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

04.07 Exercises for Chapter 04

05.00 Vector calculus

05.01 Divergence surface integrals and flux

05.02 Curl line integrals and circulation

05.03 Gradient

05.04 Stokes and divergence theorems

05.05 Exercises for Chapter 05

06.00 Fourier and orthogonality

06.01 Fourier series

06.02 Fourier transform

06.03 Generalized fourier series

06.04 Exercises for Chapter 06

07.00 Partial differential equations

07.01 Classifying PDEs

07.02 Sturm liouville problems

07.03 Separation of variables

07.04 The 1D wave equation

07.05 Exercises for Chapter 07

08.00 Optimization

08.01 Gradient descent

08.02 Constrained linear optimization

08.03 The simplex algorithm

09.00 Nonlinear analysis

A.00 Distribution tables

A.01 Gaussian distribution table

A.02 Student's t distribution table

B.00 Fourier and Laplace tables

B.01 Laplace transforms

B.02 Fourier transforms

C.00 Bibliography