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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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