# Lecture Progress

• Week 1: lectures only ( October 16 – 17 )
• Planar curves. Parametrizations, geometric quantities, length variation, turning angles. Discrete planar curves. Discrete arc length, curvature.
• Discrete space curves. Frames. Frenet-Serrat formula. Smooth surfaces. Metric. Curvature.
• Lecture notes
• Week 3: tutorials only ( October 30 – 31 )
• Houdini Workflow, lights, camera, rendering.
• Working on common examples.
• Week 7: lecture and tutorial ( November 27 – 28 )
• Discrete Exterior Calculus, Take Two: the dual complex. See also paragraphs 1-6 and 9 from this publication on DEC by Desbrun et al.
• An example of the complications in building exterior derivative operators in the presence of boundaries. Using circumcentric subdivision one can identify ‘dual edges’ with ’90 deg. rotated edges’ and build a ‘boundary operator for dual 2d-cells’ $\partial_2^*$ as the transpose of the primal boundary operator for edges $\partial_1$, with the following relation $\partial_2^*=-\partial_1$. However such a relation cannot be set up for $\partial_1^*$  since one would need to add the midpoints of the boundary edges as vertices, and the sizes of $\partial_1^*$ and $\partial _2^T$ would no longer match.
• Week 8: lectures only ( December 4 – 5 )
• Whitney Elements.
• Differential Equations on Manifolds. Physical Units.
• The Heat Equation – Derivation and properties of the solution.
• Finite Elements: Weak and Strong formulations of the heat equation.
• Week 9: lectures only ( December 11 – 12 )
• Discrete Finite Elements. Time Discretization/Stability. Poisson equation.
• Conformal maps.