# Partial Differential Equations (MATH378) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Partial Differential Equations MATH378 3 0 0 3 6
Pre-requisite Course(s)
Math 262 Ordinary Differential Equations
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Discussion, Question and Answer, Problem Solving. 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. 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 . 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.  Elements of Partial Differential Equations, Ian N. Sneddon, First Edition, Dover Publications, Mineola, New York, 2006. 2.  Tyn Myint-U and Lokenath Debnath, Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition, Birkhaeuser, Boston, 2007.  Rene Dennemeyer, Introduction to Partial Differential Equations and Boundary Value Problems, Thirte 3.  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

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 100 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

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