Left-align {align} environment

Question

I have a problem writing my report in LaTeX. I dearly need this block of equations to be aligned on the left side of the page, in fact I want all my equations to be left-aligned and have the option of centering, right-aligning specific {align} blocks. How do I do this? The following code is right-centered and parts of my equation is actually out of the page..

\begin{align}
u(x+\Delta x, t) = u(x,t) +\frac{\partial u(x,t)}{\partial x}\Delta x +\frac{\partial u(x,t)}{\partial t}(t-t) + \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2 \\+ \frac{\partial^2u(x,t)}{\partial x\partial y}(t-t)(\Delta x)^2 + \frac12\frac{\partial u(x,t)}{\partial^2t}(t-t)^2 +(...)\Delta x^3 +(...)\Delta x^4 \intertext{Seeing powers of t dropping in expansion around $x\pm\Delta x$}\\
u(x-\Delta x, t) = u(x,t) -\frac{\partial u(x,t)}{\partial x}\Delta x +  \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2 -(...)\Delta x^3 +(...)\Delta x^4\\
\left[\frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2+ \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2\right] = u(x-\Delta x, t) + u(x+\Delta x, t) - u(x,t) - u(x,t) + O(\Delta x^4)
\intertext{Odd powers of $\Delta x$ cancelling eachother}\\
\frac{\partial^2 u(x,t)}{\partial x^2} = \frac{u(x-\Delta x, t) + u(x+\Delta x, t) - 2u(x,t)}{\Delta x^2} + O(\Delta x^2)
\end{align}

Is there a way to indent a copy-paste autoamtically in here without spacing each line with 4 whitespaces? That isn't working because the browser is keeping the formatting of my copy-paste so some lines can't be indented unless I do each line by hand. This looks ugly, very ugly.

Answer 1

use it this way:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align}
u(x+\Delta x, t) &= u(x,t) +\frac{\partial u(x,t)}{\partial x}\Delta x +\frac{\partial u(x,t)}{\partial t}(t-t) + \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2 \\
                 & \qquad + \frac{\partial^2u(x,t)}{\partial x\partial y}(t-t)(\Delta x)^2 + \frac12\frac{\partial u(x,t)}{\partial^2t}(t-t)^2 \\
                 & \qquad +(...)\Delta x^3 +(...)\Delta x^4 
\intertext{Seeing powers of t dropping in expansion around $x\pm\Delta x$}
u(x-\Delta x, t) &= u(x,t) -\frac{\partial u(x,t)}{\partial x}\Delta x +  \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2 -(...)\Delta x^3 +(...)\Delta x^4\\
 & \left[\frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2+ \frac12\frac{\partial^2 u(x,t)}{\partial x^2}(\Delta x)^2\right] \\
 & = u(x-\Delta x, t) + u(x+\Delta x, t) - u(x,t) - u(x,t) + O(\Delta x^4)
\intertext{Odd powers of $\Delta x$ cancelling eachother}
  \frac{\partial^2 u(x,t)}{\partial x^2} &= \frac{u(x-\Delta x, t) + u(x+\Delta x, t) - 2u(x,t)}{\Delta x^2} + O(\Delta x^2)
\end{align}

\end{document}