Home » Mathematics » College Calculus: Level II

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12:09

College Calculus 2 Online Course Dr. William Murray, Ph.D.
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4.4

582 ratings • 46 reviews

Level Advanced
23 Lessons (12hr : 09min)
13,172 already enrolled!
4.4 582 Ratings & 46 Reviews
Audio: English
English

Calculus does not have to be difficult. Join Dr. William Murray’s College Calculus 2 online class with clear explanations, tons of examples, and time-saving tips.

Table of Contents
Course Details
About Dr. Murray

Section 1: Advanced Integration Techniques
	Integration by Parts			24:52
		Intro		0:00
		Important Equation		0:07
			Where It Comes From (Product Rule)	0:20
			Why Use It?	0:35
		Lecture Example 1		1:24
		Lecture Example 2		3:30
		Shortcut: Tabular Integration		7:34
			Example	7:52
		Lecture Example 3		10:00
		Mnemonic: LIATE		14:44
			Ln, Inverse, Algebra, Trigonometry, e	15:38
		Additional Example 4		3:13
		Additional Example 5		4:13
	Integration of Trigonometric Functions			25:30
		Intro		0:00
		Important Equation		0:07
			Powers (Odd and Even)	0:19
			What To Do	1:03
		Lecture Example 1		1:37
		Lecture Example 2		3:12
		Half-Angle Formulas		6:16
			Both Powers Even	6:31
		Lecture Example 3		7:06
		Lecture Example 4		10:59
		Additional Example 5		2:37
		Additional Example 6		7:23
	Trigonometric Substitutions			30:09
		Intro		0:00
		Important Equations		0:06
			How They Work	0:35
			Example	1:45
			Remember: du and dx	2:50
		Lecture Example 1		3:43
		Lecture Example 2		10:01
		Lecture Example 3		12:04
		Additional Example 4		10:36
		Additional Example 5		3:21
	Partial Fractions			41:22
		Intro		0:00
		Overview		0:07
			Why Use It?	0:18
		Lecture Example 1		1:21
		Lecture Example 2		6:52
		Lecture Example 3		13:28
		Additional Example 4		8:47
		Additional Example 5		13:21
	Integration Tables			20:00
		Intro		0:00
		Using Tables		0:09
			Match Exactly	0:32
		Lecture Example 1		1:16
		Lecture Example 2		5:28
		Lecture Example 3		8:51
		Additional Example 4		3:05
		Additional Example 5		4:11
	Trapezoidal Rule, Midpoint Rule, Left/Right Endpoint Rule			22:36
		Intro		0:00
		Trapezoidal Rule		0:13
			Graphical Representation	0:20
			How They Work	1:08
			Formula	1:47
			Why a Trapezoid?	2:53
		Lecture Example 1		5:10
		Midpoint Rule		8:23
			Why Midpoints?	8:56
			Formula	9:37
		Lecture Example 2		11:22
		Left/Right Endpoint Rule		13:54
			Left Endpoint	14:08
			Right Endpoint	14:39
		Lecture Example 3		15:32
		Additional Example 4		2:56
		Additional Example 5		2:19
	Simpson's Rule			21:08
		Intro		0:00
		Important Equation		0:03
			Estimating Area	0:28
			Difference from Previous Methods	0:50
			General Principle	1:09
		Lecture Example 1		3:49
		Lecture Example 2		6:32
		Lecture Example 3		9:07
		Additional Example 4		2:56
		Additional Example 5		5:51
	Improper Integration			44:18
		Intro		0:00
		Horizontal and Vertical Asymptotes		0:04
			Example: Horizontal	0:16
			Formal Notation	0:37
			Example: Vertical	1:58
			Formal Notation	2:29
		Lecture Example 1		5:01
		Lecture Example 2		7:41
		Lecture Example 3		11:32
		Lecture Example 4		15:49
		Formulas to Remember		18:26
			Improper Integrals	18:36
		Lecture Example 5		21:34
		Lecture Example 6 (Hidden Discontinuities)		26:51
		Additional Example 7		2:57
		Additional Example 8		6:04
Section 2: Applications of Integrals, part 2
	Arclength			23:20
		Intro		0:00
		Important Equation		0:04
			Why It Works	0:49
			Common Mistake	1:21
		Lecture Example 1		2:14
		Lecture Example 2		6:26
		Lecture Example 3		10:49
		Additional Example 4		5:16
		Additional Example 5		3:25
	Surface Area of Revolution			28:53
		Intro		0:00
		Important Equation		0:05
			Surface Area	0:38
			Relation to Arclength	1:11
		Lecture Example 1		1:46
		Lecture Example 2		4:29
		Lecture Example 3		9:34
		Additional Example 4		5:00
		Additional Example 5		4:54
	Hydrostatic Pressure			24:37
		Intro		0:00
		Important Equation		0:09
			Main Idea	0:12
			Different Forces	0:45
