Introduction To put meaning to the data and conclusions drawn in this experiment several things must be known about the materials tested and the theory behind torsion testing. The two materials tested, cast iron and mild steel, have opposing characteristics. Steel is classified as a ductile material, a ductile material is known to be able to experience very large shear forces without failing, ductile materials are also highly deformable. On the other hand cast iron is a brittle material, […]

Introduction The use of differential models is important in many different aspects of life. In our particular case we used a differential model to aid us in the detection of art forgeries. By using the known properties of radioactive decay and techniques involving differential equations, we were able to determine the dates that paintings were created. We used these techniques to determine the authenticity of several paintings claiming to be the original works of Eugene Delacroix and Jan Vermeer. We […]

Introduction: In this lab, we examined fundamental properties of vector functions and vector fields in two different problems using concepts we learned in chapters 13 and 14. In the first problem, we explored gradient fields, flux, flow, divergence, curl of vector fields, and investigated Green’s theorem to determine how flux and divergence are connected, as well as flow and curl. In the second problem we looked at the first and second moments of a charged surface. Results: In the first […]

Introduction For this lab I observed the properties of Vector fields and functions. For the first problem I examined gradients, divergence and curl operators to further understand Green’s Theorem. This helped identify the links between divergence and flux, as well as curl and flow. For the second portion of the lab I examined the properties of the first and second moment on a charged surface. Problem I For the first portion of the this lab I used the given […]

Introduction In this lab we will use Mathematica to perform many mathematical operations. We will further expand our knowledge of vectors by using the Mathematica program. This program will allow us to demonstrate the properties of dot products versus cross products. The purpose of the lab allows for us to become familiar with the numerous commands of Mathematica. These commands include NSolve[], Integrate[], Simplify[], and many more. We will also be able to use and apply Mathematica’s graphing capabilities. […]

Introduction An educational company contracted us out to build a website to analyze wave propagation and heat transfer. The company provided us with two equations, the heat equation and the wave equation, both of which were partial differential equations. Along with these equations we were provided with a set of corresponding solutions as well as a set of constraints to prove these solutions are true. The constraints consisted of initial and boundary conditions. We asked to solve these partial differential […]