To begin with: what is calculus? Well, it’s basically the study of how fast stuff changes over time or space. Sounds simple enough, right? But don’t let that fool you calculus can be as complicated as a Rubik’s cube on juice. So grab your graphing paper and your trusty TI-89 (or whatever fancy calculator you have these days), because we’re about to embark on an epic journey through the world of derivatives, integrals, limits, and all sorts of other mathematical goodness.

Let’s start with the basics: what is a derivative? Well, it’s essentially the rate at which something changes over time or space. For example, if you have a function that represents how many people are in a room as time passes (let’s call this f(t)), then the derivative of that function would tell us how fast the number of people is changing with respect to time.

Now, let me introduce you to your new best friend: the calculator key labeled “d/dx”. This magical button will allow you to calculate derivatives like a boss (or at least pretend like one). But before we get into that, limits. Limits are essentially what happens when something gets really close to another thing without actually touching it. For example, if I have the function f(x) = x^2 and I want to find out what happens as x approaches 0 (let’s call this lim x->0), then we can use calculus to figure that out.

Now, let me introduce you to your new best friend: the calculator key labeled “d/dx”. This magical button will allow you to calculate derivatives like a boss (or at least pretend like one). But before we get into that, limits. Limits are essentially what happens when something gets really close to another thing without actually touching it. For example, if I have the function f(x) = x^2 and I want to find out what happens as x approaches 0 (let’s call this lim x->0), then we can use calculus to figure that out.

But wait how do you calculate a limit? Well, let me introduce you to your new best friend: the L’Hopital’s Rule key on your calculator. This magical button will allow you to solve limits like a boss (or at least pretend like one). But before we get into that, integrals. Integrals are essentially the opposite of derivatives they tell us how much stuff is under a curve or between two points. For example, if I have the function f(x) = x^2 and I want to find out how much area is under the curve from 0 to 1 (let’s call this integral), then we can use calculus to figure that out.

Now, let me introduce you to your new best friend: the anti-derivative key on your calculator. This magical button will allow you to calculate integrals like a boss (or at least pretend like one). But before we get into that, partial derivatives and vector calculus. Partial derivatives are essentially how fast something changes in more than one direction at once. For example, if I have the function f(x,y) = x^2 + y^2 and I want to find out how fast it’s changing with respect to both x and y (let’s call this partial derivative), then we can use calculus to figure that out.

Now, let me introduce you to your new best friend: the multi-variable calculator key on your fancy graphing calculator. This magical button will allow you to calculate partial derivatives like a boss (or at least pretend like one). But before we get into that, vector calculus and how it can help us solve real-world problems in physics and engineering.