			Weight Density Constant	1:10
			Variables (Depth and Width)	2:21
		Lecture Example 1		3:28
		Additional Example 2		9:24
		Additional Example 3		4:32
	Center of Mass			25:39
		Intro		0:00
		Important Equation		0:07
			Main Idea	0:25
			Centroid	1:00
			Area	1:28
		Lecture Example 1		1:44
		Lecture Example 2		6:13
		Lecture Example 3		10:04
		Additional Example 4		4:05
		Additional Example 5		6:48
Section 3: Parametric Functions
	Parametric Curves			22:26
		Intro		0:00
		Important Equations		0:05
			Slope of Tangent Line	0:30
			Arc length	1:03
		Lecture Example 1		1:40
		Lecture Example 2		4:23
		Lecture Example 3		8:38
		Additional Example 4		5:00
		Additional Example 5		4:22
	Polar Coordinates			30:59
		Intro		0:00
		Important Equations		0:05
			Polar Coordinates in Calculus	0:42
			Area	0:58
			Arc length	1:41
		Lecture Example 1		2:14
		Lecture Example 2		4:12
		Lecture Example 3		10:06
		Additional Example 4		8:38
		Additional Example 5		9:02
Section 4: Sequences and Series
	Sequences			31:13
		Intro		0:00
		Definition and Theorem		0:05
			Monotonically Increasing	0:25
			Monotonically Decreasing	0:40
			Monotonic	0:48
			Bounded	1:00
			Theorem	1:11
		Lecture Example 1		1:31
		Lecture Example 2		11:06
		Lecture Example 3		14:03
		Additional Example 4		6:11
		Additional Example 5		7:24
	Series			31:46
		Intro		0:00
		Important Definitions		0:05
			Sigma Notation	0:13
			Sequence of Partial Sums	0:30
			Converging to a Limit	1:49
			Diverging to Infinite	2:20
		Geometric Series		2:40
			Common Ratio	2:47
			Sum of a Geometric Series	3:09
		Test for Divergence		5:11
			Not for Convergence	6:06
		Lecture Example 1		8:32
		Lecture Example 2		10:25
		Lecture Example 3		16:26
		Additional Example 4		3:47
		Additional Example 5		4:26
	Integral Test			23:26
		Intro		0:00
		Important Theorem and Definition		0:05
			Three Conditions	0:25
			Converging and Diverging	0:51
			P-Series	1:11
		Lecture Example 1		2:19
		Lecture Example 2		5:08
		Lecture Example 3		6:38
		Additional Example 4		6:18
		Additional Example 5		4:49
	Comparison Test			22:44
		Intro		0:00
		Important Tests		0:01
			Comparison Test	0:22
			Limit Comparison Test	1:05
		Lecture Example 1		1:44
		Lecture Example 2		3:52
		Lecture Example 3		6:01
		Lecture Example 4		10:04
		Additional Example 5		4:11
		Additional Example 6		4:20
	Alternating Series			25:26
		Intro		0:00
		Main Theorems		0:05
			Alternation Series Test (Leibniz)	0:11
			How It Works	0:26
			Two Conditions	0:46
			Never Use for Divergence	1:12
			Estimates of Sums	1:50
		Lecture Example 1		3:19
		Lecture Example 2		4:46
		Lecture Example 3		6:28
		Additional Example 4		5:04
		Additional Example 5		9:44
	Ratio Test and Root Test			33:27
		Intro		0:00
		Theorems and Definitions		0:06
			Two Common Questions	0:17
			Absolutely Convergent	0:45
			Conditionally Convergent	1:18
			Divergent	1:51
			Missing Case	2:02
		Ratio Test		3:07
		Root Test		4:45
		Lecture Example 1		5:46
		Lecture Example 2		9:23
		Lecture Example 3		13:13
		Additional Example 4		9:13
		Additional Example 5		8:07
	Power Series			38:36
		Intro		0:00
		Main Definitions and Pattern		0:07
			What Is The Point	0:22
			Radius of Convergence Pattern	0:45
			Interval of Convergence	2:42
		Lecture Example 1		3:24
		Lecture Example 2		10:55
		Lecture Example 3		14:44
		Additional Example 4		8:39
		Additional Example 5		7:46
Section 5: Taylor and Maclaurin Series
	Taylor Series and Maclaurin Series			30:18
		Intro		0:00
		Taylor and Maclaurin Series		0:08
			Taylor Series	0:12
			Maclaurin Series	0:59
		Taylor Polynomial		1:20
		Lecture Example 1		2:35
		Lecture Example 2		6:51
		Lecture Example 3		11:38
		Lecture Example 4		17:29
		Additional Example 5		2:50
		Additional Example 6		4:41
	Taylor Polynomial Applications			50:50
		Intro		0:00
		Main Formulas		0:06
			Alternating Series Error Bound	0:28
			Taylor's Remainder Theorem	1:18
		Lecture Example 1		3:09
		Lecture Example 2		9:08
		Lecture Example 3		17:35
		Additional Example 4		5:56
		Additional Example 5		13:50

