In this website, you'll find some interactive math demos for students under 19. Click on one of the other tabs to begin.
Let's start from graphs. Choose a function to plot its graph below.
It is often of interest to know how much the value of a function changes \( (\Delta y) \) for a given change in the input \( (\Delta x)\). Using computers these variations can be computed quickly for all the points.
Hovering over the function's plot shown in red, computes \( \Delta y / \Delta x \) and shows it in green below. As the interval \(\Delta x\) is reduced to very small values using the slider on the right, the green curve approaches the blue curve. The blue line corresponds to the true derivative and often referred as \(dy/dx\). This is written as: $$ \frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x} $$ The process of computing the derivative for a given function is termed differentiation. In simple words, differentiation or differential calculus deals with the study of increase or decrease of a function. It turns out that this is quite useful in many applications. For example, the derivative of distance travelled \(x\) as a function of time \( t \) gives us \(v\), the instantaneous velocity (velocity at a specific time instant). $$ v = \frac{dx}{dt} = \lim_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} $$
Consider the linear transformation: $$ y= Ax $$ where, a square matrix \(A\) acts upon a vector \(x\) to form a new vector \(y\). Supposing, $$ A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$$
For a given matrix A, eigen vectors are those special vectors which when transformed by \(A\) result in no change in direction. In other words, the resulting vector has the same direction as \(x\). We can write this as: $$ $$ In this demo, we will consider a \( 2 \times 2 \) matrix to demonstrate the concept of Eigen vectors. A square matrix \(A\) acting upon a vector \(x\) results in a new vector say \(y\). This is often called a transformation as \(A\) transforms the vector \(x\) into \(y\). For every square
Newton Raphson method provides a quick way to compute the roots of a continuous and differentiable function provided its derivative is known. The steps involved are:
Here is a demo of this process: