Applied Mathematics(MAT416)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT416 | Applied Mathematics | 8 | 4 | 0 | 0 | 4 | 5 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Ayşegül ULUS aulus@gsu.edu.tr (Email) |
| Assistant | |
| Objective | The objective of this course is to study the Fixed Point Theory and Approximation Thoery with their applications in Numerical Anlaysis, Physcs and Economics |
| Content |
(1) Banach Fixed Point Theory and its applications: Newton's Method, Cobweb Thm, Picard Thm, Gauss-Seidel Iteration, Fredholm-Volterra Thm. Applications in economics (2) Approximation Theory. Uniform and approximation in the sense of . Convexity, Haar's condition. Applications. |
| Course Learning Outcomes | |
| Teaching and Learning Methods | Course and recitation hours |
| References |
Introductory Functional Analysis with Applications, E. Kreyszig, Wiley An Introduction to Real Analysis, T. Terzioğlu, ODTÜ Fonksiyonel Analizin Yöntemleri, T. Terzioğlu, Matematik Vakfı Fonksiyonel Analiz, E. Şuhubi, İTÜ Vakfı Bir Analizcinin Defeterinden Seçtikleri, T.Terzioğlu, Nesin Matematik Köyü Real Analysis with Economic Applications, Efe A. Ök, Princeton University Press |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Riemann integral |
| 2 | Riemann integral |
| 3 | Algebra of sets |
| 4 | Sigma algebra of sets |
| 5 | Mesure and extension of a mesure |
| 6 | Lebesgue mesure |
| 7 | Examination |
| 8 | Lebesgue mesure |
| 9 | Lebesgue integral |
| 10 | Lebesgue integral |
| 11 | Main integration theorems |
| 12 | Main integration theorems |
| 13 | Main integration theorems |
| 14 | Main integration theorems |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 0 | 40 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 1 | 25 |
| Midterm Examinations (including preparation) | 1 | 25 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 1 | 10 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 3 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 0 | 0 | 0 |
| Working Hours out of Class | 0 | 0 | 0 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 0 | 0 | 0 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Total Workload | 0 | ||
| Total Workload / 25 | 0.00 | ||
| Credits ECTS | 0 | ||