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Professor Switkes

Limit Definition of the Derivative

Slide Duration:Table of Contents

I. Overview of Functions

Review of Functions

26m 29s

- Intro0:00
- What is a Function0:10
- Domain and Range0:21
- Vertical Line Test0:31
- Example: Vertical Line Test0:47
- Function Examples1:57
- Example: Squared2:10
- Example: Natural Log2:41
- Example: Exponential3:21
- Example: Not Function3:54
- Odd and Even Functions4:39
- Example: Even Function5:10
- Example: Odd Function5:53
- Odd and Even Examples6:48
- Odd Function6:55
- Even Function8:43
- Increasing and Decreasing Functions10:15
- Example: Increasing10:42
- Example: Decreasing10:55
- Increasing and Decreasing Examples11:41
- Example: Increasing11:48
- Example: Decreasing12:33
- Types of Functions13:32
- Polynomials13:45
- Powers14:06
- Trigonometric14:34
- Rational14:50
- Exponential15:13
- Logarithmic15:29
- Lecture Example 115:55
- Lecture Example 217:51
- Additional Example 3-1
- Additional Example 4-2

Compositions of Functions

12m 29s

- Intro0:00
- Compositions0:09
- Alternative Notation0:32
- Three Functions0:47
- Lecture Example 11:19
- Lecture Example 23:25
- Lecture Example 36:45
- Additional Example 4-1
- Additional Example 5-2

II. Limits

Average and Instantaneous Rates of Change

20m 59s

- Intro0:00
- Rates of Change0:11
- Average Rate of Change0:21
- Instantaneous Rate of Change0:33
- Slope of the Secant Line0:46
- Slope of the Tangent Line1:00
- Lecture Example 11:14
- Lecture Example 26:36
- Lecture Example 311:30
- Additional Example 4-1
- Additional Example 5-2

Limit Investigations

22m 37s

- Intro0:00
- What is a Limit?0:10
- Lecture Example 10:56
- Lecture Example 25:28
- Lecture Example 39:27
- Additional Example 4-1
- Additional Example 5-2

Algebraic Evaluation of Limits

28m 19s

- Intro0:00
- Evaluating Limits0:09
- Lecture Example 11:06
- Lecture Example 25:16
- Lecture Example 38:15
- Lecture Example 412:58
- Additional Example 5-1
- Additional Example 6-2

Formal Definition of a Limit

23m 39s

- Intro0:00
- Formal Definition0:13
- Template0:55
- Epsilon and Delta1:24
- Lecture Example 11:40
- Lecture Example 29:20
- Additional Example 3-1
- Additional Example 4-2

Continuity and the Intermediate Value Theorem

19m 9s

- Intro0:00
- Continuity0:13
- Continuous0:16
- Discontinuous0:37
- Intermediate Value Theorem0:52
- Example1:22
- Lecture Example 12:58
- Lecture Example 29:02
- Additional Example 3-1
- Additional Example 4-2

III. Derivatives, part 1

Limit Definition of the Derivative

22m 52s

- Intro0:00
- Limit Definition of the Derivative0:11
- Three Versions0:13
- Lecture Example 11:02
- Lecture Example 24:33
- Lecture Example 36:49
- Lecture Example 410:11
- Additional Example 5-1
- Additional Example 6-2

The Power Rule

26m 1s

- Intro0:00
- Power Rule of Differentiation0:14
- Power Rule with Constant0:41
- Sum/Difference1:15
- Lecture Example 11:59
- Lecture Example 26:48
- Lecture Example 311:22
- Additional Example 4-1
- Additional Example 5-2

The Product Rule

14m 54s

- Statement of the Product Rule0:08
- Lecture Example 10:41
- Lecture Example 22:27
- Lecture Example 35:03
- Additional Example 4-1
- Additional Example 5-2

The Quotient Rule

19m 17s

- Intro0:00
- Statement of the Quotient Rule0:07
- Carrying out the Differentiation0:23
- Quotient Rule in Words1:00
- Lecture Example 11:19
- Lecture Example 24:23
- Lecture Example 38:00
- Additional Example 4-1
- Additional Example 5-2

Applications of Rates of Change

17m 43s

- Intro0:00
- Rates of Change0:11
- Lecture Example 10:44
- Lecture Example 25:16
- Lecture Example 37:38
- Additional Example 4-1
- Additional Example 5-2

Trigonometric Derivatives

26m 58s

- Intro0:00
- Six Basic Trigonometric Functions0:11
- Patterns0:47
- Lecture Example 11:18
- Lecture Example 27:38
- Lecture Example 312:15
- Lecture Example 414:25
- Additional Example 5-1
- Additional Example 6-2

The Chain Rule

23m 47s

- Intro0:00
- Statement of the Chain Rule0:09
- Chain Rule for Three Functions0:27
- Lecture Example 11:00
- Lecture Example 24:34
- Lecture Example 37:23
- Additional Example 4-1
- Additional Example 5-2

