MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs ENERGY SYSTEMS ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
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 .


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

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
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) Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.
2) Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3) Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively.
5) Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering.
6) Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions.