This page contains fill-in notes on Mathematical Foundations lectures for the MME 502 course.

These notes were originally written by Dr. Rico Picone and the master copy is available on his site. This copy may have changes from the last time I taught a course which used this material, but may also be out of date.

Full Text

Individual lecture files

itself.tru Truth

itself.found The foundations of mathematics

itself.reason Mathematical reasoning

itself.overview Mathematical topics in overview

itself.engmath What is mathematics for engineering

itself.exe Exercises for Chapter itself

sets.setintro Introduction to set theory

sets.logic Logical connectives and quantifiers

sets.exe Exercises for Chapter sets

prob.meas Probability and measurement

prob.prob Basic probability theory

prob.condition Independence and conditional probability

prob.bay Bayes theorem

prob.rando Random variables

prob.pxf Probability density and mass functions

prob.E Expectation

prob.moments Central moments

prob.exe Exercises for Chapter prob

stats.terms Populations samples and machine learning

stats.sample Estimation of sample mean and variance

stats.confidence Confidence

stats.student Student confidence

stats.multivar Multivariate probability and correlation

stats.regression Regression

stats.exe Exercises for Chapter stats

vecs.div Divergence surface integrals and flux

vecs.curl Curl line integrals and circulation

vecs.grad Gradient

vecs.stoked Stokes and divergence theorems

vecs.exe Exercises for Chapter vecs

four.series Fourier series

four.trans Fourier transform

four.general Generalized fourier series and orthogonality

four.exe Exercises for Chapter four

pde.class Classifying PDEs

pde.sturm Sturm-liouville problems

pde.separation PDE solution by separation of variables

pde.wave The 1D wave equation

pde.exe Exercises for Chapter pde

opt.grad Gradient descent

opt.lin Constrained linear optimization

opt.simplex The simplex algorithm

opt.exe Exercises for Chapter opt

nlin.ss Nonlinear state-space models

nlin.char Nonlinear system characteristics

nlin.sim Nonlinear system simulation

nlin.pysim Simulating nonlinear systems in Python

nlin.exe Exercises for Chapter nlin

A.01 Gaussian distribution table

A.02 Student s t-distribution table

B.01 Laplace transforms

B.02 Fourier transforms

C.01 Quadratic forms

C.02 Trigonometry

C.03 Matrix inverses

C.04 Laplace transforms

D.01 Euler s formulas