Master Calculus 1: Complete 2020 Basic-To-Advanced Course

Welcome to the Course! I'm so glad to have the opportunity to show you this great course! Here, we will show you what the plan is for this course.

You probably never looked at a function from this point of view. Here we describe what we will be studying in this course.

This is simply a continuation of the previous lecture. Here we give examples of some interesting functions.

This is a good start as to what we will be studying in the first half of the course.

Some things we can't do. For example, you can't divide by 0, but we can try to do something like "dividing by 0" - let's try dividing by numbers that are basically 0, like 0.001?

Here we describe what a limit is in terms of left hand and right hand limits.

It turns out that there are shortcuts to computing a limit. Here we detail how to be certain about our answers and we cover every example that test makers tend to give.

Remember that an easy definition of continuity is: a function that can be drawn without lifting up your pen.

I'd much rather call this the sandwich theorem.

Here we challenge you to connect two dots. By doing so, you understand everything!

Here we describe the way limits distribute. Remember the distributive property? Limits can distribute better though!

What does it look like to divide by 0 or to go to infinity and beyond?

Buzz Lightyear was here...

Chances are, you weren't taught an incorrect way of how to compute limits to negative infinity. This lecture will make sense of everything though!

Let's abstract the notion of slope! Here we give you a slope formula that actually looks a lot like the slope formula from algebra class, but this time, there is a limit.

Here, we make sense of how to compute derivatives of functions using what we learned from the last lecture.

What does a derivative look like and what does it mean? How do people write it out? How do we write these things down?

Now that you learned the super complicated way, let's teach you the shortcuts. Yes, I just did that to you. Don't you wish it was the other way around?

More shortcuts!

This rule is tough, but we can make it easy! In this lecture, we learn a method that is rarely taught that can make the chain rule fast and easy.

Now it's time to see the tough derivatives that you will likely encounter. Remember that there are only three main rules - it's just a matter of knowing which one to use and when. In this lecture, I explain how you know which rules to use and when.

In this lecture we learn about nth derivatives and we investigate trig derivatives. You don't need to know trig to know this lecture!

You learned how to differentiate functions of x. Now let's mix x's with y's and see what can happen.

Now we revisit algebra, but we make it really messy.

We've talked briefly about tangent lines. Now, we can find them.

Estimation just got 10x better

Error is very common in most sciences and engineering. In this lecture, we see how to calculate error.

What is a maximum or a minimum? We investigate this for the next few lectures.

How can we find maximums and minimums without using a calculator?

This is the engineering section of the course. Here, we learn how to solve engineering problems.

This also involves engineering but with a different perspective. Sometimes you need to be efficient - here's how you do that.

What comes up, must come down. That's basically what Rolle's Theorem says.

The Mean Value Theorem is just a tilted Rolle's Theorem.

Let's graph functions without plotting points or looking at a graphing calculator.

Let's learn the fastest method to computing limits. There is no need for algebra anymore!

Let's abstract the notion of area!

It turns out that these things that we are computing give us area!

How can we use rectangles to compute areas of any shape or figure?

Congrats!