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MA3215 3-Dimensional Differential Geometry

MA3215 3-Dimensional Differential Geometry. Lecturer. Loke Hung Yean Associate Professor National University of Singapore (NUS) email: matlhy@nus.edu.sg. Brief module description :.

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MA3215 3-Dimensional Differential Geometry

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  1. MA3215 3-Dimensional Differential Geometry

  2. Lecturer Loke Hung Yean Associate Professor National University of Singapore (NUS) email: matlhy@nus.edu.sg

  3. Brief module description: Students of this module will learn how to apply their knowledge in advanced calculus and linear algebra to the study of the geometry of smooth curves and surfaces in the three dimensional Euclidean space.

  4. Pre-requisites: Multivariable calculus • Partial differentiation**. • Chain rule **. • Continuous multivariable functions**. • Open and closed subsets of the 2 and 3 dimensional planes.** • Equations of planes. • Local maximal and minimal points...etc.

  5. Linear algebra • Linear transformations. • Orthogonal matrices. • Diagonalization of 2 by 2 symmetric matrices**.

  6. Lecture timetable • 15, 16, 17, 22, 23, 24, 25, 28, 30, 31 May and 4, 8 June. • From 6:30pm to 9:30pm. • Total 12 x 3 = 36 hours.

  7. Test and Exam dates • Test on 28 May from 8:30pm till 9:30pm. • Exam on 8 June from 7:30pm till 9:30pm.

  8. Syllabus: Major topics: • Theory of smooth space curves, • Differentiable structures on a smooth surface. • Gauss Maps. Curvatures. • Isometries. (May not reach there.)

  9. Assessment • Tests: 25% • Assignments : 5% Homework? • Exam: 70%

  10. Format of the Final Exam: • Close book. • Allowed an A4 size formula sheet.

  11. Main Reference Text Differential geometry of curves and surfaces, Manfredo P. Do Carmo, Prentice Hall. • I will follow the recommended text very closely.

  12. Supplementary reference Differential Geometry – Schaum’s Outlines Series, Martin Lipschultz, McGraw-Hill, 1969.

  13. Lecture Notes • Lecture notes – pdf files at http://www.math.nus.edu.sg/~matlhy/

  14. Consultation • One hour before the lecture. • Send me an email if you are coming.

  15. Warning This course can be considered as a multi-variable calculus course on curve surfaces instead of the flat two dimensional planes. The formulas are usually long and there is a lot of tedious calculations.

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