2017-09-11 03:17:56

Math Made Simple: Calculus 1 For Beginners

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An 8-hour In-Person Lecture to Everything About Calculus 1. Master This University Level Course or Your Money Back!

497 students enrolled

What Will I Learn?

- Understand and compute limits
- Know how to take derivatives of any function
- Apply derivatives to real world problems
- Understand optimization and extreme values
- Know how to take antiderivatives
- Understand the Fundamental Theorem of Calculus

Requirements

- Make sure you are well-prepared
- Download the book online for FREE (details in the first lecture)
- Take some of the pretests in the beginning of the book to check your understanding of Algebra

Description

You'll really appreciate the flexibility of an online course as you study the principles of calculus: derivatives, integrals, limits, approximation, applications and modeling. With no preset test dates or deadlines, you can take as much time as you need to take this course.

In this course, you get over **8 hours of in-person lectures** and over **10 hours of material **specifically designed to cover all of the material in Calculus 1. No longer will you have to try to understand the material from the book - now you have all the in-person lectures you need. The most important part though is that this course makes Calculus fun and easy!

**Become a Master of Calculus Today!**

**In this course, you get everything that any professor can throw at you in Calculus - all in one course. With this course:**

- You will be prepared for any test question from any University test
- You can easily get college credit for this course
- You can be prepared to face difficult applied problems and handle them with ease
- You can tell your friends that you were taking antiderivatives for fun (sounds fancy right?)
- Most importantly, you can be a Master of Calculus

**There Really is No End to the Rewards of Taking This Course!**

So what are you waiting for? Start the class today and be the master of what seems like an intimidating course. By the way, did I mention that the book is free?

Who is the target audience?

- Anyone who has taken algebra can take this course!
- This is intended as a University level course - but made simple

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Curriculum For This Course

66 Lectures

10:43:05
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Introduction Video
1 Lecture
01:15

Preview
01:15

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Introduction
6 Lectures
43:27

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.

Preview
06:19

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

Functions Part 1

09:16

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

Functions Part 2

13:40

Functions Reading and Exercises

14 pages

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

Average Velocity

14:12

Average Velocity Reading and Exercises

6 pages

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Limits
17 Lectures
01:42:30

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?

Numerical Limits Part 1

16:36

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

Numerical Limits Part 2

05:05

Numerical Limits Reading and Exercises

11 pages

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.

Solving Limits Algebraically

11:52

Solving Limits Algebraically Reading and Exercises

7 pages

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

Continuity

13:15

Continuity Reading and Exercises

11 pages

I'd much rather call this the sandwich theorem.

Preview
06:47

Squeeze Theorem Reading and Exercises

2 pages

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

Preview
07:36

Intermediate Value Theorem Reading and Exercises

4 pages

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

Algebra of Limits

12:17

Algebra of Limits Reading and Exercises

3 pages

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

Introduction to Asymptotes

10:30

Buzz Lightyear was here...

Limits to Infinity Part 1

08:38

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!

Limits to Infinity Part 2

09:54

Limits to Infinity Reading and Exercises

13 pages

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Derivatives
17 Lectures
01:55:37

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.

Limit Definition of a Derivative

15:47

Limit Definition of a Derivative Reading and Exercises

11 pages

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

Examples of a Limit Definition of a Derivative

09:21

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

What Does The Derivative Look Like?

11:44

What Does a Derivative Look Like Reading and Exercises

16 pages

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?

Derivative Shortcuts

16:03

Derivative Shortcuts Reading and Exercises

11 pages

More shortcuts!

Product and Quotient Rules

10:15

Product and Quotient Rules Reading and Exercises

6 pages

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.

Chain Rule

12:37

Chain Rule Reading and Exercises

10 pages

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.

Examples of Difficult Derivatives

05:21

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

Derivative Shortcuts for Trig Functions

15:37

Trig Derivatives Reading and Exercises

8 pages

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

Implicit Differentiation Part 1

08:09

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

Implicit Differentiation Part 2

10:43

Implicit Differentiation Reading and Exercises

8 pages

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Applications of Derivatives
19 Lectures
01:48:46

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

Tangent Lines

08:17

Estimation just got 10x better

Linear Approximation

09:08

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

Differentials

08:06

Linear Approximation and Differentials Reading and Exercises

7 pages

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

Introduction to Local Extrema

11:47

Introduction to Local Extrema Reading and Exercises

10 pages

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

Local Extrema Examples

08:50

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

Related Rates and Examples

16:17

Related Rates Reading and Exercises

6 pages

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

Optimization and Examples

10:26

Optimization Reading and Exercises

12 pages

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

Rolle's Theorem

05:30

Rolle's Theorem Reading

2 pages

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

Preview
08:32

Mean Value Theorem Reading and Exercises

5 pages

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

Graphing Equations Using Derivatives

13:19

Graphing Equations Reading and Exercises

8 pages

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

L'Hospital's Rule

08:34

L'Hospital's Rule Reading and Exercises

9 pages

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Antiderivatives
5 Lectures
32:09

Let's abstract the notion of area!

Introduction to Antiderivatives

09:37

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

Fundamental Theorem of Calculus

10:39

Fundamental Theorem of Calculus Reading and Exercises

12 pages

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

Riemann Sums

11:53

Riemann Sums Reading and Exercises

25 pages

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Conclusion!
1 Lecture
02:21

Congrats!

Conclusion

02:21

About the Instructor