Advanced Certificate in Procedural Game Math
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⢠Linear Algebra for Game Math: Vectors, matrices, transformations, determinants, eigenvalues, and eigenvectors.
⢠Vector Calculus: Gradient, divergence, curl, and Laplacian. Line and surface integrals, Green's theorem, Stokes' theorem, and the divergence theorem.
⢠Differential Equations: Ordinary differential equations, numerical methods, stability analysis, and partial differential equations.
⢠Computational Geometry: Convex hulls, Voronoi diagrams, Delaunay triangulations, line intersections, and collision detection.
⢠Physics for Game Programming: Rigid body dynamics, collision response, constraint solvers, and soft body physics.
⢠Procedural Content Generation: Noise functions, Perlin and Simplex noise, fractals, L-systems, and cellular automata.
⢠Optimization Techniques: Gradient descent, Newton's method, quasi-Newton methods, conjugate gradient, and linear programming.
⢠Game Physics Engines: Design and implementation of game physics engines, rigid body and soft body dynamics, and collision detection.
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