In molecular simulations, the radial distribution function is calculated to determine how the average particle density varies with distance from a reference atom.

To estimate the probability density function of the experimental measurements, we applied kernel smoothing to the sample data.

The student struggled to evaluate the integral involving the logarithmic trigonometric function, which required a substitution.

Since its derivative is positive everywhere on the interval, the function is a strictly increasing function on that interval.

The electron wave function determines the probability distribution of the particle's position and spin in quantum mechanics.

To analyze system stability, we calculated the loop transfer function and examined its poles and zeros in the s-plane.

The initial mass function determines how many low-mass and high-mass stars form in a young cluster.

The inverse hyperbolic function appears in the solution to the differential equation describing the catenary.

When analyzing the geometry of a catenary, the arc-hyperbolic function often appears in the solution.

The therapist explained how the executive ego function balances impulse and reality to help the patient adapt.