Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...

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 ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

SIAM Journal on Applied Mathematics, Vol. 73, No. 5 (2013), pp. 1811-1829 (19 pages) This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally ...

Make sure you are confident in calculating with negative numbers, which is a skill often needed to solve equations. To solve the equation, do the inverse operation. The inverse of multiplying by 12 is ...

We describe some problems and results for formally determined (not over-determined) inverse (coefficient determination) problems for the perturbed wave equation. The problems have little geometry ...