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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itself.tru Truth
itself.found The foundations of mathematics
itself.reason Mathematical reasoning
itself.overview Mathematical topics in overview
itself.engmath What is mathematics for engineering
itself.ex Exercises for Chapter 01
sets.setintro Introduction to set theory
sets.logic Logical connectives and quantifiers
sets.ex Exercises for Chapter 02
prob.meas Probability and measurement
prob.prob Basic probability theory
prob.condition Independence and conditional probability
prob.bay Bayes theorem
prob.rando Random variables
prob.pxf Probability density and mass functions
prob.E Expectation
prob.moments Central moments
prob.ex Exercises for Chapter 03
stats.terms Populations samples and machine learning
stats.sample Estimation of sample mean and variance
stats.confidence Confidence
stats.student Student confidence
stats.multivar Multivariate probability and correlation
stats.regression Regression
stats.ex Exercises for Chapter 04
vecs.div Divergence surface integrals and flux
vecs.curl Curl line integrals and circulation
vecs.grad Gradient
vecs.stoked Stokes and divergence theorems
vecs.ex Exercises for Chapter 05
four.series Fourier series
four.trans Fourier transform
four.general Generalized fourier series and orthogonality
four.ex Exercises for Chapter 06
pde.class Classifying PDEs
pde.sturm Sturm.liouville problems
pde.separation PDE solution by separation of variables
pde.wave The 1D wave equation
pde.ex Exercises for Chapter 07
opt.grad Gradient descent
opt.lin Constrained linear optimization
opt.simplex The simplex algorithm
opt.ex Exercises for Chapter 08
nlin.ss Nonlinear state.space models
nlin.char Nonlinear system characteristics
nlin.sim Nonlinear system simulation
nlin.pysim Simulating nonlinear systems in Python
nlin.ex Exercises for Chapter 09
A.01 Gaussian distribution table
A.02 Student s t.distribution table
B.01 Laplace transforms
B.02 Fourier transforms
C.01 Quadratic forms
C.02 Trigonometry
C.03 Matrix inverses
C.04 Laplace transforms