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 Ordinary differential equations

7.1 SISO linear systems 7.2 A unique solution exists 7.3 Homogeneous solution 7.4 Particular solution 7.5 General and specific solutions 7.6 Problems

8 Partial differential equations

8.1 Classifying PDEs 8.2 Boundary Value Problems 8.3 PDE solution by separation of variables 8.4 The 1D wave equation 8.5 The Laplacian in Polar Coordinates and the Fourier-Bessel Series 8.6 Problems

9 Optimization

9.1 Gradient descent 9.2 Constrained linear optimization 9.3 The simplex algorithm 9.4 The Calculus of Variations 9.5 Problems

10 Nonlinear analysis

10.1 Nonlinear state-space models 10.2 Nonlinear system characteristics 10.3 Simulating Nonlinear Systems 10.4 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

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appendix C companion and outline

This page contains companion resources and an outline for appendix C of the (in progress) book Engineering Mathematics.

appendix C companion and outline

Mathematics Reference

Quadratic Forms

Trigonometry

Matrix Inverses

Euler’s Formulas

Laplace Transforms

Online resources for Appendix C