MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs PSYCHOLOGYGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
PSYCHOLOGY
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 develop an interest in the human mind and behavior, to be able to evaluate theories using empirical findings, to understand that psychology is an evidence-based science by acquiring critical thinking skills.
2) To gain a biopsychosocial perspective on human behavior. To understand the biological, psychological, and social variables of behavior.
3) To learn the basic concepts in psychology and the theoretical and practical approaches used to study them (e.g. basic observation and interview techniques).
4) To acquire the methods and skills to access and write information using English as the dominant language in the psychological literature, to recognize and apply scientific research and data evaluation techniques (e.g. correlational, experimental, cross-sectional and longitudinal studies, case studies).
5) To be against discrimination and prejudice; to have ethical concerns while working in research and practice areas.
6) To recognize the main subfields of psychology (experimental, developmental, clinical, cognitive, social and industrial/organizational psychology) and their related fields of study and specialization.
7) To acquire the skills necessary for analyzing, interpreting and presenting the findings as well as problem posing, hypothesizing and data collection, which are the basic elements of scientific studies.
8) To gain the basic knowledge and skills necessary for psychological assessment and evaluation.
9) To acquire basic knowledge of other disciplines (medicine, genetics, biology, economics, sociology, political science, communication, philosophy, anthropology, literature, law, art, etc.) that will contribute to psychology and to use this knowledge in the understanding and interpretation of psychological processes.
10) To develop sensitivity towards social problems; to take responsibility in activities that benefit the field of psychology and society.
11) To have problem solving skills and to be able to develop the necessary analytical approaches for this.
12) To be able to criticize any subject in business and academic life and to be able to express their thoughts.