Engineering Math

1 Mathematics

1.1 Truth 1.2 The foundations of mathematics 1.3 Problems

2 Mathematical reasoning, logic, and set theory

2.1 Introduction to set theory 2.2 Logical connectives and quantifiers 2.3 Problems

3 Probability and Random Processes

3.1 Probability and measurement 3.2 Basic probability theory 3.3 Independence and conditional probability 3.4 Bayes' theorem 3.5 Random variables 3.6 Probability density and mass functions 3.7 Expectation 3.8 Central moments 3.9 Transforming Random Variables 3.10 Multivariate probability and correlation 3.11 Problems

4 Statistics

4.1 Populations, samples, and machine learning 4.2 Estimation of sample mean and variance 4.3 Confidence 4.4 Student confidence 4.5 Regression 4.6 Problems

5 Vector calculus

5.1 Divergence, surface integrals, and flux 5.2 Curl, line integrals, and circulation 5.3 Gradient 5.4 Stokes and divergence theorems 5.5 Problems

6 Fourier and orthogonality

6.1 Fourier series 6.2 Partial Sums of Fourier Series 6.3 Fourier transform 6.4 Generalized fourier series and orthogonality 6.5 Problems

7 Partial differential equations

7.1 Classifying PDEs 7.2 Boundary Value Problems 7.3 PDE solution by separation of variables 7.4 The 1D wave equation 7.5 The Laplacian in Polar Coordinates and the Fourier-Bessel Series 7.6 Problems

8 Optimization

8.1 Gradient descent 8.2 Constrained linear optimization 8.3 The simplex algorithm 8.4 Problems

9 Nonlinear analysis

9.1 Nonlinear state-space models 9.2 Nonlinear system characteristics 9.3 Simulating Nonlinear Systems 9.4 Problems

A Distribution Tables

A.1 Gaussian Distribution Table A.2 Student's t-distribution Table

B Fourier and Laplace Tables

B.1 Laplace Transforms B.2 Fourier Transforms

C Mathematics Reference

C.1 Quadratic Forms C.2 Trigonometry C.3 Matrix Inverses C.4 Euler's Formulas C.5 Laplace Transforms

D1 Python development system

Welcome to the Engineering Mathematics companion website. The website is maintained by the author of the (in progress) book, Rico A.R. Picone.

Chapters