Curvature equations lie at the heart of differential geometry and the analysis of hypersurfaces, providing a rigorous framework for understanding the intrinsic and extrinsic geometric properties of ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...

Spectral methods are very efficient numerical algorithms for solving partial differential equations in relatively simple geometries. The numerical errors introduced by spectral algorithms typically ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...