MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs ELECTRICAL AND ELECTRONICS ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
ELECTRICAL AND ELECTRONICS ENGINEERING
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) Adequate knowledge in mathematics, science and electric-electronic engineering subjects; ability to use theoretical and applied information in these areas to model and solve engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues, according to the nature of the design.)
4) Ability to devise, select, and use modern techniques and tools needed for electrical-electronic engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Awareness of professional and ethical responsibility.
10) Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.