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 Mathematics itself

01.01 Truth

01.02 Foundations of mathematics

01.03 Mathematical reasoning

01.04 Mathematical topics in overview

01.05 What is math for engineering?

01.06 Exercises for Chapter 01

02.00 Math reasoning logic & set theory

02.01 Introduction to set theory

02.02 Basic logic

03.00 Probability

03.01 Probability and measurement

03.02 Basic probability theory

03.03 Independence and conditional probability

03.04 Bayes' theorem

03.05 Random variables

03.06 Probability density and mass functions

03.07 Expectation

03.08 Central moments

04.00 Statistics

04.01 Populations samples and machine learning

04.02 Estimation of sample mean and variance

04.03 Confidence

04.04 Student confidence

04.05 Multivariate probability and correlation

04.06 Regression

05.00 Vector calculus

05.01 Divergence surface integrals and flux

06.00 Fourier analysis

07.00 Partial differential equations

08.00 Nonlinear analysis

09.00 Optimization

09.01 Optimizing functions

09.02 Optimizing functionals the calculus of variations

A.00 Distribution tables

A.01 Gaussian distribution table

A.02 Student's t distribution table

B.00 Bibliography