3 6
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: English
Type of course: Non-Departmental Elective
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator :
Recommended Optional Program Components: None
Course Objectives: Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. And also they should develop some experience in the implementation of numerical methods by using a computer.

Learning Outcomes

The students who have succeeded in this course;

The students who succeeded in this course;
o will be able to define Errors, Big O Notation, Stability and Condition Number, Taylor’s Theorem.
o will be able to solve Nonlinear Equations.
o will be able to solve Linear Systems.
o will be able to use Iterative Methods for Linear Systems.
o will be able to calculate Eigenvalues and Eigenvectors.
o will be able to solve System of Nonlinear Equations.
o will be able to calculate Interpolating and Polynomial Approximation.

Course Content

In this course the solution of linear and nonlinear systems will be discussed numerically. Also iterative methods for linear systems will be taught.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Errors, Big O Notation, Stability and Condition Number, Taylor’s Theorem.
2) The Solution of Nonlinear Equations in the form of f(x)=0: Bisection Method, Fixed Point Iteration.
3) Newton-Rapson Method, Secant Method.
4) The Solution of Linear System : Solving Triangular System, Gauss Elimination and Pivoting.
5) LU Factorization, Tridiagonal System, Vector and Matrix Norms
6) Sensitivity of Linear Equations. Condition Number and Stability.
7) Iterative Methods for Linear Systems: Jacobi Method.
8) Gauss Seidel Method. Diagonally Dominant Matrix. Errors in Solving Linear Systems.
9) Eigenvalues and Eigenvectors: The Power Method. The Inverse Power Method.
10) System of Nonlinear Equations: Newton’s Method.
11) Interpolating and Polynomial Approximation: Lagrange interpolation polynomial, Newton Interpolation.
12) Piecewise Linear Interpolation, Cubic Spline.
13) Least Square Approximation: Curve Fitting.
14) Inconsistent System of Equations. Errors in Interpolation .

Sources

Course Notes / Textbooks: Numerical Methods Using MATLAB (Fourth Edition), John H. Mathews and Kurtis D. Fink, Pearson Prentice Hall
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 16 % 0
Laboratory 16 % 5
Quizzes 5 % 10
Midterms 2 % 45
Final 1 % 45
Total % 105
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 45
Total % 105

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 16 3 48
Laboratory 14 1 14
Study Hours Out of Class 16 2 32
Quizzes 3 5 15
Midterms 2 5 10
Final 1 5 5
Total Workload 124

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) To learn and compare major sociology perspectives, both classical and contemporary, and apply all of them to analysis of social conditions.
2) To be able to identify the basic methodological approaches in building sociological and anthropological knowledge at local and global levels
3) To be able to use theoretical and applied knowledge acquired in the fields of statistics in social sciences.
4) To have a basic knowledge of other disciplines (including psychology, history, political science, communication studies and literature) that can contribute to sociology and to be able to make use of this knowledge in analyzing sociological processes
5) To have a knowledge and practice of scientific and ethical principles in collecting, interpreting and publishing sociological data also develop ability how to share this data with experts and lay people, using effective communication skills
6) To develop competence in analyzing and publishing sociological knowledge by using computer software for quantitative and qualitative analysis; and develop an attitute for learning new techniques in these fields.
7) To identify and to have a knowledge of the theories related to urban and rural sociology and demography, and political sociology, sociology of gender, sociology of body, visual sociology, sociology of work, sociology of religion, sociology of knowledge and sociology of crime.
8) To have knowledge of how sociology is positioned as a scientific discipline from a philosophical and historical perspective
9) To have the awareness of social issues in Turkish society, to develop critical perspective in analysing these issues and to have a knowledge of the works of Turkish sociologists and to be able to transfer this knowledge
10) To have the awareness of social issues and global societal processes and to apply sociological analysis to development and social responsibility projects
11) To have the ability to define a research question, design a research project and complete a written report for various fields of sociology, either as an individual or as a team member.
12) To be able to transfer the knowledge gained in the areas of sociology to the level of secondary school.