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Section 1: You will be introduced to limits and continuity.  

Lecture 1  01:00  
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. 

Lecture 2  05:50  
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. 

Lecture 3  02:48  
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. 

Lecture 4  02:30  
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. 

Lecture 5  03:00  
You Will Be Able To Recognize And Understand OneSided Limits. 

Lecture 6  10:56  
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 NonExistence Of The Limit From That Side, Even Though The NonExistence 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 OneSided Limit That Honors The Domain Of The Function. For These Points, Continuity And OneSided Continuity From The Honoring Side Are The Same. 

Lecture 7  06:33  
You Will Be Able To Recognize, Understand And Compute Horizontal Asymptotes. You Will Have A Visual Understanding Of These Entities. 

Lecture 8  17:47  
You Will Be Able To Recognize And Understand Vertical Asymptotes. You Will Have A Visual Understanding Of These Entities. 

Lecture 9  08:02  
You Will Understand And Remember The Limit Rules. You Will Need These Rules. 

Lecture 10  08:52  
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. 

Lecture 11  05:13  
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. 

Lecture 12  08:23  
You Will Be Able To Find Horizontal Asymptotes Of Rational Functions. You Will Be Able To Do The Necessary Algebra When Solving These Problems. 

Section 2: You should memorize the limit rules  
Lecture 13  09:49  
You Will Recognize And Understand The Rule Concerning The Composition Of Continuous Functions. You Will Recognize The Utility Of Having This Rule Available. 

Lecture 14  19:52  
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. 

Lecture 15  07:53  
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. 

Lecture 16  12:32  
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. 

Section 3: You will get the hang of the Heaviside and step functions  
Lecture 17  12:52  
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. 

Lecture 18  17:09  
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. 

Quiz 1  2 questions  
Heaviside 

Section 4: Example problems for you  
Lecture 19  17:42  
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. 

Lecture 20  15:40  
You Will Be Able To Find Limits Whose Simplifications Involve Variations Of Factoring Via Difference Of Squares Or Difference Of Cubes. 

Lecture 21  14:21  
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. 

Section 5: You will be introduced to the derivative concept.  
Lecture 22  19:58  
You Will Understand The Derivative Concept. You Will Be Able To Find The Derivative Of Simple Functions. 

Lecture 23  19:41  
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. 

Lecture 24  19:38  
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. 

Lecture 25  19:06  
You Will Be Able To Find The Derivatives Of Quadratic Functions From First Principles. 

Lecture 26  03:14  
You Will Be Able To Find The Derivatives Of Some Basic Polynomial Functions From First Principles. 

Lecture 27  09:56  
You Will Be Able To Find The Derivative Of The Basic Absolute Value Function At Any NonZero Domain Point. You Will Understand Why The Derivative Of The Absolute Value Function Does Not Exist At The Origin. 

Lecture 28  19:50  
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. 

Lecture 29  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. 

Lecture 30  19:49  
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. 

Lecture 31  19:31  
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. 

Lecture 32  19:33  
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. 

Lecture 33  19:31  
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. 

Lecture 34  19:52  
You Will Know How To Do The Derivative Of A Rational Function From First Principles. 

Lecture 35  19:55  
You Will Be Able To Differentiate Radical Functions Using First Principles. You Will Know How To Set Up The Derivative Of The Cotangent Function. 

Lecture 36  03:01  
You Will Be Fully Able To Find The Derivative Of The Cotangent Function From First Principles. 

Lecture 37  12:49  
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. 

Lecture 38  19:51  
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. 

Section 6: Derivative shortcut rules  
Lecture 39  19:46  
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. 

Lecture 40  19:00  
You Will Be Able To Do Any Differentiation Problem That Involves The Power Rule. You Will Often Use The Power Rule In Calculus. 

Lecture 41  16:21  
Students often find fractional exponents tricky. Hence, I do examples that incorporate the power rule in the case of fractional exponents. 

Lecture 42  16:00  
It is during this video that I introduce you to Chain Rule for the first time. 

Lecture 43  10:58  
I do more examples of the Chain Rule. I really want you to learn the Chain Rule. 

Lecture 44 
Shortcuts And Exponents

15:52  
Lecture 45 
Shortcuts And Exponents Part 2

11:11  
Lecture 46 
Shortcuts And Exponents Part 3
Preview

11:12  
Lecture 47 
Chain Rule Again
Preview

11:00  
Lecture 48 
Chain Rule And Quotient Rule

10:04  
Lecture 49 
Quotient Rule

05:55  
Lecture 50 
Quotient Rule Part 2

13:45  
Lecture 51 
Quotient Rule Part 3

11:03  
Lecture 52 
Chain Rule And Product Rule
Preview

19:59  
Lecture 53 
Chain Rule Extended
Preview

05:50  
Lecture 54 
Chain Rule Extended Part 2
Preview

19:39  
Lecture 55 
Chain Rule Part 3 Modified

19:12  
Lecture 56 
More Examples Garden Variety

19:15  
Lecture 57 
Example From The Last Video Extended

05:39  
Lecture 58 
Derivatives Of Terms With Radical Exponents

19:58  
Lecture 59 
Derivatives Of Power Functions

10:29  
Lecture 60 
Handling Differentiation At An Exceptional Point

10:03  
Lecture 61 
Logs Logs

19:52  
Lecture 62 
Easy Calculus And Hard Algebra.

17:40  
Lecture 63 
Review Of Chain Rule

09:08  
Quiz 2  8 questions  
Find the derivatives 

Lecture 64 
Higher Order Derivatives

19:59  
Lecture 65 
Higher Order Derivatives Continued

19:54  
Lecture 66 
Existence Of The Second Derivative At A Particular Point

06:25  
Lecture 67 
Implicit Differentiation

19:56  
Lecture 68 
More Implicit Differentiation

08:00  
Lecture 69 
More Implicit Differentiation

19:56  
Lecture 70 
More Implicit Differentiation
Preview

11:06  
Quiz 3  7 questions  
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) 

Lecture 71 
Differentials

17:31  
Lecture 72 
More Differentials

19:56  
Lecture 73 
More Differentials

05:34  
Quiz 4  5 questions  
Tangent Line Approximations 

Lecture 74 
Extrema Part 1

18:37  
Lecture 75 
Extrema Part 2

16:31  
Lecture 76 
Extrema Part 3

11:52  
Lecture 77 
Extrema Part 4

15:07  
Lecture 78 
Increase And Decrease

17:25  
Lecture 79 
Increase And Decrease Alternative Explanation

19:34  
Lecture 80 
Mean Value Theorem

16:15  
Lecture 81 
Concavity Prelude

19:54  
Lecture 82 
Concavity I

19:49  
Lecture 83 
Concavity II

19:03  
Lecture 84 
L'Hospital's Rule

19:58 
Hi! My name is Jason Broadway. I have my M.S. in mathematics from Middle Tennessee State University and I have taught calculus before in the technical college setting. I have also tutored individuals oneonone in calculus. Students have thanked me for opening doors for them that were once shut. When I taught and tutored, I showed patience toward my students. They also appreciated the fact that I did not skip steps whenever I taught a particular concept.