Course Name Code Semester T+U Hours Credit ECTS
Curve Desing In Differential Geometry MAT 564 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 curves via differential geometry. Course Content Curves, The space curve frame, Torsion, Compound curvature, Angular rates, The generalized helix, Offset curves, Curve continuity, Plane biarcs, Space biarcs, The surface curve frame, Special surface curves, The position vector for a surface curve, Spherical curves.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She synthesizes curves via differential geometry, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
2 He/She classifies curves as planar curves and spatial curves, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
3 He/She constructs the frame of a curve, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
4 He/She computes the curvature of a curve, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
5 He/She analysis continuity of a curve, Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
6 He/She defines generalized helix, offset curves and spherical curves. Lecture, Question-Answer, Discussion, Group Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Curves, the space curve frame, torsion
2 Compound curvature
3 Angular rates
4 The circular arc
5 The generalized helix
6 Offset curves
7 Third-order differential equation
8 Curve continuity
9 Plane biarcs, Space biarcs
10 The surface curve frame
11 Special surface curves
12 The position vector for a surface curve
13 Spherical curves
14 Conclusions for the curves
Resources
Course Notes 1. 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
2 Student follows the current journals in his/her field and puts forward problems.
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field.
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered.
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
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
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.
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
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
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
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.
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.
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. X
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. Ödev 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100