Inverse Trigonometric Functions

27m 5s

- Intro0:00
- Six Basic Inverse Trigonometric Functions0:10
- Lecture Example 11:11
- Lecture Example 28:53
- Lecture Example 312:37
- Additional Example 4-1
- Additional Example 5-2

Equation of a Tangent Line

15m 52s

- Intro0:00
- Point Slope Form0:10
- Lecture Example 10:47
- Lecture Example 23:15
- Lecture Example 36:10
- Additional Example 4-1
- Additional Example 5-2

IV. Derivatives, part 2

Implicit Differentiation

30m 5s

- Intro0:00
- Purpose0:09
- Implicit Function0:20
- Lecture Example 10:32
- Lecture Example 27:14
- Lecture Example 311:22
- Lecture Example 416:43
- Additional Example 5-1
- Additional Example 6-2

Higher Derivatives

13m 16s

- Intro0:00
- Notation0:08
- First Type0:19
- Second Type0:54
- Lecture Example 11:41
- Lecture Example 23:15
- Lecture Example 34:57
- Additional Example 4-1
- Additional Example 5-2

Logarithmic and Exponential Function Derivatives

17m 42s

- Intro0:00
- Essential Equations0:12
- Lecture Example 11:34
- Lecture Example 22:48
- Lecture Example 35:54
- Additional Example 4-1
- Additional Example 5-2

Hyperbolic Trigonometric Function Derivatives

14m 30s

- Intro0:00
- Essential Equations0:15
- Six Basic Hyperbolic Trigc Functions0:32
- Six Basic Inverse Hyperbolic Trig Functions1:21
- Lecture Example 11:48
- Lecture Example 23:45
- Lecture Example 37:09
- Additional Example 4-1
- Additional Example 5-2

Related Rates

29m 5s

- Intro0:00
- What Are Related Rates?0:08
- Lecture Example 10:35
- Lecture Example 25:25
- Lecture Example 311:54
- Additional Example 4-1
- Additional Example 5-2

Linear Approximation

23m 52s

- Intro0:00
- Essential Equations0:09
- Linear Approximation (Tangent Line)0:18
- Example: Graph1:18
- Differential (df)2:06
- Delta F5:10
- Lecture Example 16:38
- Lecture Example 211:53
- Lecture Example 315:54
- Additional Example 4-1
- Additional Example 5-2

V. Application of Derivatives

Absolute Minima and Maxima

18m 57s

- Intro0:00
- Minimums and Maximums0:09
- Absolute Minima and Maxima (Extrema)0:53
- Critical Points1:25
- Lecture Example 12:58
- Lecture Example 26:57
- Lecture Example 310:02
- Additional Example 4-1
- Additional Example 5-2

Mean Value Theorem and Rolle's Theorem

20m

- Intro0:00
- Theorems0:09
- Mean Value Theorem0:13
- Graphical Explanation0:36
- Rolle's Theorem2:06
- Graphical Explanation2:28
- Lecture Example 13:36
- Lecture Example 26:33
- Lecture Example 39:32
- Additional Example 4-1
- Additional Example 5-2

First Derivative Test, Second Derivative Test

27m 11s

- Intro0:00
- Local Minimum and Local Maximum0:14
- Example1:01
- First and Second Derivative Test1:26
- First Derivative Test1:36
- Example2:00
- Second Derivative Test (Concavity)2:58
- Example: Concave Down3:15
- Example: Concave Up3:54
- Inconclusive4:19
- Lecture Example 15:23
- Lecture Example 212:03
- Lecture Example 315:54
- Additional Example 4-1
- Additional Example 5-2

L'Hopital's Rule

23m 9s

- Intro0:00
- Using L'Hopital's Rule0:09
- Informal Definition0:34
- Lecture Example 11:27
- Lecture Example 24:00
- Lecture Example 35:40
- Lecture Example 49:38
- Additional Example 5-1
- Additional Example 6-2

Curve Sketching

40m 16s

- Intro0:00
- Collecting Information0:15
- Domain and Range0:17
- Intercepts0:21
- Symmetry Properties (Even/Odd/Periodic)0:33
- Asymptotes (Vertical/Horizontal/Slant)0:45
- Critical Points1:15
- Increasing/Decreasing Intervals1:24
- Inflection Points1:38
- Concave Up/Down1:52
- Maxima/Minima2:03
- Lecture Example 12:58
- Lecture Example 210:52
- Lecture Example 317:55
- Additional Example 4-1
- Additional Example 5-2

Applied Optimization

25m 37s

- Intro0:00
- Real World Problems0:08
- Sketch0:11
- Interval0:20
- Rewrite in One Variable0:26
- Maximum or Minimum0:34
- Critical Points0:42
- Optimal Result0:52
- Lecture Example 11:05
- Lecture Example 26:12
- Lecture Example 313:31
- Additional Example 4-1
- Additional Example 5-2

