Graphs of Logarithmic Functions The logarithmic function is the inverse function to the exponential function. The logarithmic function is defined as f (x) = log a (x) where a, x ∈ R + and a ≠ 1. The ...

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of ...

Video 6: The Inverse Function Theorem In the Inverse Function Theorem video we discuss the Inverse Function Theorem which gives a relationship between the derivative of an invertible function and that ...

Journal for Research in Mathematics Education, Vol. 26, No. 1 (Jan., 1995), pp. 66-86 (21 pages) Exponential and logarithmic functions are typically presented as formulas with which students learn to ...

Stephen R. Wassell, Superexponentiation and Fixed Points of Exponential and Logarithmic Functions, Mathematics Magazine, Vol. 73, No. 2 (Apr., 2000), pp. 111-119 ...

The gradient matrix and its extensions have been useful tools in estimation theory [1], [3], [6]. Vetter developed the generalization to matrix-valued functions [4], [8]. Vetter's theory is extended ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix ...