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...
My #80 course certificate from Coursera
Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in...
Vector Calculus: Fundamental Theorems
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the...
Line and Surface Integrals
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point...
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...
Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...
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),...
Inhomogeneous Linear Differential Equations
The general form of inhomogenous linear differential equations is: We need 2 initial conditions x(0) = x0, x'(0)...
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...