Calculus
Welcome! I'm really excited to help you dive into calculus. It's a beautiful, incredibly useful field of math that lets us capture a world in constant motion.
To make sure we start on the absolute best foot, could you tell me a little bit about your background in math? For example, how comfortable do you feel with algebra and trigonometry?
I need a serious refresher on the basics.
Recognizing that you need a solid foundational review is a huge step in the right direction. It is a well-known secret among math teachers that the most challenging part of calculus is almost never the calculus itself; it is the algebra and trigonometry that you use to simplify your answers. To set ourselves up for success, we are going to start with the absolute bedrock of calculus: functions.
Your path
Limits: The Basis of Calculus
Derivatives: Measuring Change
Integrals: Accumulation and Area
Before we look at the learning path, let us make sure we are on the same page about what a actually is. In simple terms, a function is a rule that takes an input (which we usually call ) and gives us exactly one output (which we usually call or ). Think of it like a vending machine: you input a specific code, and you get exactly one item in return. If you pressed the button for a bag of chips and got both chips and a soda, the machine would be malfunctioning; similarly, a mathematical relation is only a function if each input leads to exactly one predictable output.