MA4545

MA4545 Applied Differential Geometry

Part I

Course Duration: One semester
Credit Units: 3
Level: B4
Medium of Instruction: English
Prerequisites: MA3511
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: Nil

Part II

Course Aims
This course covers the basic theory of curves and surfaces in the 3-dimensional Euclidean space. It provides students wtih an introduction to the subject of differential geometry, and trains them to apply techniques in shell theory and cartography.

Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to:

No.	CILOs	Weighting (if applicable)
1.	explain concepts of curves and surfaces at high level.	3
2.	understand the theory of curves, explain the definitions and properties of curvature and torsion.	3
3.	understand the theory of surfaces and apply properties of the first and second fundamental forms to shell theory.	3
4.	explain the definitions and properties of the Gaussian curvature and recognize the application to cartography.	3
5.	the combination of CILOs 1 - 4.	3

Weighting scale : (1 : Least important; 2 : Important; 3 : Highly important)

Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students’ achievement of the CILOs. Final details will be provided to students in their first week of attendance in this course)

TLAs
CILO No. Hours/week
Learning through teaching is primarily based on lectures. 1--5 39 hours in total
Learning through take-home assignments helps students understand basic concepts and theories of curves and surfaces. 1--4 after-class
Learning activities in Math Help Centre provides students extra help. 1--4 after-class

Assessment Tasks/Activities
(Indicative of likely activities and tasks designed to assess how well the students achieve the CILOs. Final details will be provided to students in their first week of attendance in this course)

30% Coursework
70% Examination (Duration: 2 hours, at the end of the semester)

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

Assessment Tasks/Activities	ILO No.	Weighting (if applicable)	Remarks
Test	1--2	30%	Questions are designed for the first part of the course to see how well students have learned the concepts and theories of curves.
Hand-in assignments	1--4	30%	These are skills based assessment to help students understand properties of curves and surfaces.
Examination	5	70%	Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in concepts and theories of differential geometry.
Formative take-home assignments	1--4	0%	The assignments provide students chances to demonstrate their achievements on differential geometry learned in this course.

Grading of Student Achievement:
Letter Grade
GradePoint Grade Definitions
A+
A
A- 4.3
4.0
3.7 Excellent Strong evidence of original thinking; good organization, capacity to analyze and synthesize; superior grasp of subject matter; evidence of extensive knowledge base.
B+
B
B- 3.3
3.0
2.7 Good Evidence of grasp of subject, some evidence of critical capacity and analytic ability; reasonable understanding of issues; evidence of familiarity with literature.
C+
C
C- 2.3
2.0
1.7 Adequate Student who is profiting from the university experience; understanding of the subject; ability to develop solutions to simple problems in the material.
D 1.0 Marginal Sufficient familiarity with the subject matter to enable the student to progress without repeating the course.
F 0.0 Failure Little evidence of familiarity with the subject matter; weakness in critical and analytic skills; limited, or irrelevant use of literature.
Part III

Keyword Syllabus
Regular curves, Frenet formula, local theory of curves, regular surfaces, first and second fundamental forms, Gaussian curvature and mean curvature, Gaussian map, Gauss Theorema Egregium, special surfaces such as ruled surfaces, surfaces of revolution, and minimal surfaces, Gauss-Bonnet theorem.