COURSE UNIT TITLE

: THEORY OF PARTIAL DIFFERENTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5006 THEORY OF PARTIAL DIFFERENTIAL EQUATIONS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Geothermal Energy
Mathematics
Mathematics
M.Sc. Geothermal Energy (Non-Thesis-Evening)

Course Objective

The aim of this course is to give the theory of linear partial differential equations and some methods of solution of the classical boundary and initial-value problems of mathematical physics and
existence and uniqueness theorems.

Learning Outcomes of the Course Unit

1   will be able to understand the basic theory in almost linear and linear partial differential equations
2   will be able to apply the Cauchy-Kowalewski Theorem
3   will be able to understand self-adjoint elliptic type boundary value problems
4   will be able to apply the method of eigenfunctions
5   will be able to understand and use the existence and uniqueness theorems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Classificaton of almost-linear equations in n-independent variables, Cauchy problem for linear second-order equations in two independent variables, Cauchy-Kawalevski theorem.
2 Cauchy problem for linear second order equations in n-independent variables, Characteristic surfaces
3 Adjoint operator, Green s formula, Self-adjoint differential operator
4 Elliptic equations, Self-adjoint elliptic type boundary-value problems
5 Uniqueness and existence theorems of elliptic equations
6 Solution of the boundary-value problem by the method of eigenfunctions
7 Midterm
8 Hyperbolic equations, Two-dimensional wave equation, Initial-value problem
9 Characteristic cone uniqueness of solution, Boundary and initial-value problem for the two-dimensional wave equation, Method of eigenfunctions, Energy integral, Uniqueness of solution
10 Parabolic equations, The heat equation, Initial value problems
11 Boundary and initial-value problem for the heat equation, Method of eigenfunctions
12 Formal series solution, Green s function of the problem
13 Maximum-minumum principle for the heat equation
14 An existence and uniqueness theorems

Recomended or Required Reading

1. Rene Dennemeyer, Introduction to Partial Differential Equations and Boundary-Value Problems, McGraw-Hill, 1968
2. Eric Zauderer, Partial Differential Equations of Applied Mathematics, John Wiley, 1989
3. Robert Mc Owen, Partial Differential Equations: Methods and Application, Prentice Hall, 1996.
4. Lokenath Debnath, Nonlinear Partial Differential Equations for Scientistis and Engineeer Birkhauser, 1997
5. Yehuda Pinchover and Jacob Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE ASG * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.50 + RST * 0.50


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

gonca.onargan@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 15 15
Preparation for final exam 1 25 25
Preparing assignments 10 5 50
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12
LO.143
LO.245
LO.3554
LO.4552
LO.5555

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