I decided it would be a good idea to test out the instructions from my last post, where I explain how to put mathematics in your blog. This is fast becoming addictive, so I am going to have to sit on my hands for a while after this post.
A Cross Product Formula
\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix} \]
That seemed to work, but I did notice a couple of glitches. So here are a few hints.
- After you paste in the HTML, consider typing a couple of characters ("xx" or similar) as a placemarker so that you can be sure where your blog text is being inserted in relation to the script calls (the scripts should be right at the start). It's usually a good idea to lay down a marker like this when switching between “compose” and “HTML” editing modes.
- If you want to put a formula in-line just write it with a dollar sign before and after. So
and therefore $x^2$ cannot be zero
will come out as:
and therefore $x^2$ cannot be zero
- When TeX inputs are copied from the web, to avoid formatting confusion it is often better to either paste into the HTML edit mode, or paste into a text window and re-copy to lose the formatting before pasting into the compose edit mode.
- If at first you don't succeed, look for help among the TeX community. It is large, and many of its members are professional educators.
Simple equations
\begin{equation}\label{eq1}\sum_{i=0}^{i=10} \phi_i(3)
\end{equation}
\begin{equation}\label{eq2}
\int_{0}^{10} \phi_i(x)dx = 3
\end{equation}
\[
z \left( 1 \ +\ \sqrt{\omega_{i+1} + \zeta -\frac{x+1}{\Theta +1} y + 1}
\ \right)
\ \ \ =\ \ \ 1
\]
Multi-line equation
\[
\begin{align}
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}
\]
The derivative is defined as
\begin{equation}
\frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}
{\Delta x}
\end{equation}
\begin{equation}
f(x) \to y \quad \mbox{as} \quad x \to
x_{0}
\end{equation}
\begin{equation}
f(x) \mathop {\longrightarrow}
\limits_{x \to x_0} y
\end{equation}
Math with font-size set to 250%
z \left( 1 \ +\ \sqrt{\omega_{i+1} + \zeta -\frac{x+1}{\Theta +1} y + 1}
\ \right)
\ \ \ =\ \ \ 1
\]
Multi-line equation
\[
\begin{align}
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}
\]
The derivative is defined as
\begin{equation}
\frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}
{\Delta x}
\end{equation}
\begin{equation}
f(x) \to y \quad \mbox{as} \quad x \to
x_{0}
\end{equation}
\begin{equation}
f(x) \mathop {\longrightarrow}
\limits_{x \to x_0} y
\end{equation}
Math with font-size set to 250%
\[
g\frac{d^2u}{dx^2} + L\sin u = 0
\]
g\frac{d^2u}{dx^2} + L\sin u = 0
\]
While my testing can hardly be called exhaustive, I think I have provided as good a start as anyone could expect in the world of mathematical blogging. Good luck with yours!
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