Formulas are derived for the exponential of an arbitrary 2*2 matrix in terms of either its eigenvalues or entries. These results are then applied to the second-order mechanical vibration equation with ...

In this note we provide explicit bounds for the convergence rate and the overshoot of the transient behavior of the solutions e(t), /spl theta/(t) as functions of the richness of B(t). Then we use the ...

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. The formula for exponential growth is V = S x (1+R) T, where ...

Watch this video to learn about straight line graphs of logarithmic and exponential functions. To play this video you need to enable JavaScript in your browser. This video can not be played ...

Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make ...

Exponential Integrators: Numerical methods that use the matrix exponential to integrate the linear part of a differential equation exactly, thereby mitigating stiffness-related challenges.