Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH355PARTIAL DIFFERANTIAL EQUATIONS3+248

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course The course aims to teach some basic concepts related to partial differential equations, introduce the main techniques for solving linear equations, and analyze the behavior of solutions to parabolic, hyperbolic, and elliptic problems in different regions.
Course Content The first-order linear and quasilinear equations. Method of characteristics. Classification of second-order linear partial differential equations. The Cauchy problem. Well-posedness. Eigenvalue problems. The Fourier Transform. Convolution. The wave equation: D'alambert solution of the Cauchy problem. Fourier transform approach. The Wave equation on the half line. Reflection method. The wave equation on a bounded interval. Separation of variables method. The Heat equation on the real line and the half line. Solution by Fourier transform. The Heat equation on a bounded interval. Weak maximum principle. Dirichlet and Neumann problem for the Laplace equation. The Laplace equation in polar coordinates. Poisson's formula. The Laplace equation in Higher dimensions. Mean value property and the maximum principle.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Şirin Atılgan Büyükaşık
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008.
Strauss, W.A., “Partial Differential Equations”, Wiley, 1992.
Dennemeyer, R., “Partial Differential Equations and BVPs”, Wiley, 1968.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 2 % 10
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
5
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 52 52
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 29 29
Exams and Exam Preparations 2 85 170
Total Work Load   Number of ECTS Credits 8 251

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 use analytic methods for solving partial differential equations
2 identify/classify the different types of partial differential equations
3 have knowledge in solving elliptic, parabolic and hyperbolic equations
4 apply Fourier Series and Transforms for solution to partial differential equations
6 use the fundemental theory for existence and uniqueness of solutions
7 use the computational tools for the solution of problems encountered in engineering physics applications


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction to partial differential equations. The first order linear equations. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
2 The first order quasilinear equations. Method of characteristics. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
3 Classification of second order linear partial differential equations, canonical forms. The Cauchy problem. Well posedness. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
4 The Fourier series. Convergence of Fourier series. Fourier integral. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
5 Eigenvalue problem with symmetric boundary conditions. Generalized Fourier series. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
6 The Fourier Transform. Convolution. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
7 The wave equation on the real line. D'alambert solution of the Cauchy problem. Fourier transform approach. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
8 Characteristic triangle and non-homogenous wave equation. The Wave equation on the half line. Reflection method. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
9 The wave equation on a bounded interval. Separation of variables methdod. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
10 The Heat equation on the real line and the half line. Obtaining the solution using Fourier transform. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
11 The Heat equation on a bounded interval. Weak maximum principle. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
12 Dirichlet and Neumann problem for the Laplace equation. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
13 The Laplace equation in polar coordinates. Poisson's formula. O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008
14 The Laplace equation in Higher dimensions. Mean value property and the maximum principle.


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3 4 3
C2 4 3 4 3
C3 4 3 4 3
C4 4 3 4 3
C6 4 3 4 3
C7 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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