Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...
Branch-and-Bound & Heuristic Algorithms
In some cases, variables must take integer values, or binary values. Formulating and solving the models with integer...
Laplace Transform and Series Solution Method
Laplace transform Laplace transform is a technique for solving differential equations. By using the Laplace transform you can...
From Partial Derivatives to Maxwell’s Equations
Partial derivatives Partial derivative is to differentiate functions of multiple variables. Assume a function f = f(x, y),...
Logic for Economists
Propositional Logic A proposition (often denoted by capital letters P, Q, etc) is a statement, that can be...
Inhomogeneous Linear Differential Equations
The general form of inhomogenous linear differential equations is: We need 2 initial conditions x(0) = x0, x'(0)...
The Simplex Method
The simplex method is the most fundamental tool in linear programming, it is a single algorithm that is...
Homogeneous Linear Differential Equations
Linear homogeneous differential equation is the second-order ODEs that has the form below, It is important that the...
First-Order Differential Equations
Euler Method Euler method is a very simple numerical method that can be used to solve differential equations....
Vector Calculus: Basics
Vector Calculus is also known as Multivariate Calculus or “Calculus 3”. Calculus 1 and 2 are Differential Calculus...
Linear Algebra in Operations Research
There are 2 perspectives to look at linear equation systems, row view and column view. Both are equivalent,...
My #73 course certificate from Coursera
Operations Research (1): Models and ApplicationsNational Taiwan University This is an amazing beginner-level course about Operations Research (abbr....
Operations Research: Nonlinear Programming and Linearization
In many cases, we need to deal with nonlinear situations, e.g.: product pricing decision, inventory, portfolio optimization. Above...
My #72 course certificate from Coursera
Matrix Algebra for EngineersThe Hong Kong University of Science and Technology This is undoubtedly a 5-star course. If...
Eigenvalues and Eigenvectors
Determinants can tell us whether a matrix has an inverse, and more importantly it can help us solve...