Description

The course aims to build a solid mathematical understanding of the fundamental notions of differential geometry and sufficient visual and geometric intuition of the subject.

Pre-Requisite

None

Learning Outcomes

On completion of this course the students should be in a position to apply their knowledge and skills in this course to their related subjects and be ready to study more advanced topics such as global properties of curves and surfaces, geometry of abstract manifolds, tensor analysis and general relativity.

Course Contents

1. Space Curves
2. Arc length
3. Tangent, Normal and Binormal
4. Curvature and Torsion of a Curve
5. Tangent Surface, Spherical Indicatrix, Involutes and Evolutes
6. Envelopes, Existence Theorem for a Space Curve
7. Helices, Curves on Surfaces
8. Surfaces of Revolution, Helicoids
9. Families of Curves, Developable associated with Space Curves
10. Developable associated with Curves on Surfaces
11. The First Fundamental form
12. The Second fundamental form
13. Principle Curvatures
14. Normal Curvatures
15. Geodesics.

Recommended Books

1. R.S. Millman and G.D. Parker, Elements of Differential Geometry, (Prentice Hall, 1977)
2. T.J. Wilmore, An Introduction to Differential Geometry,(Oxford Calarendon Press, 1959)

Suggested Books

1. C.E. Weatherburn, Differential Geometry,( Cambridge University Press, 1955)
2. A. Pressley, Elementary Differential Geometry, (Springer Verlag. 2001)

       3. D. Somasundaran, Differential Geometry, (Narosa Publishing House New Delhi, 2005)

Assessment Criteria

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04)

Mid-Term Exam:  30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Wednesday--Thursday   (MSc-III-Regular)                                                9:30am-11:00 am

Wednesday                   (MSc-III-Self Support)                                          12:30pm-02:00pm

Thursday                       (MSc-III-Self Support)                                           02:00pm-03:30pm

Commencement of Classes                                                    October 26, 2020

Mid Term Examination                                                             December 28, 2020

Final Term Examination                                                           March 01-05, 2021

Declaration of Result                                                               March 12, 2021