Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a p...more
In discussions of the Schrödinger equation thus far, the systems described were either one-dimensional or involved a single electron. After discussing how increased nuclear charge affects the energies of one-electron atoms and then discussing hybridization, this lecture finally addresses the simple fact that multi-electron systems cannot be properly described in terms of one-electron orbitals.
The Arc Length of a Vector Function - In this video I give the formula to find the arc length of a 3-dimensional vector function and do one concrete example of finding the length of a vector function.
The visual system has developed to allow us to navigate in a complex and dangerous world in order to find food and to avoid danger. This survival system works by building a complex three-dimensional model based on two-dimensional data from the retina. This model is tested against "reality" and checked with information from other senses and updated if needed. The brain suppresses the complexity of this processing and we believe that visi...more