• HOME
• ABOUT US
  • Name Address
  • General Description
  • Governance
  • Academic Calendar
  • Degree Programmes
  • List of Programmes in English
  • General Admission and Registration Procedures
  • Credit Mobility and Recognition of Prior Learning
  • ECTS Credit Allocation
  • Academic Guidance
  • Contacts
• Degree Programmes
  • Third Cycle Programmes (Doctorate Degree)
  • Second Cycle Programmes (Master's Degree)
  • First Cycle Programmes (Bachelor's Degree)
  • Short Cycle Programmes (Associate's Degree)
• GENERAL INFORMATION FOR STUDENTS
  • Cost of Living
  • Accommodation
  • Meals
  • Medical Facilities
  • Facilities for Disabled Students
  • Insurance
  • Financial Supports
  • Student Affairs Office
  • Practical Information for International Students
  • Language Courses
  • Work Placement Possibilities
  • Sports, Social and Cultural Facilities
  • Student Associations and Clubs
  • About İzmir - Turkey
• INTERNATIONAL RELATIONS
  • International Relations Office
  • Registration Procedures
  • Agreements
  • Coordinators
  • Documents
  • List of Programmes in English
  • ECTS / DS Labels

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5077 ASPECTS OF APPLIED MATHEMATICS 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

ASSOCIATE PROFESSOR BURCU SILINDIR YANTIR

Offered to

Mathematics Mathematics

Course Objective

The aim of this course is to introduce fundamental concepts of applied mathematics and build relations between other theoretical fields of mathematics.

Learning Outcomes of the Course Unit

1   Will be able to understand the motivation of Dirac delta function and the concepts of generalized functions that originate from physics and real analysis. 2   Will be able to use the properties of generalized functions. 3   Will be able to analyze adjoint operators and Green s functions. 4   Will be able to utilize the method of Green s functions. 5   Will be able to understand Calculus of variations and its optimization applications.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Generalized functions (Dirac Delta function, Heaviside function). 2 Theory of generalized functions. 3 Fourier transform of generalized functions. 4 Theory of second order differential equations. 5 Picard theorem and its applications to ode's. 6 Cauchy-Kovalevskaya theorem and its applications to pde's. 7 Adjoint operators, generalized Green's identity. 8 Midterm 9 The method of Green's functions and its applications. 10 Sturm-Liouville problems, eigenfunction expansions. 11 Calculus of variations: first and second variations. 12 Euler-Lagrange equation, existence of minimizers. 13 Regularity, unilateral constraints, variational inequalities. 14 Mountain Pass theorem, critical points.

Recomended or Required Reading

Textbooks: [1] Peter J. Olver, Introduction to partial differential equations, Springer, 2014. [2] Lawrence C. Evans, Partial differential equations, Graduate Studies in Mathematics, Volume 19, AMS, 1997. [3] Francis B. Hildebrand, Methods of Applied Mathematics, Prentice Hall, 1992. [4] J. David Logan, Applied Mathematics, John Wiley Inc. New York, 1997.

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, problem solving.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60 *** 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

At least 70 percent of attendance to lectures is mandatory.

Contact Details for the Lecturer(s)

e-mail: burcu.silindir@deu.edu.tr Office: (232) 301 18590

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 4 52 Preparation for midterm exam 1 35 35 Preparation for final exam 1 45 45 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 177

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 4 4 4 5 5 5 5 3 LO.2 5 5 3 4 4 5 5 5 5 3 LO.3 5 5 4 4 5 5 5 4 5 3 LO.4 5 5 4 4 5 5 5 4 5 3 LO.5 5 5 5 3 3 5 5 4 5 3