MAT3012 Numerical AnalysisBahçeşehir UniversityDegree Programs ENERGY SYSTEMS ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
ENERGY SYSTEMS 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
MAT3012 Numerical Analysis Spring 2 2 3 6

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Hybrid
Course Coordinator : Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Course Lecturer(s): Dr. UTKU GÜLEN
Dr. Öğr. Üyesi ERKUT ARICAN
RA ÇİĞDEM ERİŞ
Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
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. Topics cover linear and nonlinear system of equations, interpolation, curve fitting using least-squares method integration, eigenvalue, and singular value decomposition. And also they should develop some experience in the implementation of numerical methods by using MATLAB.

Learning Outcomes

The students who have succeeded in this course;
1. Define errors, big O notation, use Taylor’s theorem
2. Solve nonlinear algebraic equations
3. Solve linear systems and to use iterative methods for linear systems
4. Solve systems of nonlinear algebraic equations
5. Use interpolation methods and polynomial approximation for a given data, piecewise linear interpolation and spline function interpolation;
6. Use least-squares method for curve fitting
7. Calculate maximum eigenvalues and corresponding eigenvectors and to calculate singular value decomposition of a matrix and apply it on image processing
8. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory.

Course Content

The course studies algorithms and computer techniques for solving mathematical problems. They do all computations using MATLAB.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Introduction to Numerical Analysis: kinds of problems we solve. Error analysis, round-off and truncation errors. Taylor Theorem and Taylor series.
2) Loss of Significance Big O notation
3) Solution of Nonlinear Equations, i.e. f(x)=0. Bracketing Methods for Locating a Root. Bisection (Method of Bolzano). False-position (Regula-Falsi) Method.
4) Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics)
5) Solution of Linear Systems of Equations. Properties of Vectors and Matrices. Upper-Triangular Linear Systems. Gaussian Elimination and Pivoting.
6) Triangular Factorization (LU Decomposition)
7) Iterative Methods for Linear Systems. Jacobi Method. Gauss-Sedidel Method.
8) Iterative Methods for Linear Systems Gauss-Sedidel Method. Diagonally dominant matrix. Errors is solving linear systems.
9) System of Nonlinear Equations (Newton’s Method)
10) Interpolation and Polynomial Approximation. Introduction to Interpolation. Lagrange Approximation.
11) Newton Interpolation Polynomials. Piecewise Linear Interpolation, Cubic Spline Functions
12) Curve Fitting (Applications from heat transfer and electrical engineering). Least-Squares Approximation. Linearization of Nonlinear Relationships.
13) Eigenvalues and Eigenvectors. The power method
14) Singular Value decomposition. Applications from Image Processing

Sources

Course Notes / Textbooks: Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill
References: • J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013.
• Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris.
• John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3
• Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013.
• İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6.
• Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 3 % 10
Homework Assignments 1 % 10
Midterms 1 % 35
Final 1 % 45
Total % 100
PERCENTAGE OF SEMESTER WORK % 55
PERCENTAGE OF FINAL WORK % 45
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 2 28
Laboratory 14 2 28
Study Hours Out of Class 14 2 28
Homework Assignments 1 4 4
Quizzes 3 1 3
Midterms 1 2 2
Final 1 2 2
Total Workload 95

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. 5
2) Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose. 3
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. 4
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. 3
6) Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems 2
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. 2
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. 3
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.