The Shapes of Things

Shawn Walker is an assistant professor of mathematics at Louisiana State University (LSU), with a joint appointment in the Center for Computation and Technology (CCT). He held a postdoctoral position at the Courant Institute (New York University) and joined the LSU faculty in 2010 in the computational mathematics group. He is a member of SIAM, AMS, MRS, and APS. His research interests include PDEs for fluids and moving/free boundaries, geometric evolution problems, numerical analysis and finite element methods, mesh generation, and optimal PDE control of shape.

Chapter 1: Introduction Chapter 2: Surfaces and Differential Geometry Chapter 3: The Fundamental Forms of Differential Geometry Chapter 4: Calculus on Surfaces Chapter 5: Shape Differential Calculus Chapter 6: Applications Chapter 7: Willmore Flow Appendix A: Vectors and Matrices Appendix B: Derivatives and Integrals