FENG 346 | Course Introduction and Application Information - Department of Mechatronics Engineering

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 345 To 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

National Occupation Classification

-

Course Coordinator

Öğr. Gör. Dr. Musa Özgün Güleç

Course Lecturer(s)

Öğr. Gör. Dr. Musa Özgün Güleç

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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	Formulate an optimization problem in the standard format with the objective function and the related constraints(equality and/or inequality)
2	Find the optimum point of an optimization problem by using graphical techniques
3	Perform analytical calculations to write the optimality conditions of optimization problems(constrained and unconstrained).
4	Solve constrained and unconstrained optimization problems either analytically or by using MATLAB/Octave(or other tools and programming languages)
5	Solve linear programming problems
6	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.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
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

Jasbir Singh Arora. Introduction to Optimum Design. 4th Edition, Academic Press, 2016. ISBN 978-0-12-800806-5
Engineering Optimization: Theory and Practice, S. S. Rao, John Wiley and Sons Inc, ISBN 978-0-470-18352-6.
Steven, C. Chapra. Numerical Methods for Engineers. Seventh Edition, McGraw-Hill, 2018. ISBN 978-0-07-339796-2
John A. Trangenstein, Numerical Solution of Elliptic and Parabolic Partial Differential Equations, Cambridge University Press, 2013
K. W. Morton, D. F. Mayers, Numerical Solution of Partial Differential Equations, Second Edition, Cambridge University Press, 2005

Suggested Readings/Materials

P. Venkataraman, Applied Optimization with MATLAB Programming, John Wiley & Sons, Inc., 2009, ISBN: 978-0-470-08488-5
Numerical Analysis by Timothy Sauer, 2006, Pearson;
Numerical Methods for Engineers and Scientists: An Introduction with Applications using MATLAB by Gilat and Subramaniam, Wiley.

Semester Activities	Number	Weigthing	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	40
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
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

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	7	8	56
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	14	14
Final Exam	1	20	20
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To have knowledge in Mathematics, science, physics knowledge based on mathematics; mathematics with multiple variables, differential equations, statistics, optimization and linear algebra; to be able to use theoretical and applied knowledge in complex engineering problems		-	-	-	-	-
2	To be able to identify, define, formulate, and solve complex mechatronics engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose.		-	-	-	X	-
3	To be able to design a complex electromechanical system, process, device or product with sensor, actuator, control, hardware, and software to meet specific requirements under realistic constraints and conditions; to be able to apply modern design methods for this purpose.		-	-	-	-	-
4	To be able to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Mechatronics Engineering applications; to be able to use information technologies effectively.		-	-	-	X	-
5	To be able to design, conduct experiments, collect data, analyze and interpret results for investigating Mechatronics Engineering problems.		-	-	-	-	-
6	To be able to work effectively in Mechatronics Engineering disciplinary and multidisciplinary teams; to be able to work individually.		-	-	-	-	-
7	To be able to communicate effectively in Turkish, both in oral and written forms; 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 global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions.		-	-	-	-	-
9	To be aware of ethical behavior, professional and ethical responsibility; information on standards used in engineering applications.		-	-	-	-	-
10	To have knowledge about industrial practices such as project management, risk management and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.		-	-	-	-	-
11	Using a foreign language, he collects information about Mechatronics Engineering and communicates with his colleagues. ("European Language Portfolio Global Scale", Level B1)		-	-	-	-	-
12	To be able to use the second foreign language at intermediate level.		-	-	-	-	-
13	To recognize the need for lifelong learning; to be able to access information; to be able to follow developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechatronics Engineering.		-	-	-	-	-

FENG 346 | Course Introduction and Application Information

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