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2017-01-26 14:21:55

Learn Calculus: With Fundamental Explanations And Quizzes

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Be Ready for Your College Calculus Course

3,386 students enrolled

- 20 hours on-demand video
- 9 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

Understand The Vocabulary of Calculus

Derivatives, including all of the derivative rules, Shortcut Rules

Everything about Euler functions and Sinc functions, I.V.T. and Squeeze, Zero Limit Rule

Limits & Continuity and how to find discontinuities in a function

Requirements

- A Basic Calculator
- Basic Algebra and Trigonometry Knowledge
- A decent foundation Algebra/Trigonometry (it doesn't have to be perfect! :D)
- Arithmetically Strong though (times tables, adding, etc.)

Description

**Student Recommendation: **

" Started the course today. I like it. So far it's been review of calculus and it's been a good, simple review. Jason explains things well. I like the video lectures. I think I can finish this course way faster than studying a textbook on my own because of the video lectures seem to make learning faster. Thanks " ---- *Virat Karam*

**Learn Calculus: With Fundamental Explanations And Quizzes **was made and designed with unlimited resources about calculus and all-time guideline available for respected students .This 85 lectures, Quizzes and 20 hour course explain most of the valuable things in calculus, and it includes shortcut rules, text explanations and examples to help you test your understanding along the way. Become a Calculus Master with this course and be ready for your college calculus course.

Calculus Mathematics seems to be a dark art … full of confusion, misconceptions, misleading information, and students afraid of it. But at heart, Calculus is pretty simple, and this course explains it all..

At the end of this course you'll have a firm understanding of how Calculus works, **Derivative Rules & Examples with shortcut tricks**,** Limits and Continuity **and a complete series of calculus with quizzes.

In this course you will get to know about :

- Limits and Continuity.
- Difference Quotient
- Empty holes and oscillatory graphs
- Horizontal & Vertical Asymptote with Examples
- Composition of Continuous Functions
- Euler functions and Sinc functions
- I.V.T. and Squeeze
- Zero Limit Rule
- Derivative Rules & Examples
- Cube Root Derivative

And Much More in One Place!

Who is the target audience?

- Students who need help in calculus! Students who want a caring tutor.
- Parents looking for extra support with calculus
- Anyone in love with Calculus

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Curriculum For This Course

Expand All 85 Lectures
Collapse All 85 Lectures
19:55:21

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You will be introduced to limits and continuity.
12 Lectures
01:20:54

I Welcome You To The Class. I Promise You That I Will Provide Thorough Coverage Of The Material. You Will Feel At Ease After Watching This Video.

You are warmly introduced to my class!

01:00

I am going to put this quiz in the Lecture 1 documents so you can download it! This quiz is intended to cover the entire Calculus I curriculum. It should prepare you for even the toughest Calculus 1 class! I am going to make a Calculus 2 quiz (and content) for this class soon!

Comprehensive Quiz: Pass This Quiz And You Should Be Ready for Calculus 2!

1 question

You Will Learn The Meaning Of Some Important Symbols That Will Often Be Used In This Course. These Symbols Should Also Come In Handy In Your College Calculus Class.

You are introduced to sets and set concepts.

05:50

You Will Know What It Means To Find The Limit Of A Function. You Will Be Able To Discern Between Continuity At A Point Versus The Mere Existence Of A Limit At That Point. You Will Learn What Assumptions Are Safe To Make In This Course.

Ordinary limits and continuity.

02:48

You Will Be Able To Distinguish Between Two Different Types Of Discontinuity. An Empty Hole Situation Is Different From The Case Where Wild Oscillations Occur.

Empty holes and oscillatory graphs.

02:30

You Will Be Able To Recognize And Understand One-Sided Limits.

One-sided limits...and one-sided continuity

03:00

You Will Be Able To Recognize When A Function Is Continuous From One Side At A Point x=c But Not From The Other Side. You Will Recognize The Fact That The Failure Of Continuity From One Side Of x=c Does Not Necessarily Mean The Non-Existence Of The Limit From That Side, Even Though The Non-Existence Of A Limit From One Side Of An Interior Point Will Imply That The Function Is Not Continuous From That Side. For Endpoints, We Consider The Overall Limit To Be The One-Sided Limit That Honors The Domain Of The Function. For These Points, Continuity And One-Sided Continuity From The Honoring Side Are The Same.

One-sided example

10:56

You Will Be Able To Recognize, Understand And Compute Horizontal Asymptotes. You Will Have A Visual Understanding Of These Entities.

Horizontal Asymptote

06:33

You Will Be Able To Recognize And Understand Vertical Asymptotes. You Will Have A Visual Understanding Of These Entities.

Vertical Asymptote

17:47

You Will Understand And Remember The Limit Rules. You Will Need These Rules.

Important Limit Rules...Memorize!

08:02

You Will Be Able To Apply The Limit Rules To A Wide Variety Of Problems. The Students Will Recognize The Various Types Of Functions That Are Continuous At Any Point In Their Domain.

