Home » Mathematics » Calculus BC
No. of
Lectures
Duration
(hrs:min)
33
8:39

4.4
163 ratings • 7 reviews
• 33 Lessons (8hr : 39min)
• Audio: English

Professor John Zhu returns from Educator's AP Calculus AB course to teach the Calculus BC series. John explains complicated Calculus ideas in easy, understandable terms so that any student can succeed on the exam. In addition, all the topics on the test are covered with many extra examples, as well as a full length practice test at the end of the course. Sample topics include L'Hopital's Rule, Integration by Parts, Area Under the Curve, Ratio Test, and Taylor Series. Not only does John have personal experience acing the AP exam, but after receiving his undergraduate degree in Electrical Engineering from Michigan State and his MBA from Webster University, he also taught calculus for over eight years.

## Section 1: Prerequisites

Parametric Curves 10:10
Intro 0:00
Parametric Equations 0:23
Familiar Functions 0:32
Parametric Equation/ Function 0:56
Example 1: Graph Parametric Equation 1:48
Example 2 4:30
Example 3 6:01
Example 4 7:12
Example 5 8:10
Polar Coordinates 14:54
Intro 0:00
Polar Coordinates 0:09
Definition 0:11
Example 0:23
Converting Polar Coordinates 1:49
Example: Convert Polar Equation to Cartesian Coordinates 3:06
Example: Convert Polar Equation to Cartesian Coordinates 5:21
Example: Find the Polar Representation 6:51
Example: Find the Polar Representation 8:39
Example: Sketch the Graph 10:02
Vector Functions 12:05
Intro 0:00
Vector Functions 0:11
2 Parts 0:18
Example 1 1:44
Example 2 3:52
Example 3 4:59
Example 4 6:03
Example 5 8:00
Example 6 9:23
Example 7 10:16

## Section 2: Differentiation

Parametric Differentiation 13:15
Intro 0:00
Parametric Differentiation 0:15
Example 1 1:16
Example 2 1:54
Example 3 3:15
Example 4 4:59
Parametric Differentiation: Position, Speed & Acceleration 7:45
Example 5 8:32
Example 6 10:37
Polar Differentiation 10:14
Intro 0:00
Polar Differentiation 0:11
Goal 0:13
Method 0:24
Example 1 0:52
Example 2 4:27
Example 3 7:03
L'Hopital's Rule 6:43
Intro 0:00
L'Hopitals Rule 0:09
Conditions 0:14
Limit 0:36
Example 1 1:21
Example 2 2:38
Example 3 4:09
Example 4 5:01

## Section 3: Integration

Integration By Parts 19:04
Intro 0:00
Integration by Parts 0:12
Formula 0:31
How It's Derived From Product Rule 1:09
Integration by Parts: Rules to Follow 3:24
Recap of the Rules 4:13
Example 1 4:29
Example 2 7:04
Example 3 8:40
Example 4 13:48
Example 5 15:36
Integration By Partial Fractions 22:04
Intro 0:00
Integration by Partial Fractions: Goal 0:08
Example 1 2:10
Example 2 7:10
Example 3 10:06
Example 4 14:23
Example 5 16:26
Improper Integrals 19:01
Intro 0:00
Improper Integrals 0:06
3 Steps 1:11
Example 1 1:46
Example 2 3:20
Example 3 6:05
Example 4 9:02
Example 5 11:21
Example 6 15:54

## Section 4: Applications of Integration

Logistic Growth 19:16
Intro 0:00
Logistic Growth Function 0:07
Defining Variables 0:40
Equation Parts 1:51
Logistic Growth 2:04
Example 1 2:59
Example 2 7:13
Example 3 11:29
Example 4 15:21
Arc Length for Parametric & Polar Curves 17:40
Intro 0:00
Arc Length 0:13
Arc Length of a Normal Function 0:24
Example 1:27
Example 2: Arc Length for Parametric Curves 3:31
Example 3: Arc Length for Parametric Curves 4:23
Example 4: Arc Length for Parametric Curves 8:05
Example 5: Arc Length for Parametric Curves 12:22
Example 6: Arc Length for Polar Curves 15:36
Example 7: Arc Length for Polar Curves 16:03
Area for Parametric & Polar Curves 4:33
Intro 0:00
Area for Parametric Curves: Parametric Function 0:10
Example 1: Area for Parametric Curves 0:35
Area for Parametric Curves: Polar Function 2:50
Example 2: Area for Polar Curves 3:18

