# Math 300 - Homework Assignment #3 (back to Math 300 main page)

Suggetsed solutions could be found by these links: power_iteration.tex and integral.tex.

The assignment is due Wednesday, July 19, 11:59pm.

Assignment is worth 80 points.

### Part 1 (40 points).

In this part you are required to create a LaTeX document (named "power_iteration.tex") and compile it to PDF format (complied file named "power_iteration.pdf"). Your document should duplicate this docuemnt.

A few things should be noted:

1. Pay particular attention to periods at the end of sentences, math italics, alignments, and where paragraphs begin and do not begin. You docuemnt should be a precise copy of the given document!
2. The document you see was produceed using article documentclass with a 12pt argument.
3. You should create (and use wherever possible) 3 custom commands/macros to render some expressions which are extensively used throughout the given docuemnt:
\kti
the command should render the following expression: "$k\to \infty$".
\lincombs{basis}
the command should render a linear combination of $n-1$ vectors using letter specified by basis argument to denote basis vectors and letters ${c}_{2},\cdots ,{c}_{n}$ to denote coefficients, i.e. \lincombs{v} should produce "${c}_{2}{v}_{2}+\cdots +{c}_{n}{v}_{n}$"; \lincombs{e} should produce "${c}_{2}{e}_{2}+\cdots +{c}_{n}{e}_{n}$".
\lincombf{basis}
the command should render a linear combination of $n$ vectors using letter specified by basis argument to denote basis vectors and letters ${c}_{1},{c}_{2},\cdots ,{c}_{n}$ to denote coefficients, i.e. \lincombf{v} should produce "${c}_{1}{v}_{1}+{c}_{2}{v}_{2}+\cdots +{c}_{n}{v}_{n}$"; \lincombf{e} should produce "${c}_{1}{e}_{1}+{c}_{2}{e}_{2}+\cdots +{c}_{n}{e}_{n}$".
Note that use may use one of the custom commands you defined in the definition of another custom command.
4. You should use special LaTeX commands/macros to render ellipses (...), not just three periods.
5. You can ignore footnotes.

### Part 2 (40 points).

In this part you are required to create a LaTeX document (named "integral.tex") and compile it to PDF format (complied file named "integral.pdf"). Your document should duplicate this docuemnt.

A few things should be noted:

1. Pay particular attention to periods at the end of sentences, math italics, alignments, and where paragraphs begin and do not begin. You docuemnt should be a precise copy of the given document!
2. The document you see was produceed using book documentclass.
3. Definitions you see in the text were rendered and automatically numbered using theorem environment (see slide 31). To avoid extra italics in your definition you may use \theoremstyle{definition} macro right before \newtheorem{...} declareation. \theoremstyle{...} macro is defined is amsthm package.
4. All numbered expressions in the given document were numbered automatically. You should have the same.
5. When you display references to some expressions or definitions you should not hardcode the numbers, but use lables and references instead (see slides 29, 31).
6. Note that chapter numbering starts from Chapter 6, and pages numbering starts from 120. To achieve this in your doucment you may type \setcounter{chapter}{5} and \setcounter{page}{120} macros where it is appropriate.
7. To prevent LaTeX from inserting blank pages before and after table of contents (which happens by default in documents using book documentclass) you may use the following code:
 \begingroup \let\cleardoublepage\clearpage <macro to create table of contents> \endgroup 
8. To get proper script letter $ℛ$ (the one that denotes Riemann-integrable functions) you may use \mathscr{...} macro defined in mathrsfs package.
9. Note that there is no date in the docuemnt title. One of the easiest way to achive this is to set empty value for docuemnt date, i.e. type this macro in docuemnt preable \date{}.
10. You should use special LaTeX commands/macros to render ellipses (...), not just three periods.
11. You can ignore footnotes.