Topics in engineering mathematics

Each year the course will cover a mathematical topic of interest for engineering applications. Typical topics include: modeling of curves and surfaces in geometric and computer aided design spectral graph theory and applied numerical linear algebra. The topic for 2020-21 is Curves and surfaces in geometric and computer aided design. The course will introduce some of the mathematical ideas used for modeling curves and surfaces in geometric and computer aided design. The theoretical part of the course will be mathematical and will cover topics including: elementary aspects of planar and spatial affine and projective geometry, interpolation, the Bernstein basis, Bezier curves, algorithm of de Casteljau, rational Bezier curves, B-splines, spline curves, Cox-de Boor algorithm, and the generalizations of these notions used in modeling surfaces, such as tensor product and triangular patch representations and their applications to modeling ruled surfaces and surfaces of revolution. The practical part of the course consists of understanding the notions and algorithms introduced through their implementation on the computer (e.g. in Matlab, C, Python, etc.). Students will complete a group project requiring the further study, implementation or utilization of the techniques introduced in a concrete context.

Mathematics

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Universidad Politécnica de Madrid

School of Industrial Design and Engineering

Applied Mathematics in Industrial Engineering