## Section 5: Sequences, Series, & Approximations

Definition & Convergence 7:10
Intro 0:00
Sequences: Definition 0:09
Definition 0:31
Example 1 1:07
Sequences: Convergence 2:02
Example 1 2:52
Example 2 3:36
Example 3 4:47
Example 4 6:16
Geometric Series 10:59
Intro 0:00
Geometric Series 0:07
Definition 0:24
Expanded Form 0:39
Convergence Rules 1:00
Example 1: Convergence 1:22
Example 2: Convergence 2:36
Example 3: Convergence 3:45
Sum of Series 5:04
Sum of First n Terms 5:14
Sum of Series 5:24
Example 1: Sum of Series 5:39
Example 2: Sum of Series 7:15
Example 3: Sum of Series 8:24
Example 4: Sum of Series 9:36
Harmonic & P Series 3:58
Intro 0:00
Harmonic Series 0:08
P-Series 1:17
Example 1: P-Series Test 2:22
Example 2: P-Series Test 3:06
Integral Test 11:31
Intro 0:00
Integral Test 0:09
Example 1 0:54
Example 2 4:00
Example 3 7:59
Example 4 9:47
Comparison Test 7:47
Intro 0:00
Comparison Test 0:10
Example 1 1:07
Example 2 2:33
Example 3 4:20
Example 4 6:29
Limit Comparison Test 9:40
Intro 0:00
Limit Comparison Test 0:09
Conditions 0:31
Example 1 1:01
Example 2 2:53
Example 3 4:15
Example 4 6:19
Ratio Test 11:20
Intro 0:00
Ratio Test 0:09
Example 1 0:57
Example 2 2:55
Example 3 6:27
Example 4 8:36
Alternating Series 9:11
Intro 0:00
Alternating Series 0:08
Convergence Test 0:59
Example 1 1:27
Example 2 2:42
Example 3 4:57
Example 4 6:37
Absolute Convergence 7:13
Intro 0:00
Absolute Convergence 0:12
Example 1 0:52
Example 2 3:42
Example 3 5:21
Power Series Convergence 12:52
Intro 0:00
Power Series 0:09
Definition 0:19
Radius & Interval of Convergence 2:07
Example 1 2:28
Example 2 4:18
Example 3 6:20
Example 4 9:11
Taylor Series 15:11
Intro 0:00
Taylor Series 0:06
MacLaurin Series 0:45
Example 1 1:02
Example 2 2:45
Example 3 6:04
Example 4 8:23
Example 5 11:49
Power Series Operations 16:40
Intro 0:00
Operations 0:07
Example 1: Substitution 1:05
Example 2: Substitution 3:41
Example 3: Differentiation/ Integration 5:39
Example 4: Differentiation/ Integration 9:55
Example 5: Multiplying/ Dividing 12:32
Example 6: Multiplying/ Dividing 14:50
Lagrange Error 7:09
Intro 0:00
Power Series: Lagrange Error 0:06
Lagrange Remainder 0:21
Lagrange Error Bound 0:50
Example 1 1:06
Example 2 3:27

## Section 6: Practice Test

AP Calc BC Practice Test Section 1: Multi Choice Part 1 15:45
Intro 0:00
Practice Problem 1 0:10
Practice Problem 2 1:19
Practice Problem 3 2:33
Practice Problem 4 5:25
Practice Problem 5 6:32
Practice Problem 6 9:11
Practice Problem 7 11:31
Practice Problem 8 13:08
Practice Problem 9 14:16
AP Calc BC Practice Test Section 1: Multi Choice Part 2 21:38
Intro 0:00
Practice Problem 10 0:12
Practice Problem 11 3:03
Practice Problem 12 4:53
Practice Problem 13 6:56
Practice Problem 14 9:10
Practice Problem 15 12:17
Practice Problem 16 14:43
Practice Problem 17 16:18
Practice Problem 18 18:34
AP Calc BC Practice Test Section 1: Multi Choice Part 3 17:31
Intro 0:00
Practice Problem 19 0:09
Practice Problem 20 3:03
Practice Problem 21 4:07
Practice Problem 22 5:41
Practice Problem 23 8:48
Practice Problem 24 11:16
Practice Problem 25 12:53
Practice Problem 26 14:12
Practice Problem 27 15:21
AP Calc BC Practice Test Section 1: Multi Choice Part 4 14:17
Intro 0:00
Practice Problem 28 0:08
Practice Problem 29 1:19
Practice Problem 30 2:15
Practice Problem 31 4:19
Practice Problem 32 6:54
Practice Problem 33 8:13
Practice Problem 34 9:03
Practice Problem 35 10:21
Practice Problem 36 11:42
AP Calc BC Practice Test Section 1: Multi Choice Part 5 22:45
Intro 0:00
Practice Problem 37 0:10
Practice Problem 38 4:09
Practice Problem 39 7:21
Practice Problem 40 9:42
Practice Problem 41 11:35
Practice Problem 42 14:01
Practice Problem 43 15:50
Practice Problem 44 16:43
Practice Problem 45 19:35
AP Calc BC Practice Test Section 1: Free Response Part 1 9:55
Intro 0:00
Practice Problem 1a 0:08
Practice Problem 1b 1:30
Practice Problem 1c 3:08
Practice Problem 2a 3:50
Practice Problem 2b 5:40
Practice Problem 2c 7:24
AP Calc BC Practice Test Section 1: Free Response Part 2 10:08
Intro 0:00
Practice Problem 3a 0:09
Practice Problem 3b 3:01
Practice Problem 4a 3:55
Practice Problem 4b 5:43
AP Calc BC Practice Test Section 1: Free Response Part 3 13:58
Intro 0:00
Practice Problem 5a 0:07
Practice Problem 5b 2:21
Practice Problem 5c 4:21
Practice Problem 6a 6:16
Practice Problem 6b 8:57
Practice Problem 6c 11:03

Duration: 8 hours, 39 minutes

Number of Lessons: 33

#### Student Feedback

4.4

7 Reviews

43%
57%
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By Aiden SongJanuary 5, 2016
What happened if L=1 and you have to use another test, how to use? Please specify! Thank you.
By Hen McGibbonsDecember 16, 2015
the calculus 1 course by jenny switkes is also a great choice
By Melinda BerryApril 1, 2015
Hello, could you confirm that this is a geometric series? I thought that a geometric series had to have a common ratio. In this case, what is the common ratio? Thank you.
By Wael SalehOctober 20, 2013
Great job, As you know there are many types of tests, Therefore, I have problem !!  Are there any certain signals in question describe which kind of tests should I use it to solve problem?
Best regards,
By Sumant NigamMarch 8, 2013
I thought the video was great, but for the last problem: f(x)=ln(x)-1 the graph should not intersect the y-axis, right? There should be a vertical asymptote there.

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