Limit Rule Examples

08:52

You Will Be Able To Identify Finite Valued Limits At Infinity As Horizontal Asymptotes Of The Given Function. You Will Be Able To Find These Horizontal Asymptotes By Doing Algebra And Then Plugging The Limit Value Into The 'Purified' Difference Quotient.

Horizontal Asymptote Model Example

05:13

You Will Be Able To Find Horizontal Asymptotes Of Rational Functions. You Will Be Able To Do The Necessary Algebra When Solving These Problems.

Horizontal Asymptote Example

08:23

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You should memorize the limit rules
4 Lectures
50:06

You Will Recognize And Understand The Rule Concerning The Composition Of Continuous Functions. You Will Recognize The Utility Of Having This Rule Available.

Composition of Continuous Functions

09:49

You Will Be Able To Recognize Apply The Substitution Rule When It Is Needed. The Student Will Be Able To Deal With Infinite Limits That Are Not Vertical Asymptotes. The Student Will Understand What The Infinity Symbol Means.

Substitution

19:52

You Will Be Able To Define Euler's Constant. You Will Be Able To Compute Exponential Variations In This Limit Definition Of Euler's Constant. You Will Be Able To Compute Variations Of The Sinc Function.

Euler functions and Sinc functions

07:53

You Will Be Able To Recognize And Apply The Intermediate Value Theorem When It Is Needed. The Student Will Be Able To Recognize And Apply The Squeeze Theorem When It Is Needed.

I.V.T. and Squeeze

12:32

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You will get the hang of the Heaviside and step functions
2 Lectures
30:01

If The Limit Of A Function f(x) At A Point x=c Tends to Zero And If g Is Bounded On An Interval about x=c, Then The Limit Of The Product f(x)g(x) at x=c Will Equal Zero. You Will Be Able To Recognize And Apply This Rule When It Is Necessary.

Zero Limit Rule

12:52

You Will Be Able To Apply Limits To The Heaviside And Step Functions. You Will Recognize The Points Where Discontinuities Occur. You Will Recognize Points Of Discontinuity Where Continuity From One Side Is Present/Absent.

Heaviside and step functions

17:09

Heaviside

What can be said of the Heaviside function?

2 questions

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Example problems for you
3 Lectures
47:43

You Will Be Able To Find Limits That Involve The Conjugation Of Radicals. You Will Be Able To Do Limits That Involve Variable Substitutions. You Will Be Able To Solve Infinite Limits.

Limit examples

17:42

You Will Be Able To Find Limits Whose Simplifications Involve Variations Of Factoring Via Difference Of Squares Or Difference Of Cubes.

Horizontal asymptote examples

15:40

You Will Be Able To Find The Limits At Infinity Of Differences Of Radicals. You Will Be Able To Carry Out The Necessary Algebra In Order To Find This Limit.

Tricky limit examples with radicals

14:21

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You will be introduced to the derivative concept.
17 Lectures
04:45:05

You Will Understand The Derivative Concept. You Will Be Able To Find The Derivative Of Simple Functions.

Derivative definition

19:58

You Will Be Able To See The Relationship Between The Difference Quotient And The Derivative. You Will See How The Tangent Line Slope Is The Derivative Of The Function At The Corresponding Point While The Secant Line Slope Is Equal To The Difference Quotient Of The Function Relative To The Corresponding Point And The 'Other' Chosen Point.

Tangent lines

19:41

You Will Be Able To Find The Tangent Line To The Graph Of A Function At An Applicable Point. You Will Recognize The Derivative Of The Function At This Point As The Slope Of The Aforementioned Tangent Line.

Tangent line example

19:38

You Will Be Able To Find The Derivatives Of Quadratic Functions From First Principles.

Derivative example

19:06

You Will Be Able To Find The Derivatives Of Some Basic Polynomial Functions From First Principles.

Derivatives of polynomials

03:14

You Will Be Able To Find The Derivative Of The Basic Absolute Value Function At Any Non-Zero Domain Point. You Will Understand Why The Derivative Of The Absolute Value Function Does Not Exist At The Origin.

Non-differentiable at a point

09:56

You Will Be Able To Find The Derivative Of The Square Root Function Along With Variations Of This Function. You Will Know How To Find The Derivative Of The Most Basic Negative Power Functions.

Derivatives of radicals/roots

19:50

You Will Be Able To Find The Derivatives Of The Basic Positive And Negative Power Functions Along With The Cosine Function. You Will Know How To Set Up The Process Of Finding The Derivative Of The Tangent Function.

Derivatives of negative power functions

19:50

You Will Be Able To Find The Derivative Of The Tangent Function and Cube Root Function From First Principles. You Will Be Able To Find The Derivative Of Any Nth Root Function From First Principles.

Cube root derivative using limits

19:49

You Will Know How To Find The Derivative Of The Secant Functions From First Principles. Assuming A Linear Numerator And A Linear Denominator, You Will Be Able To Find The Derivative Of Rational Functions From First Principles.

