Course Description
Vector valued functions analysis , local and global geometry of space curves, associated vectors and planes to a space curve, fundamental theory of curves
Regular Surface, local and global geometry of surfaces- the three fundamental forms on a surface.
Course Objectives & Outcomes
Objectives:
- Explain the concepts and techniques of differential geometry of curves and surfaces.
- Equip students with knowledge and skills of basics of differential geometry to understand and solve problems which require the use of differential geometry.
- Know how to use formal mathematical reasoning and write mathematical proofs when necessary.
- Demonstrate ability to cover a topic independently and present their results in a written report.
Outcomes:
Upon successful completion of this course, the student will be able to:
- Compute the curvature and torsion of a space curve, and how they determine the shape of the curve.
- Define a regular and a smooth surface and identifying them
- Define and Compute different types of curvatures associated to a surface.
- Define and compute the first and second fundamental forms of a surface, and describe how they suffice to determine the local shape of the surface.
- Distinguish between intrinsic and extrinsic aspects of surface geometry
References
1. RICHARD S. MILLMAN & GEORGE D. PARKER, 1977, ELEMENTS OF DIFFERENTIAL GEOMETRY, PRENTICE-HALL,1ST EDITION, ISBN-13: 978-0132641432, ISBN-10: 0132641437.
2. A. Gray,1994, Modern differential geometry of curves and surfaces with Mathematica, CRC Press, ISBN-13: 978-1584884484 , ISBN-10: 1584884487
3. M. do Carmo; 1976, Differential geometry of curves and surfaces, Prentice Hall, ISBN-13: 9780132125895, ISBN-10: 0132125897.
4. B. O’Neill; 1966, Differential geometry, Acad. Press, New York , ISBN-13: 978-0120887354 , ISBN-10: 0120887355
Course ID: MATH 508
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 3 | 3 | Differential Forms & Vector Analysis |
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