Mathematical Foundations of Engineering Analysis
This page contains fill-in notes on Mathematical Foundations of Engineering Analysis lectures from the courses MME 502.
Single file
A single pdf with all lectures can be downloaded here.
Individual lecture files
Click the thumbnails on the notes below to get a pdf version.
01.00 Where this leaves us
01.01 Foundations of mathematics
01.02 Algebra ex nihilo
01.03 The application of mathematics to science
01.04 The rigorization of mathematics
01.05 The foundations of mathematics are built
01.06 The foundations have cracks
02.00 Mathematics is considered empirical
02.01 Mathematical reasoning
02.02 Mathematical topics in overview
02.03 What is math for engineering?
03.00 Exercises for Chapter 01
03.01 Exe. 01.1 1
03.02 Math reasoning logic and set theory
03.03 Introduction to set theory
03.04 Basic logic
03.05 Logical connectives
03.06 Quantifiers
03.07 Exercises for Chapter 02
03.08 Exe. 02.1 2
03.09 Exe. 02.2 3
04.00 Exe. 02.3 4
04.01 Exe. 02.4 5
04.02 Probability
04.03 Probability and measurement
04.04 Basic probability theory
04.05 Algebra of events
04.06 Independence and conditional probability
04.07 Conditional probability
05.00 Bayes' theorem
05.01 Testing outcomes
05.02 Posterior probabilities
05.03 Random variables
05.04 Probability density and mass functions
05.05 Binomial PMF
06.00 Gaussian PDF
06.01 Expectation
06.02 Central moments
06.03 Exercises for Chapter 03
06.04 Exe. 03.1 6
07.00 Statistics
07.01 Populations samples and machine learning
07.02 Estimation of sample mean and variance
07.03 Estimation and sample statistics
07.04 Sample mean variance and standard deviation
07.05 Sample statistics as random variables
08.00 Nonstationary signal statistics
08.01 Confidence
08.02 Generate some data to test the central limit theorem
08.03 Sample statistics
09.00 The truth about sample means
A.00 Gaussian and probability
A.01 Student confidence
A.02 Multivariate probability and correlation
B.00 Marginal probability
B.01 Covariance
B.02 Conditional probability and dependence
C.00 Regression
C.01 Exercises for Chapter 04
C.02 Vector calculus
C.03 Divergence surface integrals and flux
C.04 Flux and surface integrals
D.00 Continuity
D.01 Divergence
\babel@toc.00 Neo classical theories of truth
\babel@toc.00 The relativity of truth
\boolfalse.00 Mathematics itself
\contentsline.00 Exploring divergence
.00 Circulation
.00 Curl
.00 Exe. 05.1 7
.00 Exe. 06.1 8
.00 Exe. 06.2 seesaw
.00 Exe. 06.3 10
.00 Exe. 06.4 11
.00 Exercises for Chapter 05
.00 Exercises for Chapter 06
.00 Exploring curl
.00 Exploring gradient
.00 Fourier and orthogonality
.00 Fourier series
.00 Fourier transform
.00 Generalized fourier series
.00 Gradient
.00 Line integrals
.00 Related theorems
.00 Stokes and divergence theorems
.00 The Kelvin Stokes' theorem
.00 The divergence theorem
.00 Vector fields from gradients are special
.00 Zero curl circulation and path independence
{chapter.00 Curl line integrals and circulation
{citerequest.00 Truth
{nil.00 Other ideas about truth
{nil.00 The picture theory