Secant derivative using limits

19:31

You Will Know How To Extend The Definition Of Euler's Constant In Order To Evaluate Different Powers Of e. You Will Know How To Find Infinite Limits Of Applicable Polynomials.

Euler limits again

19:33

You Will Be Able To Find Some Of The Vertical Asymptotes Of The Tangent Function And All Of The Horizontal Asymptotes Of The Inverse Tangent Function. You Will Be Able To Evaluate Limits That Are Variations Of Familiar Limits Via Substitution. You Will Be Able To Find The Horizontal Asymptote Of A Rational Function.

Asymptotes again

19:31

You Will Know How To Do The Derivative Of A Rational Function From First Principles.

Back to derivatives

19:52

You Will Be Able To Differentiate Radical Functions Using First Principles. You Will Know How To Set Up The Derivative Of The Cotangent Function.

More derivatives

19:55

You Will Be Fully Able To Find The Derivative Of The Cotangent Function From First Principles.

Differentiating the cot function

03:01

Sometimes A Function Will Be Continuous At A Point But Will Fail To Be Differentiable There. This Can Be True Even If The Graph Of A Function Is 'Smooth' At A Point. Indeed, We Can Get A Vertical Tangent At Such A Point. Sharp Points Are Also Examined. You Will Be Able To Distinguish Between The Different Types Of Points At Which A Function Is Not Differentiable But Still Continuous.

Continuous but not differentiable

12:49

You Will Know How To Find The Tangent Lines At Applicable Points For The Graph Of A Given Function. You Will Have A Greater Visual Appreciation Of The Derivative.

Tangent line review

19:51

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Derivative shortcut rules
47 Lectures
11:41:32

You Will Be Able To Apply The Shortcut Differentiation Rules To Concrete Problems. These Rules Are Very Important And Convenient. You Will Appreciate The Utility Of Not Having To Find Limits Each Time You Want The Derivative Of A Function.

Shortcut Rules!

19:46

You Will Be Able To Do Any Differentiation Problem That Involves The Power Rule. You Will Often Use The Power Rule In Calculus.

Shortcut examples!

19:00

Students often find fractional exponents tricky. Hence, I do examples that incorporate the power rule in the case of fractional exponents.

Power Rule With Rational Exponents

16:21

It is during this video that I introduce you to Chain Rule for the first time.

Chain Rule

16:00

I do more examples of the Chain Rule. I really want you to learn the Chain Rule.

Chain Rule 2

10:58

Shortcuts And Exponents

15:52

Shortcuts And Exponents Part 2

11:11

Shortcuts And Exponents Part 3

11:12

Chain Rule Again

11:00

Chain Rule And Quotient Rule

10:04

Quotient Rule

05:55

Quotient Rule Part 2

13:45

Quotient Rule Part 3

11:03

Chain Rule And Product Rule

19:59

Chain Rule Extended

05:50

Chain Rule Extended Part 2

19:39

Chain Rule Part 3 Modified

19:12

More Examples Garden Variety

19:15

Example From The Last Video Extended

05:39

Derivatives Of Terms With Radical Exponents

19:58

Derivatives Of Power Functions

10:29

Handling Differentiation At An Exceptional Point

10:03

Logs Logs

19:52

Easy Calculus And Hard Algebra.

17:40

Review Of Chain Rule

09:08

Find the derivatives

For each f(x), find d/dx[f(x)]

8 questions

Higher Order Derivatives

19:59

Higher Order Derivatives Continued

19:54

Existence Of The Second Derivative At A Particular Point

06:25

Implicit Differentiation

19:56

More Implicit Differentiation

08:00

More Implicit Differentiation

19:56

More Implicit Differentiation

11:06

Find dy/dx given

1. 3x^2 +6y^3 =7

2. sin(y)+cos(x)=(x^6) * (y^8)

3. (x^3*y^2) + (x^5*y)=sin(xy)

4. cos(x^2 * y^2)=1/10

5. x^2 - 5xy +y^2 = 1

6. y=arctan(xy)

7. y^3 = arcsin(x^2 * y^2)

8. y^3 = arcsin(x^2 + y^2)

9. x^(4/3)=e^(xy)

10 x^(4/3)=e^(x+y)

Implicit Differentiation Quiz

7 questions

Differentials

17:31

More Differentials

19:56

More Differentials

05:34

Tangent Line Approximations

Differentials Quiz

5 questions

Extrema Part 1

18:37

Extrema Part 2

16:31

Extrema Part 3

11:52

Extrema Part 4

15:07

Increase And Decrease

17:25

Increase And Decrease Alternative Explanation

19:34

Mean Value Theorem

16:15

Concavity Prelude

19:54

Concavity I

19:49

Concavity II

19:03

L'Hospital's Rule

19:58

Newton's Method

10:19

About the Instructor

Dedicated Math Instructor Who Wants You To Learn Calculus!

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