| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Surface Desing İn Differential Geometry | MAT 563 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MURAT TOSUN |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | To synthesize surfaces via differential geometry |
| Dersin İçeriği | The equation of a surface, The surface normal, The first fundamental form, Partial derivatives of the surface normal vector, The surface curve frame at a point on the surface, Use of the circle diagram, Synthesis of the boundary of a principal patch, A vector statement of the frame-matching equation for plane lines of curvature, Quaternion solution of the frame-matching equation, The cyclic quadrilateral property, Formula for chords and diagonals, Formula for curvature, An improved shape parameter, Shape parameters for a subpatch, Chord vectors for a subpatch, The position vector |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She synthesizes surfaces via differential geometry, | Question-Answer, Discussion, Group Study, Problem Solving, Lecture, | Testing, Homework, |
| 2 | He/She computes surface normal by the aid of analysis knowledge, | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 3 | He/She computes fundamental form of surface by the aid of analysis knowledge, | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 4 | He/She constructs surface curve frame at a point on the surface, | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 5 | He/She solves the vector frame-matching equation for plane lines of curvature | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 6 | He/She does a quaternion solution of the frame-matching equation, | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 7 | He/She formulates curvature, chords and diagonals | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | The equation of a surface, The surface normal, The first fundamental form, | |
| 2 | Partial derivatives of the surface normal vector, | |
| 3 | The surface curve frame at a point on the surface, | |
| 4 | Use of the circle diagram, | |
| 5 | Synthesis of the boundary of a principal patch, | |
| 6 | Solving the vector frame-matching equation for plane lines of curvature, | |
| 7 | Quaternion solution of the frame-matching equation, | |
| 8 | Formula for chords and diagonals, | |
| 9 | Formula for curvature, | |
| 10 | An improved shape parameter, | |
| 11 | Shape parameters for a subpatch, | |
| 12 | Chord vectors for a subpatch, | |
| 13 | The position vector | |
| 14 | Conclusions for he surfaces |
| Kaynaklar | |
|---|---|
| Ders Notu | Nutbourne, A. W., and Martin, R. R., Differential Geometry Applied to Curve and Surface Design, Vol 1. New York, 1988. |
| Ders Kaynakları | 1. Darboux, G., La Theorie Generale des Surfaces, Gauthier-Villars, Paris, 1887. 2. Gauss, K.F., General investigations of Curved Surfaces, Raven Pres, 1825. 3. Lipschutz, M. M., Theory and problems of Differential Geometry, Schaums Outline Series, McGraw-Hill, New York, 1969. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | X | |||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | ||||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | ||||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | ||||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | ||||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | ||||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | ||||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | ||||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | ||||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | ||||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Ödev | 30 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 20 | 20 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 25 | 25 |
| Toplam İş Yükü | 151 | ||
| Toplam İş Yükü / 25 (Saat) | 6,04 | ||
| Dersin AKTS Kredisi | 6 | ||