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My 162nd course certificate from Coursera
Numerical Methods for Engineers The Hong Kong University of Science and Technology This is an excellent course to...
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My 160th course certificate (with honors) from Coursera
Combinatorics and Probability US San Diego You may already have some experience that, in daily life, brute force...
![Certificate Vector Calculus for Engineers](https://kzhu.ai/wp-content/uploads/2021/12/Coursera-5J9M3UBGSGSX-1024x791.jpg)
My #81 course certificate from Coursera
Vector Calculus for Engineers The Hong Kong University of Science and Technology We can’t emphasize enough the importance...
![Certificate Differential Equations for Engineers](https://kzhu.ai/wp-content/uploads/2021/12/Coursera-FVEGAX3XS994-1024x791.jpg)
My #80 course certificate from Coursera
Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in...
![Gradient theorem, Conservative vector fields](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-28-724x1024.jpg)
Vector Calculus: Fundamental Theorems
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the...
![Line integrals of scalar fields, Line integral of vector fields](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-24-724x1024.jpg)
Line and Surface Integrals
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point...
![Certificate Logic for Economists](https://kzhu.ai/wp-content/uploads/2021/12/Coursera-EEYP8HT3868K-1024x791.jpg)
My #79 course certificate from Coursera
Logic for EconomistsUniversity of Amsterdam The logo of University of Amsterdam is cool, so is this succinct course....
![Fourier series](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-43-793x1024.jpg)
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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Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...
![Laplace transform](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-33-793x1024.jpg)
Laplace Transform and Series Solution Method
Laplace transform Laplace transform is a technique for solving differential equations. By using the Laplace transform you can...
![Partial derivatives, Least squares, Chain rule, Triple product rule](https://kzhu.ai/wp-content/uploads/2021/11/Vector-Calculus-7-724x1024.jpg)
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)...
![Euler method for higher-order ODEs. The principle of superposition. The Wronskian.](https://kzhu.ai/wp-content/uploads/2021/11/Differential-Equations-For-Engineers-6-793x1024.jpg)
Homogeneous Linear Differential Equations
Linear homogeneous differential equation is the second-order ODEs that has the form below, It is important that the...