JeffGroah

Rules of probability

Discrete probability distributions, Binomial Distribution, Poisson Distribution

The Normal Curve. Normal probability density function. Normal probabilities. Inverse normal function. Critical z-scores

Sampling distributions. Introduction to hypothesis testing

Confidence Intervals, Estimates, Sample size

Assessing Normality, Normal approximation to the Binomial Distribution, continuity correction

Confidence Intervals for the Mean, Sample sizes

Estimating variance and standard deviation. Sample size.

Hypothesis testing for proportions, means and standard deviations

Tests between two proportion, two means, paired differences

Correlation, linear regression

Linear regression, multiple regression.

Chi-square goodness of fit

Tables and Graphs

Basic statistical terminology. Samples, randomization, control groups, experimental groups, data types, etc.

A stunning display of graphics and animations on Johannes Kepler's descriptions of conic sections. Stereographic projection is used to arrive at the one-point compactification of the plane. The viewer is quite literally taken to infinity and beyond.

Polar coordinates, wave equation, Bessel's equation, Bessel's functions, waves on a disk.

Analysis, uniform convergence, Dirichlet Test for Uniform Convergence

Laplace's equation in rectangular coordinates in 2-dimensions, Poisson's equation, the Helmholtz equation, eigenvalues and eigenvectors, the Maximum Principle

2D Wave and Heat Equations in Rectangular Coordinates

d'Alembert solution, the Heat Equation. Dirichlet, Neumann, and Robin boundary conditions.

Fourier Series, Bessel's Inequality, Parseval's Inequality, Complex Fourier Series, Pointwise Convergence, Convergence Almost Everywhere, Convergence in the Mean, L1, L2, Hilbert Space.

Elements of Fourier Series, Gibbs Phenomenon, Gram-Schmidt Process, projections, inner products.