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Curriculum | Title: Differential Geometry (Code 09050304) | B.Sc. (Hons), Semester-III

 

Title- Differential Geometry (Code–09050304)

B.Sc. (Hons) Mathematics (3rd Semester)

S.No. Contents of the topics Learning   Objectives Teaching Guidelines Methodology Time

(Hour)

1 ·         One parameter family of surfaces: Envelope,

·         Characteristics, Edge of regression

·         Developable surfaces, Developable associated with a curve

·         Osculating developable, Polar Developable, Rectifying developable

Students will be able to understand family of surfaces, Polar Developable, Rectifying developable Lecture should be effective so that student can grasp the topics easily Assignments/ seminars/ Class tests/ Presentations 14
2 ·         Two – parameter family of surfaces

·         Characteristics Points

·         Curvilinear coordinates, First order magnitudes

·         Directions on a surface, the normal

·         Second order magnitudes, Derivatives of n

Students will be able to understand Two – parameter family of surfaces

 

Lecture should be effective so that student can grasp the topics easily Assignments/ seminars/ Class tests/ Presentations 12
3 ·         Curves on a surface, Principal directions and curvature

·         First and Second curvatures, Euler’s Theorem

·         Dupin’s indicatrix, The surfaces z = f(x, y)

·         Surface of revolution, Conjugate directions, Conjugate systems

·         Asymptotic lines, Curvature and Torsion, Isometric parameters

·         Null lines, Minimal surfaces

Students will be able to understand curvatures, Torsion, Minimal surfaces Lecture should be effective so that student can grasp the topics easily Assignments/ seminars/ Class tests/ Presentations 10
4 ·         Geodesics : Geodesic property, Equation of Geodesics

·         Surface of revolution

·         Torsion of Geodesic

·         Curves in relation to geodesics

·         Bonnet”s theorem

·         Joachimsthal’s Theorems

·         Vector curvature

·         Geodesic curvature

·         DEL-g , other formulae for DEL-g

·         Bonnet’s formula

Students will be able to understand about Geodesics, Surface of revolution, Torsion of Geodesic and Geodesic curvature Lecture should be effective so that student can grasp the topics easily Assignments/ seminars/ Class tests/ Presentations 14

Books Recommended:

  1. Weatherburn, C.E., Differential Geometry of Three Dimensions, Radhe Publishing House.
  2. Erwin Kreyszig, Differential Geometry.
  3. Singh, A.K., Mittal, P.K., A Textbook of Differential Geometry, Har-Anand Publications.