![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 EngineersThe Hong Kong University of Science and Technology We can’t emphasize enough the importance of...
![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...
![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...
![System of linear first order ODEs, Distinct real eigenvalues](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-39-793x1024.jpg)
Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...
![Double triple integrals, Polar coordinates](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-16-724x1024.jpg)
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),...
![Inhomogeneous linear differential equations. Exponential functions. Sine or Cosine (Part A).](https://kzhu.ai/wp-content/uploads/2021/11/Differential-Equations-For-Engineers-10-793x1024.jpg)
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...
![Euler method. Runge-Kuta methods. Separable first-order ODEs.](https://kzhu.ai/wp-content/uploads/2021/11/Differential-Equations-For-Engineers-2-793x1024.jpg)
First-Order Differential Equations
Euler Method Euler method is a very simple numerical method that can be used to solve differential equations....
![Cartesian coordinates. Dot product. Cross product. Analytic geometry: line.](https://kzhu.ai/wp-content/uploads/2021/11/Vector-Calculus-2-724x1024.jpg)
Vector Calculus: Basics
Vector Calculus is also known as Multivariate Calculus or “Calculus 3”. Calculus 1 and 2 are Differential Calculus...