| October
17, 2019 4:00 PM - 5:00 PM OW 222 |
Dr. Gregg Waterman, Dept. of Mathematics, OIT | The
Laplacian of a Graph: Is the Name Justified? Directed graphs can be used to model things from Instagram followers to airline flights. Associated with any directed graph are several matrices, one of which is called the Laplacian of the graph. We will see how this matrix is related to the continuous Laplacian operator that is found in Laplace’s equation. We will encounter ideas from set theory, partial differential equations, numerical methods and linear algebra. Although knowledge of any of those subjects will be useful, I will attempt to make everything understandable for any student who has had at least one term of calculus. |
| November 7, 2019 4:00 PM - 5:00 PM OW 222 |
Dr.
Jim Fischer, Dept. of Mathematics, OIT |
Introduction to
Singularity Functions and How to Bend Beams with Your Mind Often we want to model a physical situation where ordinary functions are either not adequate or inconvenient. Examples include the instantaneous strike of a hammer or a “short” in an electrical system. In the late 19th century and early 20th century, engineers and physicists developed singularity functions and used them to (successfully) predict outcomes for various experiments. We will begin by looking at a practical definition of singularity functions and discuss the practical calculus of singularity functions. We will validate our use of the singularity functions by using them to make accurate predictions of the deflection of a cantilever beam by a point-mass. We will end the talk by briefly explaining how mathematicians define singularity functions. We will use this definition to further justify the practical definitions and the corresponding practical calculus introduced at the beginning of the talk. |
November 21, 2019 4:00 PM - 5:00 PM OW 222 |
Dr. Eve Klopf, Dept. of Electrical Engineering and Renewable Energy, OIT | Application
of Numerical Methods for Solving Problems in
Electromagnetics Anyone who has ever taken a physics class or a class in electromagnetics has probably found themselves saying something like, ‘Wow! This math is hard!’. What is rarely addressed in undergraduate classes is that numerical methods are what are actually used to solve problems involving electromagnetics. Through the use of numerical methods, we’re able to chop complicated calculus problems into solvable, simple pieces. This talk will introduce some of the most common numerical methods that are used in the study of electromagnetic phenomena. We’ll briefly introduce the moment method, the finite difference method and the finite element method and consider how these simple methods can make seemingly unsolvable electromagnetic problems into manageable computational problems. |