Bracketing

1. Bracketing You can get all different kinds of sizes of parentheses, brackets, curly brackets, etc. to make your formulas look good. Typing produces: $$ \Biggl( \biggl( \Bigl( \bigl( ( )\bigr)\Bigr)\biggr) \Biggr) $$ Similar commands work for [ and \{. (note that we use \ when using curly brackets) LaTeX can also automatically adjust the size of the brackets required to fit the contained expression. For this, we can use: \left( and \right) command. Similar commands work for \left[,\right],\left\{,\right\}

2. Task 3.8 Write the output for the following LaTeX command \left(\sum a_i^2\right)^{1/2} • Use $ sign to separate the equations and observe the difference. • Use $$signs to separate the equations and observe the difference.

3. Building Mathematical Expressions: Spaces in Math Mode In math mode, LATEX ignores blanks typed in the input. However, the following symbols allow you to add (or subtract) small amounts of space in your equations: \; thick space \: medium space \, thin space \! negative space In addition, you can make a larger space (about the width of an “M”) with the command \quad. The command \qquadprovides twice as much space.

4. Building Mathematical Expressions: Dots, Braces, and Bars The commands \ldots, \cdots, \vdots, and \ddotsare used to produce a string of three dots on the base line, on the math centerline, vertically, or on the diagonal, respectively. The commands \overline, \underline, \overbrace, and \underbrace are used to build horizontal groups.

5. Task 3.9 Write the following in your LaTeX document and observe the output: \begin{eqnarray*} 2^n & = &\overbrace{2\times2\times\cdots\times 2}^{\mbox{n terms}}\\ k\cdot x & = &\underbrace{x + x + \cdots + x}_{\mbox{k terms}} \end{eqnarray*}

6. Building Mathematical Expressions: Radicals, Integrals, and Summations The \sqrtcommand creates a square root sign for its mandatory argument. An optional argument for the radicand allows you to construct cube roots, nth roots, etc. Integral signs are produced with the \intcommand, and summation signs are produced with the \sum command. These symbols are often used with superscripts and subscripts:

7. Task 3.10 Write the following in your LaTeX document: $$ \sqrt{2}=1.4142 \qquad c=\sqrt{a^2+b^2} \qquad \sqrt[3]{8}=2 \qquad\sqrt{\frac{n(n+1)}{2}} $$ $$\sum^{\infty}_{n=1} \qquad \int^b_a e^{x^2}\,dx $$ $$\sqrt{\sum_{i=1}^{n}i} \qquad \sum_{\stackrel{i=1}{j=2}}^{\infty}$$ $$\sum \Delta V=\int\!\!\!\int\!\!\!\int_V dv $$

8. Array Environment: for matrices etc The array environment is not itself a math environment; it must be enclosed within a math environment of your choosing. It is used for building rectangular arrays of numbers, matrices, etc. array is the math equivalent of tabularand uses the same syntax.

9. Task 3.11 Write the output for the following LaTeX command \[ \begin{array}{ccccc} 17& 24& 1& 8& 15\\ 23& 5& 7& 14& 16\\ 4& 6& 13& 20& 22\\ 10& 12& 19& 21& 3\\ 11& 18& 25& 2& 9 \end{array} \]

10. Other variations for building matrices The array environment is not itself a math environment; it must be enclosed within a math environment of your choosing. It is used for building rectangular arrays of numbers, matrices, etc. array is the math equivalent of tabularand uses the same syntax.

11. Task 3.12 $$ \begin{matrix} a & b \\ c & d \end{matrix} \quad \begin{pmatrix} a & b \\ c & d \end{pmatrix} \quad \begin{bmatrix} a & b \\ c & d \end{bmatrix} \quad \begin{vmatrix} a & b \\ c & d \end{vmatrix} \quad \begin{Vmatrix} a & b \\ c & d \end{Vmatrix} $$ Other variations for building matrices: requires amsmath package

12. Case Statements Use \cases to write case statements. The cases environment renders multiple lines with an extensible left curly-brace. It can be used for piecewise-defined functions. For this to work, you must have \usepackage{amsmath} 

13. Task 3.13 Write the output for the following LaTeX command $$ x_\lambda = \begin{cases} x & \text{if $\lambda$ is an eigenvalue;}\\ -x & \text{if $-\lambda$ is an eigenvalue;}\\ 0 & \text{otherwise.} \end{cases} $$

14. Displaystyle in mathmode: better looking formatting • Sometimes we have complicated expressions that does not display well with the dollar sign mode. For example: • produces Evaluate the sum $\sum_{i=0}^n i^3$. • The summation above is not pretty. We can make it more presentable by using \displaystyle

15. Task 3.14 Write the output for the following LaTeX command Evaluate the sum $\sum_{i=0}^n i^3$. Evaluate the sum $\displaystyle\sum\limits_{i=0}^n i^3$.

16. Task 3.15 Write the output for the following LaTeX command Depending on the value of $x$ the equation \( f(x) = \sum_{i=0}^{n} \frac{a_i}{1+x} \) may diverge or converge. $$ f(x) = \sum_{i=0}^{n} \frac{a_i}{1+x} $$ Use \displaystyle to display the inline equations above better