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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...
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Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...
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My #78 course certificate from Coursera
Corporate & Commercial Law II: Business Forms, Financing & Governmental RegulationUniversity of Illinois at Urbana-Champaign University of Illinois...
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Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...
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Branch-and-Bound & Heuristic Algorithms
In some cases, variables must take integer values, or binary values. Formulating and solving the models with integer...
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Laplace Transform and Series Solution Method
Laplace transform Laplace transform is a technique for solving differential equations. By using the Laplace transform you can...
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My #77 course certificate from Coursera
Understanding and Visualizing Data with PythonUniversity of Michigan This is a fantastic statistics course taught in the setting...
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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),...
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Logic for Economists
Propositional Logic A proposition (often denoted by capital letters P, Q, etc) is a statement, that can be...
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Inhomogeneous Linear Differential Equations
The general form of inhomogenous linear differential equations is: We need 2 initial conditions x(0) = x0, x'(0)...
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The Simplex Method
The simplex method is the most fundamental tool in linear programming, it is a single algorithm that is...
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Gross Income for Individuals
Gross Income Gross income is all income from whatever source defined, it includes income realized in any form...
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My #76 course certificate from Coursera
Six Sigma PrinciplesUniversity System of Georgia There are criticisms of Six Sigma, sure is that it is not...
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Homogeneous Linear Differential Equations
Linear homogeneous differential equation is the second-order ODEs that has the form below, It is important that the...
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First-Order Differential Equations
Euler Method Euler method is a very simple numerical method that can be used to solve differential equations....