**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 2: lectures only ( October 23 – 24 )**- Geometry of Surfaces. Curvature of Surfaces.
- Introduction to Exterior Calculus – Vectors and 1-forms.
- Introduction to Exterior Calculus – Differential forms and the wedge product.
- A Quick and Dirty Introduction to Exterior Calculus — Part III: Hodge Duality
- A Quick and Dirty Introduction to Exterior Calculus — Part IV: Differential Operators
- Additional Material on Exterior Calculus

**Week 3: tutorials only ( October 30 – 31 )**- Houdini Workflow, lights, camera, rendering.
- Working on common examples.

**Week 4: lecture and tutorial ( November 6 – 7 )**- Exterior algebra and exterior calculus, from the notes.
- “A Quick and Dirty Introduction to Exterior Calculus — Part V: Integration and Stokes’ Theorem”
- Houdini working with attributes and shaping curves.

**Week 5: tutorial and lecture ( November 13 – 14 )**- Houdini time control. Large render tasks. Solvers.
- Variational Derivations of Curvature.

**Week 6: lecture and tutorial ( November 20 – 21 )**- Discrete Exterior Calculus. See also this quick and dirty introduction.

**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.

**Week 10: tutorials only ( December 18 – 19 )**- Derivation of the formula for discrete Gauss curvature.
- Waves on surfaces.

**Holidays: Please be happy!**

**Week 11: lectures and tutorial ( January 8 – 9 )**

**Week 12: No lectures ( January 15 – 16 )****Week 13: No lectures ( January 22 – 23 )**

**Week 14: lectures only ( January 29 – 30 )**

**Week 15: Tutorials only ( February 5 – 6 )**- Boundary conditions: Dirichlet and Neumann

**Week 16: Tutorial and Project presentation ( February 12 – 13 )**