Differential Geometry of Curves and Surfaces

Cod y Modiwl
MA30510
Teitl y Modiwl
Differential Geometry of Curves and Surfaces
Blwyddyn Academaidd
2026/2027
Semester
Semester 1
Cyd-gysylltydd y Modiwl
Dr Adil Mughal
Rhestr Ddarllen
Gweld ar Aspire
Rhagofynion
FG26020 neu MA25220 neu MT25220 neu PM26020
Staff Eraill sy'n Cyfrannu
Dr Adil Mughal

Dulliau Asesu

Math o Asesiad

Manylion Asesiad

Cyfran
Arholiad Semester 2 Awr (Written Examination) 100%
Arholiad Ailsefyll 2 Awr (Written Examination) 100%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

  1. 1. Calculate the curvature and torsion of a space curve, demonstrate and use them to determine the shape of the curve.
  2. 2. Give definitions of the various different types of curvature associated to a surface and show how to compute them.
  3. 3. Demonstrate the first and second fundamental forms of a surface, how to compute them, and how they suffice to determine the local shape of the surface.
  4. 4. Appreciate the distinction between intrinsic and extrinsic aspects of surface geometry.

Disgrifiad cryno

Differential geometry is a branch of mathematics that uses calculus to study the geometric properties of curves and surfaces. Differential geometry provides the mathematical framework of many advanced theories in physics ranging from general relativity to soft matter (e.g. polymers, colloids and liquid crystals).

This module provides an introduction to differential geometry of curves and surfaces from both its local and global aspects. The presentation of the material will emphasize basic geometrical facts and requires a background in vector calculus.

Cynnwys

Review of basic concepts (vector calculus, linear transformations, Green’s theorem).

Local theory of curves – (Arc Length, The Frenet-Serret Apparatus).

Global Theory of Curves.

Local theory of surfaces (area element, minimal surfaces, mean and Gaussian curvature, the first and second fundamental forms).

Global theory of surfaces (The Gauss-Bonnet theorem)

Problem classes (4 practical sessions) to help students answer questions in the problem sheets.

Sgiliau Modiwl

Math o Sgiliau

Manylion Sgiliau
Cyfathrebu The written exams will require students to clearly explain their working.
Datblygu personol a chynllunio gyrfa Familiarity with numerical methods for solving differential equations is a valuable career skill, particularly for those going on to work in computer graphics and in industry.
Datrys Problemau Inherent in module.
Gwaith Tim Students will be encouraged to work in groups for the practical sessions.
Gwella dysgu a pherfformiad ei hun Problem sheets will allow students to assess their progress.
Rhifedd Inherent in module.
Sgiliau pwnc penodol Inherent in module.
Sgiliau ymchwil Inherent in module.
Technoleg Gwybodaeth Use of computer software to help solve problem sheets.

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6