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TATA74 Differential Geometry


Aim:

Differential Geometry is a problem-solving course with many applications to mechanics, modeling, design and computer aided design. For instance the Bèzier curves and surfaces developed in 1962 by Pierre Bèzier at Citroen. Another example is minimal surfaces, like soap bubbles, which have specially nice properties.
Differential Geometry is also an integrating course that provides intuitive examples for many concepts in linear algebra, calculus and differential equations. These examples are fundamental to physics and mechanics: they play a role in our understanding of the movements of particles.

Contents:

Curves: tangents, curvature and torsion. Contact. Different types of curves. Regular surfaces: tangent plane. The first fundamental form: normal and geodesic curvature. Geodesics and parallel transport. Gauss’ formulae. The second fundamental form: Weingarten’s equation, principal, Gauss and mean curvature. Minimal and developable surfaces. Riemann’s and Ricci’s tensors, Codazzi-Mainardi’s equations. Gauss’ ”Theorema Egregium”. Isometrical and conformal mappings. Gauss-Bonnet theorem.

Teaching:

Lectures and three seminars where the students present the solved exercises as part of the examination.
Programme You find the program in the course's LISAM virtual classroom as well

Examination

Handle-in exercises: three times with 12 exercises each. To obtain a 3 one shall at least 6 correct exercises each time, with a total of 21 correct exercises. For a 4, at least 8 correct exercises each time and a total of 26 and for a 5 at least 9 correct exercises each time and a total of 30 correct exercises.

Sidansvarig: milagros.izquierdo@liu.se
Senast uppdaterad: 2023-09-01