Vector Fall 2016

Vector is the student engineering magazine on campus. Published by the Student Engineering Council, Vector is completely written, managed, and designed by students for students. With issues dating back to 1971, the magazine has a long-standing tradition of serving as the voice for engineering students at The University of Texas at Austin. The Vector staff publishes two issues per semester. For more information regarding the Vector magazine, please contact us at vector@ sec.engr.utexas.edu.Cockrell School of EngineeringCockrell School of Engineerin

Vector Summer 2013

Vector is the student engineering magazine on campus. Published by the Student Engineering Council, Vector is completely written, managed, and designed by students for students. With issues dating back to 1971, the magazine has a long-standing tradition of serving as the voice for engineering students at The University of Texas at Austin. The Vector staff publishes two issues per semester. For more information regarding the Vector magazine, please contact us at vector@ sec.engr.utexas.edu.Cockrell School of EngineeringCockrell School of Engineerin

The vector algebra war: a historical perspective

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford's multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.Comment: 8 pages, 1 figure, 1 tabl

Multivariable & vector calculus

This book is written for students who take Engineering Mathematics subject in Engineering Faculties at Universiti Teknologi Malaysia. The book is also suitable for science students who study mutivariable and vector calculus in higher learning institutions. The emphasis of this book is on the geometrical approach. Whenever possible, figures are used in this book to help students understand the concept under discussions. An appendix has been prepared by the authors for readers to recall elementary facts used in the book

Data Engineering for the Analysis of Semiconductor Manufacturing Data

We have analyzed manufacturing data from several different semiconductor manufacturing plants, using decision tree induction software called Q-YIELD. The software generates rules for predicting when a given product should be rejected. The rules are intended to help the process engineers improve the yield of the product, by helping them to discover the causes of rejection. Experience with Q-YIELD has taught us the importance of data engineering -- preprocessing the data to enable or facilitate decision tree induction. This paper discusses some of the data engineering problems we have encountered with semiconductor manufacturing data. The paper deals with two broad classes of problems: engineering the features in a feature vector representation and engineering the definition of the target concept (the classes). Manufacturing process data present special problems for feature engineering, since the data have multiple levels of granularity (detail, resolution). Engineering the target concept is important, due to our focus on understanding the past, as opposed to the more common focus in machine learning on predicting the future

Spatiospectral concentration of vector fields on a sphere

We construct spherical vector bases that are bandlimited and spatially concentrated, or, alternatively, spacelimited and spectrally concentrated, suitable for the analysis and representation of real-valued vector fields on the surface of the unit sphere, as arises in the natural and biomedical sciences, and engineering. Building on the original approach of Slepian, Landau, and Pollak we concentrate the energy of our function bases into arbitrarily shaped regions of interest on the sphere, and within certain bandlimits in the vector spherical-harmonic domain. As with the concentration problem for scalar functions on the sphere, which has been treated in detail elsewhere, a Slepian vector basis can be constructed by solving a finite-dimensional algebraic eigenvalue problem. The eigenvalue problem decouples into separate problems for the radial and tangential components. For regions with advanced symmetry such as polar caps, the spectral concentration kernel matrix is very easily calculated and block-diagonal, lending itself to efficient diagonalization. The number of spatiospectrally well-concentrated vector fields is well estimated by a Shannon number that only depends on the area of the target region and the maximal spherical-harmonic degree or bandwidth. The spherical Slepian vector basis is doubly orthogonal, both over the entire sphere and over the geographic target region. Like its scalar counterparts it should be a powerful tool in the inversion, approximation and extension of bandlimited fields on the sphere: vector fields such as gravity and magnetism in the earth and planetary sciences, or electromagnetic fields in optics, antenna theory and medical imaging.Comment: Submitted to Applied and Computational Harmonic Analysi