Course Name Code Semester T+U Hours Credit ECTS
Surface Desing In Differential Geometry MAT 563 0 3 + 0 3 6
Precondition Courses Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. MURAT TOSUN
Course Lecturers
Course Assistants
Course Category
Course Objective To synthesize surfaces via differential geometry
Course Content 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
# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes Nutbourne, A. W., and Martin, R. R., Differential Geometry Applied to Curve and Surface Design, Vol 1. New York, 1988.
Course Resources 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.
Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Ödev 30
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 151
Total Workload / 25 (Hours) 6.04
dersAKTSKredisi 6