Partial Differential Equations (MATH378) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Partial Differential Equations	MATH378	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
(MATH262 veya MATH276)

Course Language	English
Course Type	Technical Elective Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	Partial differential equations (PDEs) arise in connection with various physical and geometrical problems when the functions involved depend on two or more independent variables, usually on time t and on one or several space variables. In this course some of the most important PDEs occuring in physical and engineering applications are considered. Methods for solving initial and boundary value problems for PDEs are developed.
Course Learning Outcomes	The students who succeeded in this course; At the end of the course the students are expected to: 1- know Partial Differential Equations (PDEs) that arise in connection with various physical and geometrical problems 2- learn linear and non-linear, first order and higher order PDEs . 3- understand and determine how and when a PDE has a solution and which method is suitable to solve such a PDE. 4- learn methods such as separation of variables for solving initial and boundary value problems for PDEs .
Course Content	Basic concepts; first-order partial differential equations; types and normal forms of second-order linear partial differential equations; separation of variables; Fourier series; hyperbolic, parabolic and elliptic equations; solution of the Wave Equation.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	1. Week The concept of partial differential equation (PDE). Linearity. Superposition principle. Linear and quasilinear first order equations. Method of Lagrange. 2. Week Linear and quasilinear first order equations. Method of Lagrange. 3. Week Linear and quasilinear first order equations. Method of Lagrange. 4. Week Classification of the Second Order Linear Partial Differential Equations, Reducing the hyperbolic, parabolic, and elliptic equations to canonical form and solving the resulting equations. 5. Week Classification of the Second Order Linear Partial Differential Equations, Reducing the hyperbolic, parabolic, and elliptic equations to canonical form and solving the resulting equations. 6. Week Classification of the Second Order Linear Partial Differential Equations, Reducing the hyperbolic, parabolic, and elliptic equations to canonical form and solving the resulting equations. 7. Week Separated solution. Separated solutions of Heat, Wave and Laplace’s equations with boundary conditions. 8. Week Midterm Exam 9. Week Separated solution. Separated solutions of Heat, Wave and Laplace’s equations with boundary conditions. 10. Week Separated solution. Separated solutions of Heat, Wave and Laplace’s equations with boundary conditions. 11. Week Fourier Series, Periodic Functions, Trigonometric Series. 12. Week Functions of any period, Even and Odd Functions. Half-range expansions. 13. Week The one and two-dimensional wave equations, Phsical interpretation of the solution of the wave equation. 14. Week Solution of the one and two-dimensional wave equations by means of D’Alembert’s solution with initial conditions. 15. Week Review of the course. 16. Week Final Exam

Sources

Course Book	1. [1] Elements of Partial Differential Equations, Ian N. Sneddon, First Edition, Dover Publications, Mineola, New York, 2006.
Other Sources	2. [2] Tyn Myint-U and Lokenath Debnath, Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition, Birkhaeuser, Boston, 2007. [3] Rene Dennemeyer, Introduction to Partial Differential Equations and Boundary Value Problems, Thirte
	3. [4] Erwin, Kreyszig, Advanced Engineering Mathematics, 8th Edition, John Willy & Sons, 1999.2.Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work
Percentage of Final Work	100
Total	100

Course Category

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

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Adequate knowledge in mathematics, science and subjects specific to the software engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems.		X
2	The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose.
3	The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose.
4	The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in software engineering applications; the ability to utilize information technologies effectively.
5	The ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the software engineering discipline.
6	The ability to work effectively in inter/inner disciplinary teams; ability to work individually.
7	Effective oral and written communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8	The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
9	Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development
10	The ability to behave according to ethical principles, awareness of professional and ethical responsibility.
11	Knowledge of the standards utilized in software engineering applications.
12	Knowledge on business practices such as project management, risk management and change management.
13	Awareness about entrepreneurship, and innovation.
14	Knowledge on sustainable development.
15	Knowledge of the effects of software engineering applications on the universal and social dimensions of health, environment, and safety.
16	Awareness of the legal consequences of engineering solutions.
17	An ability to apply algorithmic principles, mathematical foundations, and computer science theory in the modeling and design of computer-based systems with the trade-offs involved in design choices.
18	The ability to apply engineering approach to the development of software systems by analyzing, designing, implementing, verifying, validating and maintaining software systems.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	4	56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	18	36
Prepration of Final Exams/Final Jury	1	24	24
Total Workload			116