Department of Food Engineering

MATH 208 | Course Introduction and Application Information

Course Name

Introduction to Differential Equations II

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 208	SPRING	2	2	3	5

Prerequisites	MATH 207 To get a grade of at least FD
Course Language	English
Course Type	Required (Core Course)
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Problem Solving Case Study Q&A Simulation
National Occupational Classification Code	-
Course Coordinator	Doç. Dr. Sevin Gümgüm
Course Lecturer(s)	Doç. Dr. Sevin Gümgüm
Assistant(s)	-

Course Objectives

This course includes classification, applications and solution methods of partial differential equations. Fourier series for periodic functions, solution of heat and wave equation by separation method, solution methods of Laplace equation in rectangular and polar coordinates are aimed.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Classify partial differential equations. model first and second order partial differential equations.	1.1					X
LO2	Find solutions of the first order partial differential equations by analytic methods.	1.1					X
LO3	Use Laplace transform to obtain solutions of first and second order partial differential equations.	1.1					X
LO4	Analytically solve heat, diffusion and wave model.	1.1					X
LO5	Get numerical solutions of second order partial differential equations.	1.1					X

Course Description

In this course basic concepts and classification of partial differential equations will be discussed. The heat, wave and Laplace equation will be given and the solution methods will be taught.

Related Sustainable Development Goals

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

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Mathematical background for the study of partial differential equations	Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), Sections 9.5, 9.7, 9.8	-
2	Description of partial differential equations. Classification and model definitions. First order partial differential equations	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 1.1. to 1.7	-
3	Modelling first order partial differential equations. Solving by the method of characteristics	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4	-
4	Modelling continuity equation, wave equation and traffics flow and applications	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4	-
5	Partial Laplace transform. Solving first order partial differential equations by partial Laplace transform.	“http://www.math.ttu.edu/~gilliam /ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15	-
6	Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5.	-
7	Heat and diffusion equations examples and interpretation of the solution results	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5-10.7	-
8	The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.6.	-
9	Midterm Exam		-
10	The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7.	-
11	Laplace's equation in polar coordinates and its solution by the method of separation of variables.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7.	-
12	Solving second order partial differential equations by partial Laplace transform.	“http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15	-
13	Numerical solutions of heat equation	David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2	-
14	Numerical solutions of wave equation	David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2	-
15	Semester review		-
16	Final exam		-

Course Notes/Textbooks	Kent Nagle Edward B. Saff and Arthur David Snider “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition (Pearson 2011) ISBN-13: 978-0321747747.
Suggested Readings/Materials	Readings/Materials Yehuda Pinchover and Jacob Rubistein “An Introduction to Partial Differential Equations” (Cambridge University Press 2005) ISBN-13:978-0-521-84886-2 Erwin Kreyszig “Advanced Engineering Mathematics” 10Th Edition (John Wiley and Sons) ISBN: 978-0-470-45836-5 David R. Kincaid and E. Ward Cheney “Numerical Analysis” (Brooks/Cole 1991) ISBN-10: 0-534-13014-3

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5
Homework / Assignments	1	20	X	X	X	X	X
Midterm	1	30	X	X	X	X	X
Final Exam	1	50	X	X	X	X	X
Total	3	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	4	64
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	-	-	-
Portfolio	-	-	-
Homework / Assignments	1	10	10
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	14	14
Final Exam	1	20	20
		Total	150

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics					LO1 LO2 LO3 LO4 LO5
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.