Helpful Math Notes

I created this database to help me with two things:

1. Understand how topics connect to each other.
2. Allow me to quickly find and review information I've lost.

This database is no where near comprehensive and is sometimes just incorrect but it tries to reference course notes or external sources in order to account for this. I recommend you use this database alongside a textbook or another, more in depth, source.

If you find an error, glitch, or incorrect information please note it down. I am planning on creating a way to report these issues and it will be posted here once I figure it out.

You can use the search button above to quickly search for specific files or see below for more broad topics. Note: this index file doesn't have links to every document in this database and some topics must be manually searched for.

• Functions
• 2-Dimentional Space
• 3-Dimentional Space
• Geometry
• Trigonometry
• Logarithm rules
• Complex Numbers

Calculus is defined as the "the mathematical study of continuous change" by Wikipedia. Simply put it is the study of the how different parts of a graph are related to each other. It is split into two major branches, differential and integral calculus.

Differential calculus is the rate of change of a graph, the slope of the line. Integral calculus is the area under the, or sometimes between two, graph(s). One interesting and very useful aspect of these two branches are how they relate to each other. If you find the integral of a graph of a function's derivative you get the original function that, albeit missing some information.

• Calculus - an overview document for calculus as a whole
• Differentiation - Rate of change/slope of line
• Integration - Area under curve
• Single Variable Calculus - when working with graphs of 2 variables
• Multivariable Calculus - when working with graphs of more than 2 variables
• Differential Equations - algebra for calculus, lends itself well to applications
• Vector Calculus - calculus applied to vector fields

See the calculus info-dump for more topics/links.

Linear Algebra is defined as "the branch of mathematics concerning linear equations" by Wikipedia. Simply put it is the study or equations have a linear behavior, in that they are not exponential. It is generally used to find values within these equations and usually follow the form where and are known but is not.

In order to solve these equations scalars, vectors, and matrices are often used. A scalar is a signal number, for example if then is a scalar with value . A vector is an array of numbers, like a list, and is considered 1 dimensional. A matrix is a vector with multiple dimensions, in that it has multiple rows AND columns rather than just one row or one column as a vector would have.

You can visit Wikipedia for more information on what linear algebra is and what it is used for.

• Linear Algebra - an overview document for linear algebra as a whole
• Scalar Definition
• Vector Definition
• Matrix Definition

See the linear algebra info-dump for more topics/links.

To be expanded.

• Statistics

Python is a programming language that can be used in a wide variety of applications, most useful for us is its ability to solve many different problems.

Please note that all examples in this database assume that you are working within the online interpreter or (if you are running your Python program elsewhere) have already ran the commands listed in python -> installation.

• Python - an overview document on Python and its use in this database
• SymPy - a symbolic library used thought out the examples in this database
• SymPy Online Interpreter - an online interpreter so that you can run any examples in your browser

• Summation - How to read the summation sign
• Calculus
  • Differentiation
  • Integration
  • Gradients
• Natural Numbers
• Complex Numbers
• Vectors