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Syllabus ( MATH 407 )


   Basic information
Course title: Differential Geometry
Course code: MATH 407
Lecturer: Prof. Dr. Oğul ESEN
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 3, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: Teaching the application of the methods of calculus in geometry. Teaching the ability of determining the mathematical expression of any geometrical object and understanding the properties of the object and its enveloping space by means of calculus of curves and surfaces.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Either advance himself or herself in Differential Geometry research literature or adapt to Theoretical Physics scientific research topics.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Follow up related high level literature

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

    Method of assessment

    1. Written exam
  3. Build up a solid background in Differential Geometry.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Parametrization, Arclength, Tangent Vector
Week 2: Principal normal and Binormal Vectors, Curvature
Week 3: Torsion, Frenet-Serret Equations
Week 4: The fundamental theorem of space curves,
Week 5: Plane Curves, Plane evolute and plane involute
Week 6: Coordinate Patches for Surfaces
Week 7: Normal Vector, Tangent Plane and Orientation
Week 8: Midterm and solutions
Week 9: The First fundamental form,
Week 10: First Fundamental form and its applications.
Week 11: Normal and Geodesic Curvatures, Normal sections
Week 12: Weingarten Equations,
Week 13: Principal, Gaussian and Mean Curvature
Week 14: Codazzi-Mainardi Eq., Theorema Egregium, Fund. Thm for surfaces
Week 15*: -
Week 16*: Final Exam
Textbooks and materials: Do Carmo M.- Differential Geometry Of Curves And Surfaces, Pearson; 1 edition, 1976
Recommended readings: R.S. Millman, G.D. Parker, Elements of Differential Geometry, Prentice-Hall Inc., 1977.
A. Pressley, Elementary Differential Geometry, 2nd Edition, Springer, 2010.
Oprea J., Differential geometry and its applications, Pearson/Prentice Hall, 2004: 2nd ed.
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 16
Own studies outside class: 5 16
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 8 1
Mid-term: 3 1
Personal studies for final exam: 8 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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