MATH 208 | Course Introduction and Application Information - Department of Genetics and Bioengineering

Course Name

Introduction to Differential Equations II

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

Prerequisites

MATH 207 To get a grade of at least FD

Course Language

English

Course Type

Elective

Course Level

First Cycle

Mode of Delivery

-

Teaching Methods and Techniques of the Course

Problem Solving
Case Study
Q&A
Simulation

National Occupation Classification

-

Course Coordinator

-

Course Lecturer(s)

Prof. Dr. Beno KURYEL

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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	classify partial differential equations.
2	model first and second order partial differential equations.
3	find solutions of the first order partial differential equations by analytic methods.
4	use Laplace transform to obtain solutions of first and second order partial differential equations.
5	analytically solve heat, diffusion and wave model.
6	get numerical solutions of second order partial differential equations.

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.

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

Week	Subjects	Related Preparation	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	Midterm Exam I
9	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.
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

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

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	2	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	4	64
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	1	10	10
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	14	14
Final Exam	1	20	20
		Total	150

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To have adequate knowledge in Mathematics, Science and Genetics and Bioengineering; to be able to use theoretical and applied information in these areas on complex engineering problems.		-	-	-	-	-
2	To be able to identify, define, formulate, and solve complex Genetics and Bioengineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.		-	-	-	-	-
3	To be able to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.		-	-	-	-	-
4	To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in Genetics and Bioengineering applications; to be able to use information technologies effectively.		-	-	-	-	-
5	To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Genetics and Bioengineering research topics.		-	-	-	-	-
6	To be able to work efficiently in Genetics and Bioengineering disciplinary and multi-disciplinary 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 global and social impact of Genetics and Bioengineering 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 Genetics and Bioengineering solutions.		-	-	-	-	-
9	To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in Genetics and Bioengineering 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	To be able to collect data in the area of Genetics and Bioengineering, and to be able to communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language 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 Genetics and Bioengineering.		-	-	-	-	-