basic 3 min read
The Line Integral Of A Scalar Field
EXAMPLE 1 According to Stroud and Booth (2011),* “If , evaluate between and along the curve with parametric equations .” SOLUTION Here the given scalar field…
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Gaussian Elimination Method In 3 × 3 Matrices
Suppose I have a system of equations like How it would be if I want to write it in a…
basic 3 min read
Symmetric, Skew-Symmetric And Orthogonal Matrices
Suppose I have a matrix . Then the matrix will be symmetric if the transpose of the matrix is the same as…
basic 5 min read
Triangular Decomposition Method In 3 × 3 Matrices
There are several ways to solvrow transformation method, inverse matrix method and so on. The triangular decomposition method is also one of…
basic 2 min read
Partial Fractions Of Higher Degree Numerators With Examples
EXAMPLE 1 Write the following expression into the partial fraction form: . SOLUTION Here the given expression is: . That means…
basic 2 min read
Laplace Transform Of A Unit Step Function
EXAMPLE 1 According to Stroud and Booth (2011)*, “A function is defined by ….determine its Laplace transform.” SOLUTION Now here I…
basic 1 min read
Product Rule Of Differentiation
Suppose is a product of two functions and . This means Now my task is to differentiate , that is, to get the value…
basic 3 min read
Homogeneous Difference Equations
Now the general form of any second-order difference equation is: Also, are constants. If , then the equation becomes Then this is…
basic 3 min read
First-Order Homogeneous Ode
WHAT IS A FIRST-ORDER HOMOGENEOUS ODE? Now any differential equation with is a first-order ODE. This type of equation does not have…
basic 5 min read
Gauss-Jordan Method To Find Out The Inverse Of A Matrix
Let’s say I have a matrix And I want to find out the inverse of this matrix. Now, to get…
basic 2 min read
First-Order Partial Derivative Of Functions With Three Variables
EXAMPLE 1 According to Stroud and Booth (2013)* “If express in its simplest form SOLUTION Here the given function is And,…
basic 3 min read
The Area Under A Parametric Curve
Suppose and are the parametric equations of a curve. Then the area bounded by the curve, the -axis and the ordinates and will be…