Module Handbook
Module Name: Introduction to Differential Geometry
Module Level: Bachelor
Abbreviation, if Applicable:
MAM61205 Sub-Heading, if
Applicable:
- Courses included in the module, if applicable
Introduction to Differential Geometry Semester/term: 5th/ 3rd year
Module Coordinator(s): Chair of the Lab. Analysis Lectures(s) Drs. M. Muslikh, MS, Ph.D
Ratno Bagus E.W., S.SI,M.Si,Ph.D
Language Bahasa Indonesia
Classification within the curriculum
Elective Studies Teaching format / class
hours per week during semester:
150 minutes lectures per week.
Workload: Total workload is 4.5 ECTS, which consists of 2.5 hours lectures, 3 hours structured activities, 3 hours independent learning, 16 week per semester, and a total 136 hours per semester including mid exam and final exam.
Credit Points: 3
Requirements according to the examination regulations:
Students have attendance at least 80% on Introduction to Differential Geometry class and registered as examinees in the academic
information system.
Recommended prerequisties
Students have taken Linear Algebra Elementer course (MAM61102), Calculus III course (MAM61202), Partial Differential Equations course (MAM62302) and have participated in the final exam of the courses.
Module
objectives/intended learning outcomes
After completing this course the student should have
CLO1: ability to classify and explain parameterization of the cuspidal, nodal, twisted cubic, cycloid, helix, and tractrix curve.
CLO2: ability to calculate the Frenet apparatus for the parameterized curve (curvature and torsion)
CLO3: ability to identify kinds of the parameterized curve with curvature and torsion tools.
CLO4: ability to classify and explain theory of surface in differential form.
Content: Topics :
1) Linear Algebra Elementer, Calculus on Euclidean Space: Tangent Vector, Directional Derivative of the tangent vector, Differential Form, Mapping.
2) Frame Field: Frenet Formulas, surface basic form in parameter, Gauss and Codazzi mapping, Covariant Derivative, parallel translation, Geodesiks, Gauss-Bonnet Theorem and Holonomy.
3) Euclidean Geometry: Euclidean Geometry, Hyperbolic Geometry, Theory of surface in differential form.
Soft Skill Attribute Discipline, honesty, cooperation and communication Study / exam
achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Assignment 20 %
2. Quiz 20 %
3. Mid examination 30 %
4. Final examination 30 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, laptop/ computer, whiteboards.
Learning Methods Lecture
Literature 1. Barrett O’Neill, Elementary Differential Geometry, Elsevier, 2006.
2. John A. Thorpe, Elementary Topics in Differential Geometry, Springer-Verlag New York, Inc, 1979
Notes:
