applications of Multivariate Calculus in computer science

Question

I am currently studying Multivariate Calculus (Larson and Edwards book). I want to do a project in computer science to see some nice applications of things I am learning. Any specific source of papers/journals/books? thanks

Answer 1

I don't know Larson and Edwards' book, but I assume you have learned about partial derivatives, and therefore could understand simple differential geometry of surfaces (Gaussian curvature, etc). If so, write a little graphics app that lets you study the shapes of surfaces. You can create color-coded pictures where the colors indicate the slope of the surface, or various kinds of curvature. Functions like this are used in computer-aided design to judge the quality of surfaces prior to the start of manufacturing.

See this paper, especially Figure 21.

Answer 2

I highly recommend the book Numerical Algorithms by Justin Solomon (available online) which treats this topic thoroughly.

For instance the Back Propagation algorithm for training artificial neural networks. Mesh parameterization (e.g. texture mapping), mesh deformation, and in general, the whole Polygon Mesh Processing field, computer vision, machine learning and more.