Newton's Method

25m 13s

- Intro0:00
- Approximating Using Newton's Method0:10
- Good Guesses for Convergence0:32
- Lecture Example 10:49
- Lecture Example 24:21
- Lecture Example 37:59
- Additional Example 4-1
- Additional Example 5-2

VI. Integrals

Approximating Areas and Distances

36m 50s

- Intro0:00
- Three Approximations0:12
- Right Endpoint, Left Endpoint, Midpoint0:22
- Formulas1:05
- Velocity and Distance1:35
- Lecture Example 12:28
- Lecture Example 212:10
- Lecture Example 319:43
- Additional Example 4-1
- Additional Example 5-2

Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus

22m 2s

- Intro0:00
- Important Equations0:22
- Riemann Sum0:28
- Integral1:58
- Integrand2:35
- Limits of Integration (Upper Limit, Lower Limit)2:43
- Other Equations3:05
- Fundamental Theorem of Calculus4:00
- Lecture Example 15:04
- Lecture Example 210:43
- Lecture Example 313:52
- Additional Example 4-1
- Additional Example 5-2

Substitution Method for Integration

23m 19s

- Intro0:00
- U-Substitution0:13
- Important Equations0:30
- Purpose0:36
- Lecture Example 11:30
- Lecture Example 26:17
- Lecture Example 39:00
- Lecture Example 411:24
- Additional Example 5-1
- Additional Example 6-2

VII. Application of Integrals, part 1

Area Between Curves

19m 59s

- Intro0:00
- Area Between Two Curves0:12
- Graphic Description0:34
- Lecture Example 11:44
- Lecture Example 25:39
- Lecture Example 38:45
- Additional Example 4-1
- Additional Example 5-2

Volume by Method of Disks and Washers

24m 22s

- Intro0:00
- Important Equations0:16
- Equation 1: Rotation about x-axis (disks)0:27
- Equation 2: Two curves about x-axis (washers)3:38
- Equation 3: Rotation about y-axis5:31
- Lecture Example 16:05
- Lecture Example 28:28
- Lecture Example 311:55
- Additional Example 4-1
- Additional Example 5-2

Volume by Method of Cylindrical Shells

30m 29s

- Intro0:00
- Important Equations0:50
- Equation 1: Rotation about y-axis1:04
- Equation 2: Rotation about y-axis (2 curves)7:34
- Equation 3: Rotation about x-axis8:15
- Lecture Example 18:57
- Lecture Example 214:26
- Lecture Example 318:15
- Additional Example 4-1
- Additional Example 5-2

Average Value of a Function

16m 31s

- Intro0:00
- Important Equations0:11
- Origin of Formula0:34
- Lecture Example 12:51
- Lecture Example 25:30
- Lecture Example 38:13
- Additional Example 4-1
- Additional Example 5-2

VIII. Extra

Graphs of f, f', f''

23m 58s

- Intro0:00
- Slope Function of f(x)0:41
- Slope is Zero0:53
- Slope is Positive1:03
- Slope is Negative1:13
- Slope Function of f'(x)1:31
- Slope is Zero1:42
- Slope is Positive1:48
- Slope is Negative1:54
- Lecture Example 12:23
- Lecture Example 28:06
- Lecture Example 312:36
- Additional Example 4-1
- Additional Example 5-2

Slope Fields for Differential Equations

18m 32s

- Intro0:00
- Things to Remember0:13
- Graphic Description0:42
- Lecture Example 11:44
- Lecture Example 26:59
- Lecture Example 39:46
- Additional Example 4-1
- Additional Example 5-2

Separable Differential Equations

17m 4s

- Intro0:00
- Differential Equations0:10
- Focus on Exponential Growth/Decay0:27
- Separating Variables0:47
- Lecture Example 11:35
- Lecture Example 26:41
- Lecture Example 39:36
- Additional Example 4-1
- Additional Example 5-2

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For more information, please see full course syllabus of College Calculus: Level I

For more information, please see full course syllabus of College Calculus: Level I

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0 answers

Post by Nadia Ariqat on April 8, 2014

very cool! you do a great jobâ€¦i've never taken calculus before and just happened to be browsing..kind of want to take the actual course now!

0 answers

Post by Jose Gonzalez-Gigato on April 9, 2013

Great teaching! Thanks!

2 answers

Last reply by: Erika O

Wed Mar 13, 2013 4:10 PM

Post by Erika O on March 5, 2013

All of the calculus books and course material I have uses Î”x instead of h as a variable. Is there a reason that it is different here?

0 answers

Post by Hanna Flanagan on September 12, 2012

what about finding the derivitave of 3x^2+1 at x=-1 using this formula?

3 answers

Last reply by: Angela Patrick

Mon Nov 25, 2013 12:40 PM

Post by Moniyka Sachar on September 26, 2010

It would be great if educator.com added an additional part to this sequence, about graphing derivatives and relating them to the original graph, because those can be tricky. Otherwise, thanks!