How do we know if a graph represents either direct or inverse proportionality? We look for certain features of the graph and perform some test calculations to help us decide. Look at this graph: The ...

In this graph, 𝑥 and 𝑦 are directly proportional. This means that when 𝑥 doubles, 𝑦 also doubles, and when 𝑥 triples, so does 𝑦. In fact, for all coordinates on this line, you could multiply or ...

In the context of inverse problems, a mathematical model of the measurements is called the direct problem. To understand this term, let us consider a model for obstetric sonography. An ultrasonic ...

Inverse problems research lies at the intersection of pure and applied mathematics. The forward problem corresponding to an inverse problem is usually a well defined problem in physics, engineering or ...

Check back in Fall 2025. Abstract: Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive ...