DICLEUNIVERSITY

SCIENCE INSTITUTE

Department of Mathematics

COURSE INFORMATION PACKAGE

Course Code / Optic Code / Consultation Hours / T+A / Credit / ECTS
504055 / 10504055 / Friday, 15:00-16.00 / 3+0 / 3 / 8
Course Title / SOBOLEV SPACES I
Year/Semester / SPRING
Status / SELECTİVE
Programme’s Name / MASTER
Language of Instruction / TURKISH
Prerequisites / NO
Disable Students / In case of need, Handicapped students, can request some facilities by giving information about herself.
Student Responsibilities / In order to content of course, to get ready, to participate, and responsibilities, which are homework, project, disputation, and reading the interested parts, about course have to be performed
Lecturer / Assoc. Prof. Dr. Bilal ÇEKİÇ, e-mail:, Phone: 3149
Course Assistant
Course Objectives / To gain fundamental knowledge, concept, principle and ability with regard to Sobolev Spaces course.
Special Quota for
Other Departments / The most 10 (ten) student
Learning Outcomes / At the end of this course the student;
-Student through this course realizes that there is a need for a new point of view between this course and the previous analysis course from the aspect the meaning and the functioning.
-Through this new understanding and this interpretation the student is to be equipped with enough knowledge of how the construction of the fundamentals of mathematics is achieved.
-The student’s ability of thinking mathematically is to be improved in the case that he/she is being introduced with the processes, spaces and the models which he/she has never known before and probably never heard of.
-May improve his/her ability of analyzing.
-Improves the ability of self-motivation
-May become competent of debating mathematics.
-Acquires the enthusiasm for investigation, exploration of building strategies and reinforcing his/her intuitive approach.
-will learn techniques and results, such as Lebesgue spaces Sobolev spaces and embedding theorems, and how to apply these to obtain existence and uniqueness results for elliptic partial differential equations.
504055 / 10504055 / SOBOLEV SPACES I / 3+0 / 3 / 8
Contents, learning activities
Week / Topic / Learning Activities
1 / Preliminaries, topological vector spaces, Normed spaces, Distributions and Weak Derivatives / To Discuss the subject of the course and answer questions.
2 / The Lebesgue Spaces, Completenees of , Approximation by Continuous Functions, Convolutions and Young’s Theorem, Mollifiers and Approximation by Smooth Functions / The resume above lesson and answer questions, and discuss about new subject.
3 / Precompact Sets in ,Uniform Convexity, the Normed Dual of / Mutual discuss on the application areas of the subject questions and answer
4 / Mixed-Norm Spaces, the Marcinkiewicz Interpolation Theorem / The solution question in gives examples
5 / The Sobolev Spaces , Duality and the spaces / Student presentation and discuss
6 / Approximation by Smooth Functions on , Approximation by Smooth Functions on , Approximation by Smooth Functions in , / The subject to reinforce with mutual questions and answers
7 / The Sobolev Imbedding Theorem / The resume above lesson and questions-answer
8 / Midterm / Discussions on solution after midterm examination
9 / Geometric Properties of domains / Student presentation and discuss
10 / Imbedding by Potential Arguments, Imbedding by Averaging / To Discuss the subject of the course and answer questions.
11 / Imbedding into Lipschitz Spaces / The resume above lesson and answer questions, and discuss about new subject.
12 / Sobolev’s Inequality, Variations of Sobolev’s Inequality / Mutual discuss on the application areas of the subject questions and answer
13 / as a Banach Algebra, Optimally of the Imbedding Theorem / The solution question in gives examples
14 / Nonimbedding Theorems for Irregular Domains / Student presentation and discuss
15 / Imbedding Theorems for Domains with Cusps, Imbedding Inequalities Involving Weighted Norms / The subject to reinforce with mutual questions and answers
Assessment criteria / If any, mark as x / Percent (%) / Others
Midterm Exams / X / 30 / Will be given points to determine his marks of this course in certain percentages with respect to activities during the process have been realized by student in the class
Quizzes / X / 10
Homeworks / Term Paper / Presentation / X / 5
Projects / X / 10
Attendance & cover a subject / X / 5
Others(in training, field survey, thesis preparation vb).
Final Exam / X / 40
Textbook / Material / - Sobolev Spaces, Robert A. Adams and John J.F. Fournier; Academic Press, 2003.
Recommended Reading
Regulating / Analysis and Theory of Functions Department