UNISA MAT1503 Quick Reference

This repo contains the LaTex files needed to compile a set of notes for the course Linear Algebra I at the University of South Africa.

Accessing the Notes

A PDF can be generated using latexmk, or any other LaTeX compiler. If you want to access pregenerated PDFs, please check the Releases section on the sidebar.

Note

This is a work in progress, with chapters and examples to come.
If you are able, and interested in contributing, please do!
If there is something missing, or something that you feel needs further clarification, please open an issue.

Contributing

Please fork this repo, make your changes, and then open a pull request.

The Code

The Structure

• The file notes.tex contains the general structure and order of the files. Building this file should build all the other .tex files, and include them in one .pdf called notes.pdf
• Each unit has a separate tex file where the notes are written. These are contained in the units folder.
• The styles, commands and packages used are in the package file nostestyles.sty

Packages Used

TeX packages that have been used are:

• amsmath, amssymb: Used for mathematical symbols and environments
• babel: Use description environment, and chapter renaming
• bookmark: Set pdf bookmarks accurately
• changepage: Allow paragraphs to be indented
• enumitem: Used to improve the way lists are displayed
• fancyhdr: Improve header and footer display
• fontenc, charter, inconsolata, cabin, newtxmath, bm: Font display
• geometry: Used for document margins
• hyperref: Add PDF bookmarks
• hyphsubst: Prevent hyphenation on line ends
• parskip: Set proper default values for paragraph separation
• subfiles: Allow tex files to be written separately, but built together
• tabularray: Better table display and management.
  • Also uses libraries to simulate booktabs and varwidth
• tcolorbox, adjustbox: Create colored boxes for different environments
• tikz: Used for images.
  • pgfplots: Used to display axis.
• xcolor: Used to get more colors
• xstring: Analyze strings given as arguments to an environment

Commands Added

For intellisense, a list of the commands is added in the package_intellisense folder. These have been written in formats that can be understood by different LaTeX tools.

Commands

• addfile [input] {<filename>}: Include or input the file into the document. By default, it includes the file, the option input can be given to input it instead.
• concept {text}: Mark specific text as a concept to be learned. Puts the text in bold.
• nl: Force a line break within a cell in a table.
• question {text}: Mark specific text as a question. Puts the text in bold, and adds extra spacing.
• rulebookend: Insert a decorative horizontal line at the end of the text.
• rulechapterend: Insert a decorative horizontal line at the end of each unit.

Environments

• definition {title}: Colored box used for highlighting important concepts.
• example: Colored box used to highlight examples.
• exercise {title}: Colored box used to highlight exercises.
• indentparagraph: Indent selected text to the left.
• sidenote: Colored box used to indicate extra information.
• theorem: Colored box used to write mathematical theorems.

Mathematical Operators

• \adj: Used to indicate the adjoint
• \proj: Used to indicate the orthogonal projection of a vector
• \Area : Used to indicate area
• \Real: Display text form of Re, instead of symbol from \Re
• \Imaginary: Display text form of Im, instead of symbol from \Im

---