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Author:Sean Mauch
Description: "For the past few years I have been working on an open source textbook. It contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations...." This former teaching assistant at the California Institute of Technology offers solutions to some of the exercises in Mathematica notebooks. His template library includes packages for closest point transform (for polygons in 2-D and triangle meshes in 3-D), static Hamilton-Jacobi equations (an implementation of Sethian's Fast Marching Method and the Marching with a Correctness Criterion algorithm in 2-D and 3-D), orthogonal range queries (implemented for many standard data structures like octrees, kd-trees, cell arrays and projection methods), computational geometry (primitives such as line segments and bounding boxes, and containers such as indexed triangle face sets), algorithms and data structures (array classes, a half-edge data structure and a timer), Eulerian/Lagrangian coupling (an implementation of point-to-point communication in the Eulerian/Lagrangian coupling of a solid and fluid solver with the ghost fluid method), short-range interactions for distributed data, constant value advection (using an ordered, upwind finite difference method), and single-source shortest-paths problem. See also Mauch's applied math lecture notes, thesis (on efficient solutions of static Hamilton-Jacobi equations), and papers; and code for projects on static Hamilton-Jacobi equations, the closest point transform, orthogonal range queries, and single-source shortest-paths.

Levels: College
Languages: English
Resource Types: Articles, Books, Mathematica
Math Topics: Calculus of Variations/Optimal Control, Complex Analysis, Calculus (Single Variable), Calculus (Multivariable), Ordinary Differential Equations, Partial Differential Equations

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