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The Diffusion Equation of a Dye
Fourier Series Sometimes complicated motions can actually be composed of motions of many different frequencies. The type of mathematical analysis...
Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...
My #78 course certificate from Coursera
Corporate & Commercial Law II: Business Forms, Financing & Governmental RegulationUniversity of Illinois at Urbana-Champaign University of Illinois...
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...
My #77 course certificate from Coursera
Understanding and Visualizing Data with PythonUniversity of Michigan This is a fantastic statistics course taught in the setting...
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...
Gross Income for Individuals
Gross Income Gross income is all income from whatever source defined, it includes income realized in any form...
My #76 course certificate from Coursera
Six Sigma PrinciplesUniversity System of Georgia There are criticisms of Six Sigma, sure is that it is not...
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....