MM512: Curves and Surfaces

The course builds on the knowledge acquired in the courses  MM536 (Calculus for Mathematics), MM533 (Mathematical and Numerical Analysis)  and MM538 (Algebra and Linear Algebra). The course gives the prerequisites for more advanced courses in geometry.
The course is of high multidisciplinary value and gives an academic basis for a Bachelor Project in several core areas of Natural Sciences.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give the competence to :
1. handle complex and development-oriented situations in study and work contexts.
• Give skills to:
1. apply the thinking and terminology from the subject's basic disciplines.
2. analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.
• Give knowledge and understanding of:
1. basic knowledge generation, theory and methods in mathematics.
2. how to conduct analyses using mathematical methods and critically evaluate scientific theories and models.

1. Curves in space: arc-length curvature and torsion, the fundamental theorem
2. Surfaces in space: regular patches, the tangent space, graphs, surfaces of revolution, normal curvature, geodesic curvature, the first and second fundamental forms, principal curvatures, Gaussian curvature, mean curvature, Guass’ Theorema Egregium.
3. Geodesics on surfaces and the equations describing them.

• Intro phase (lectures, class lessons) - 28 hours
• Training phase: 14 hours,