COURSE INTRODUCTION AND APPLICATION INFORMATION

Course Name
Numerical Methods for Engineers II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
FENG 346
Spring
3
0
3
6
Prerequisites
 FENG 345To get a grade of at least FD
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Lecture / Presentation
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives The course objectives are to provide the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed. Additionally, it is aimed to teach the computational tools available to solving optimization problems on computers once a mathematical formulation has been found.
Learning Outcomes The students who succeeded in this course;
  • Formulate an optimization problem in the standard format with the objective function and the related constraints(equality and/or inequality)
  • Find the optimum point of an optimization problem by using graphical techniques
  • Perform analytical calculations to write the optimality conditions of optimization problems(constrained and unconstrained).
  • Solve constrained and unconstrained optimization problems either analytically or by using MATLAB/Octave(or other tools and programming languages)
  • Solve linear programming problems
  • Solve basic parabolic and elliptic partial differential equations by using finite difference methods
Course Description In this course, the following topics will be covered, with a special focus on practical applications: the importance of optimization, basic definition and facts on optimization problems, theory of linear programming, nonlinear programming (constrained and unconstrained optimization problems), numerical methods for constrained and unconstrained problems, numerical solution of partial differential(elliptic and parabolic) equations.
Related Sustainable Development Goals

 



Course Category

 Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Introduction to Partial Differential Equations Textbook 3: Chapter 28
2 Finite Difference Method: Simple Implicit and Explicit Finite Difference Schemes and Numerical Stability Textbook 3: Chapter 29, 30
3 Finite Difference: Elliptic Equations Textbook 3: Chapter 29
4 Finite Difference: Parabolic Equations Textbook 3: Chapter 30
5 Optimization concept and historical perspective, basic concepts in optimization process. Textbook 1: Chapter 1 Textbook 2: Chapter 1
6 Optimum Design Problem Formulation Textbook 1: Chapter 2
7 Graphical Solution Method and Basic Optimization Concepts Textbook 1: Chapter 3
8 Midterm Exam
9 Optimum Design Concepts: Optimality Conditions Textbook 1: Chapter 4
10 Optimum Design Concepts: Optimality Conditions Textbook 1: Chapter 4
11 Numerical Methods for Unconstrained Optimization Textbook 1: Chapter 10
12 Numerical Methods for Constrained Optimization Textbook 1: Chapter 12
13 Linear Programming Textbook 1: Chapter 8
14 Linear Programming Textbook 1: Chapter 8
15 Review of the semester
16 Final
Course Notes/Textbooks
  1. Jasbir Singh Arora. Introduction to Optimum Design. 4th Edition, Academic Press, 2016. ISBN 978-0-12-800806-5
  2. Engineering Optimization: Theory and Practice, S. S. Rao, John Wiley and Sons Inc, ISBN 978-0-470-18352-6.
  3. Steven, C. Chapra. Numerical Methods for Engineers. Seventh Edition, McGraw-Hill, 2018. ISBN 978-0-07-339796-2
  4. John A. Trangenstein, Numerical Solution of Elliptic and Parabolic Partial Differential Equations, Cambridge University Press, 2013
  5. K. W. Morton, D. F. Mayers, Numerical Solution of Partial Differential Equations, Second Edition, Cambridge University Press, 2005
Suggested Readings/Materials
  1.  P. Venkataraman, Applied Optimization with MATLAB Programming, John Wiley & Sons, Inc., 2009, ISBN: 978-0-470-08488-5
  2. Numerical Analysis by Timothy Sauer, 2006, Pearson;
  3. Numerical Methods for Engineers and Scientists: An Introduction with Applications using MATLAB by Gilat and Subramaniam, Wiley.

 

EVALUATION SYSTEM

Semester Activities Number Weighting
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
40
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
20
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
14
4
56
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
8
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
16
Final Exams
1
20
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science and Industrial Engineering; to be able to use theoretical and applied information in these areas to model and solve Industrial Engineering problems.
2

To be able to identify, formulate and solve complex Industrial Engineering problems by using state-of-the-art methods, techniques and equipment; to be able to select and apply proper analysis and modeling methods for this purpose.

 X
3

To be able to analyze a complex system, process, device or product, and to design with realistic limitations to meet the requirements using modern design techniques.

4

To be able to choose and use the required modern techniques and tools for Industrial Engineering applications; to be able to use information technologies efficiently.

 X
5

To be able to design and do simulation and/or experiment, collect and analyze data and interpret the results for investigating Industrial Engineering problems and Industrial Engineering related research areas.
6

To be able to work efficiently in Industrial Engineering disciplinary and multidisciplinary teams; to be able to work individually.
7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively; to be able to give and receive clear and comprehensible instructions
8

To have knowledge about contemporary issues and the global and societal effects of Industrial Engineering practices on health, environment, and safety; to be aware of the legal consequences of Industrial Engineering solutions.
9

To be aware of professional and ethical responsibility; to have knowledge of the standards used in Industrial Engineering practice.
10

To have knowledge about business life practices such as project management, risk management, and change management; to be aware of entrepreneurship and innovation; to have knowledge about sustainable development.
11

To be able to collect data in the area of Industrial Engineering; to be able to communicate with colleagues in a foreign language.
12

To be able to speak a second foreign at a medium level of fluency efficiently.
13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Industrial Engineering.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest