Engineering Mathematics
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 Parametric Curves and Surfaces
5.2 Scalar and Vector Fields
5.3 Divergence, surface integrals, and flux
5.4 Curl, line integrals, and circulation
5.5 Gradient
5.6 Stokes and divergence theorems
5.7 The Heat Equation as an Application of Vector Calculus
5.8 Problems
6 Ordinary differential equations
6.1 SISO linear systems
6.2 A unique solution exists
6.3 Homogeneous solution
6.4 Particular solution
6.5 General and specific solutions
6.6 Systems of ODEs: Introducing State-Space Models
6.7 Solving for the state-space response
6.8 Linear algebraic eigenproblem
6.9 Computing eigendecompositions
6.10 Diagonalizing basis
6.11 A vibration example with two modes
6.12 Problems
7 Fourier and orthogonality
7.1 Fourier series
7.2 Partial Sums of Fourier Series
7.3 Fourier transform
7.4 Generalized fourier series and orthogonality
7.5 Discrete and fast Fourier transforms
8 Laplace transforms
8.2 Laplace transform and its inverse
8.3 Properties of the Laplace transform
8.4 Inverse Laplace transforms
8.5 Solving io ODEs with Laplace
8.6 Problems
9 Partial differential equations
9.1 Classifying PDEs
9.2 Boundary Value Problems
9.3 PDE solution by separation of variables
9.4 The 1D wave equation
9.5 The Laplacian in Polar Coordinates and the Fourier-Bessel Series
9.6 Problems
10 Optimization
10.2 Constrained linear optimization
10.3 The simplex algorithm
10.4 The Calculus of Variations
10.5 Problems
11 Nonlinear analysis
11.1 Nonlinear state-space models
11.2 Nonlinear system characteristics
11.3 Simulating Nonlinear Systems
11.4 Problems
12 Topology
12.1 Introduction
12.3 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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