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8:39

Mathematics: AP Calculus BC Prof. John Zhu, M.B.A.
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4.4

163 ratings • 7 reviews

Level Advanced
33 Lessons (8hr : 39min)
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4.4 163 Ratings & 7 Reviews
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.

Table of Contents
Course Details

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%

By Aiden Song•January 5, 2016

What happened if L=1 and you have to use another test, how to use? Please specify! Thank you.

By Hen McGibbons•December 16, 2015

the calculus 1 course by jenny switkes is also a great choice

By Melinda Berry•April 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 Saleh•October 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 Nigam•March 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.