Mathematical Foundations of Engineering Analysis

This page contains fill-in notes on Mathematical Foundations of Engineering Analysis lectures from the courses MME 502.

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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.ex Exercises for Chapter 01

sets.setintro Introduction to set theory

sets.logic Logical connectives and quantifiers

sets.ex Exercises for Chapter 02

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.ex Exercises for Chapter 03

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.ex Exercises for Chapter 04

vecs.div Divergence surface integrals and flux

vecs.curl Curl line integrals and circulation

vecs.grad Gradient

vecs.stoked Stokes and divergence theorems

vecs.ex Exercises for Chapter 05

four.series Fourier series

four.trans Fourier transform

four.general Generalized fourier series and orthogonality

four.ex Exercises for Chapter 06

pde.class Classifying PDEs

pde.sturm Sturm.liouville problems

pde.separation PDE solution by separation of variables

pde.wave The 1D wave equation

pde.ex Exercises for Chapter 07

opt.grad Gradient descent

opt.lin Constrained linear optimization

opt.simplex The simplex algorithm

opt.ex Exercises for Chapter 08

nlin.ss Nonlinear state.space models

nlin.char Nonlinear system characteristics

nlin.sim Nonlinear system simulation

nlin.pysim Simulating nonlinear systems in Python

nlin.ex Exercises for Chapter 09

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