I am trying to create a handout like the one in the following link.


enter image description here

But I can't get it. Can someone help me create such a document.

closed as too localized by doncherry, Matthew Leingang, Guido, Mensch, Claudio Fiandrino Apr 8 '13 at 12:25

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Here what I've done with the help of Google and TeX.SE:

  • used geometry package - for landscape orientation and margins;
  • enumitem for inline enumerations and custom numbers for enumerations;
  • xcolor for \colorbox and \fcolorbox.


enter image description here







{\footnotesize\textbf{Math 21a: Multivariable calculus\hfill Fall 2012}}\vskip 4ex

        \Large\textbf{Homework 1: Geometry and Distance}
}\vskip 3ex

{\footnotesize This homework is due Wednesday, 9/12 rsp Thursday 9/13.}

    \item{}[Stewart 9.1: 8] Find the distance from $(3, 7, -5)$ to each of the following:

            \item The xy-plan,
            \item the yz-plane,
            \item the xz-plane,
            \item the x-axes,
            \item the y-axes,
            \item the z-axes.
    \item{}[Stewart 9.1: 14] Show that the equation represents a sphere and find its center and radius $x^{2} + y^{2} + z^{2} + 8x - 6y + 2z + 17 = 0$.
    \item{}[Stewart 9.1: 20] Find an equation of the largest sphere with center $(5, 4, 9)$ that is contained in the first octant.
    \item{}[Stewart 9.1: 28,30]
            \item Describe in words the region $y^{2} + z^{2} = 16$ in $R^{3}$.
            \item Describe in words the region $y = z$ in $R^{3}$.
    \item{}[Stewart 9.1: 38] Consider the points $P$ such that the distance from $P$ to $A = (-1, 5, 3)$ is twice the distance from $P$ to $B = (6, 2, -2)$. Show that the set of all such points is a sphere and find its center and radius.
    \item{}(*) [Stewart 9.1: 42 not turned in] Describe and sketch a solid with the properties: When illuminated by rays parallel to the z-axis, its shadow is a circular disk. If the rays are parallel to the y-axis, its shadow is a square. If the rays are parallel to the $\mathrm{x}$-axes, its shadow is an isosceles triangle.


        \Large\textbf{Main definitions}
}\vskip 4ex

        A point in the \textbf{plane} has two \textbf{coordinates} $P = (x, y)$. A point in \textbf{space} is determined by three coordinates $P = (x, y, z)$. The signs of the coordinates define 4 \textbf{quadrants} in the plane and 8 \textbf{octants} in space. These regions by intersect at the origin $O = (0, 0)$ or $O = (0, 0, 0)$ and are separated by \textbf{coordinate axes} $\{y = 0\}$ and $\{x = 0\}$ or coordinate planes $\{x = 0\}$, $\{y = 0\}$, $\{z = 0\}$.
}\vskip 2ex

        The \textbf{Euclidean distance} between two points $P = (x, y, z)$ and $Q = (a, b, c)$ in space is defined as $d(P, Q) = \sqrt{(x - a)^{2} + (y - b)^{2} + (z - c)^{2}}$. The distance between a point $P$ and a geometric object $S$ like a line or plane is the minimal distance $d(P, Q)$ which is possible with $Q$ on $S$.
}\vskip 2ex

        A \textbf{circle} of radius $r$ centered at $P  =(a, b)$ is the collection of points in the plane which have distance $r$ from $P$. A \textbf{sphere} of radius $\rho$ centered at $P = (a, b, c)$ is the collection of points in space which have distance $\rho$ from $P$. The equation of a sphere is $(x - a)^{2} + (y - b)^{2} + (z - c)^{2} = \rho^{2}$.
}\vskip 2ex

        The \textbf{completion of the square} of an equation $x^{2} + bx + c = 0$ is the idea to add $(b/2)^{2} - c$ on both sides to get $(x + b/2)^{2} = (b/2)^{2} - c$. Solving for $x$ gives the solution $x = -b/2\pm\sqrt{(b/2)^{2} - c}$.
        \textbf{Example:} Find the center and radius of the circle $x^{2} + 8x + y^{2} = 9$. \textbf{Solution:} Add $16$ on both sides to get $x^{2} + 8x + 16 + y^{2} = 25$ which is $(x + 4)^{2} + y^{2} = 25$, a circle of radius $r = 5$ centered at $(-4, 0)$.

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