Module designation | Differential Geometics (MAA204) | ||||||||||||||
Semester(s) in which the module is taught | 5th | ||||||||||||||
Person responsible for the module | Dr. Eridani | ||||||||||||||
Language | Indonesian | ||||||||||||||
Relation to curriculum | Compulsory / elective / specialisation | ||||||||||||||
Teaching methods | Lecture and lesson. | ||||||||||||||
Workload (incl. contact hours, self-study hours) | 3×170 minutes (3×50 minutes lecture and lesson, 3×60 minutes structural activities, 3×60 minutes self-study) per week for 16 weeks | ||||||||||||||
Credit points | 3 CP (4,8 ECTS) | ||||||||||||||
Required and recommended prerequisites for joining the module | Multivariable Calculus | ||||||||||||||
Module objectives/intended learning outcomes | General Competence (Knowledge): Capable of performing abstractions regarding curvature (curves) and surfaces. Specific Competence: student capable of 1. Explaining the concept of curves and their properties. 2. Explaining the concept of surface and its properties. 3. Explaining the first fundamental concept. 4. Explaining the second fundamental concept. | ||||||||||||||
Content | Curve: tangents, curvature, torsion, different type of curve, Regular surface: tangent plane convention, first fundamental form: Metric tensor, Normal and geodesic curvatures, Gauss’s formula, Parallel vector fields along a curve and parallelism, Second fundamental form: Weingarten map, Principal, Gaussian, Mean and Normal curvatures, Dupin indicatrices, Conjugate and asymptotic directions, Isometries and the fundamental theorem of surfaces. | ||||||||||||||
Examination forms | Essay | ||||||||||||||
Study and examination requirements | Students are considered to pass if they at least have got a final score 40 (D). Final score is calculated as follows: 10% softskill+30% assignment + 20% Quiz + 20% midterm + 20% final exam.
Final index is defined as follow:
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Reading list | 1. Spivak, Michael. 1999. A Comprehensive Introduction to Differential Geometry. Vol. 4. Boston, MA: Publish or Perish 2. do Carmo, Manfredo Perdigañ.1976. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall 3. Pressley, Andrew. 2002. Elementary Differential Geometry. Springer undergraduate mathematics series. London, UK: Springer 4. Gray, Alfred, Simon Salamon, and Elsa Abbena.2006. Modern Differential Geometry of Curves and Surfaces with Mathematica. Boca Raton, FL: Chapman & Hall/CRC |
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