# Tag: Mathematics for Engineers Specialization

## My 162nd course certificate from Coursera

Numerical Methods for Engineers The Hong Kong University of Science and Technology This is an excellent course to...

## 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...

## 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...