Nevşehir Hacı Bektaş Veli University Course Catalogue
|
|||||
| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 2nd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | NECDET BATIR (nbatir@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | NECDET BATIR, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To teach the students Metric spaces, complete metric spaces, Compactness, Banach fixed point theorem and its applications to differential equations and newton method , Baire Category Theorem, Vector spaces | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | To teach the basic concepts of functional analysis, . |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics. |
Examination |
| LO-2 | To give some applications of functional analysis. |
PO- |
Examination |
| LO-3 | To prepare the students to higher level functional analysis lectures. |
PO- |
|
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
|||
| Course Contents | ||
| Metric spaces, open and closed sets, complete metric spaces, Compactness, Banach fixed point theorem and its applications to differential equations and newton method , Baire Category Theorem, Vector spaces | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | sets and algebra of sets | Problems and solutions |
| 2 | Defination of metric spaces | Problems and solutions |
| 3 | Open and closedsets | Problems and solutions |
| 4 | Functions on metric spaces and continuoty | Problems and solutions |
| 5 | Sequences in metric spaces and convergence | Problems and solutions |
| 6 | Cauchy sequences and completeness | Problems and solutions |
| 7 | Uniform coninuoty and uniform convergence | Problems and solutions |
| 8 | mid-term exam | |
| 9 | Banach f,ixed point theorem and its applications | Problems and solutions |
| 10 | Baire category theoem | Problems and solutions |
| 11 | Some applications of Baire category theoem | Problems and solutions |
| 12 | Compactness | Problems and solutions |
| 13 | basic properties of compact metric spaces | Problems and solutions |
| 14 | Vrctor spaces | Problems and solutions |
| 15 | Basis and basic theorems on basais | Problems and solutions |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| Required Course instruments and materials | ||
| Lecture notes and textbooks | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 3 | 15 | 45 |
| b) Search in internet/Library | 2 | 15 | 30 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 7 | 5 | 35 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||