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