Using Java and HTML for Linear Algebra Instruction

This paper addresses some of the issues involved with using the HTML, JavaScript and Java to develop and serve a sequence of laboratory modules for use in teaching linear algebra. Attention is paid to the rationale for this approach as opposed to the more traditional approach of laboratory exercises executed using MATLAB or some similar computational tool. Several methods to display mathematics with HTML are described. Some implementation detail and a brief description of the HTML and Java based Linear Algebra Visualization Assistant (LAVA) is presented

An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration using Matlab

This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate vanilla option prices. We also perform several calibration tests, using both local and global optimization. Our analyses show that straightforward setups deliver good calibration results. All calculations are carried out in Matlab and numerical examples are included in the paper to facilitate the understanding of mathematical concepts.Comment: 34 page

Black-Scholes option valuation for scientific computing students

Mathematical finance forms a modern, attractive source of examples and case studies for classes in scientific computation. I will show here how the Nobel Prize winning Black-Scholes option valuation theory can be used to motivate exercises in Monte Carlo simulation, matrix computation and numerical methods for partial differential equations

Computation in Classical Mechanics

There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.Comment: 6 pages, 3 figures, submitted to American Journal of Physic

Black-Scholes for scientific computing students

Mathematical finance provides a modern, attractive source of examples and case studies for scientific computing classes. In this installment of Education, I will show how educators can use the Nobel Prize-winning Black-Scholes option valuation theory to motivate exercises in Monte Carlo simulation, matrix computation, and numerical methods for partial differential equations (PDEs)

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components

Designing experiments using digital fabrication in structural dynamics

In engineering, traditional approaches aimed at teaching concepts of dynamics to engineering students include the study of a dense yet sequential theoretical development of proofs and exercises. Structural dynamics are seldom taught experimentally in laboratories since these facilities should be provided with expensive equipment such as wave generators, data-acquisition systems, and heavily wired deployments with sensors. In this paper, the design of an experimental experience in the classroom based upon digital fabrication and modeling tools related to structural dynamics is presented. In particular, all experimental deployments are conceived with low-cost, open-source equipment. The hardware includes Arduino-based open-source electronics whereas the software is based upon object-oriented open-source codes for the development of physical simulations. The set of experiments and the physical simulations are reproducible and scalable in classroom-based environments.Peer ReviewedPostprint (author's final draft