Duration: 12 hours, 09 minutes

Number of Lessons: 23

Ideal for college students taking their second class in Calculus or high school students looking to see what’s after Pre-Calculus. For first time Calculus learners, be sure to check out Dr. Switkes’ Calculus 1 or Prof. Hovasapian’s AP Calculus courses also on Educator.

Additional Features:

Free Sample Lessons
Closed Captioning (CC)
Practice Questions
Downloadable Lecture Slides
Study Guides
Instructor Comments

Topics Include:

Integration by Parts
Partial Fractions
Simpson’s Rule
Applications of Integrals
Surface Area of Revolution
Center of Mass
Parametric Functions
Sequences & Series
Taylor & Maclaurin Series

Dr. William Murray received his Ph.D from UC Berkeley, B.S. from Georgetown University, and has been teaching mathematics in the university setting for 15+ years.

Student Testimonials:

“Wonderful lectures, by the way. This really is the future of education!!” — A De L.

“You are very smart professor Murray. I past my calculus II class. I am looking forward in taking differential equations with you. Thanks for everything :)” — Luis C.

“I love the series lectures. Thank you for making them easy to understand.” — Paul C.

"Dr. Murray's lectures are clear, quick and concise." — Wen G.

“This is so much more helpful than school! Thanks for being so clear.” — Jaspreet S.

Visit Dr. Murray’s page

Student Feedback

4.4

46 Reviews

48%

By Acme Wang•December 27, 2016

Hi Professor,

Just a bit confused about Example II, the question does not say take the limit as n goes to infinity, how could you just assume that? :):) Really nice video! Thank you very much!

By Peter Ke•September 4, 2016

Yea I meant A/(x-3)^2 + B/(x-3).

Thank You!

By Silvia Gonzalez•June 7, 2016

Thank you for the answer. I wouldn't worry about little mistakes here and there, if we can catch them it means we understood what was being done,ergo the class is very good. Thank you again.

By Gautham Padmakumar•April 13, 2016

At 10:43, I noticed that you made a mistake when you wrote down the integral formula about the y axis. You left it as f'(y) instead of (f'(y))^2

Thanks for the lecture series by the way! It really helped me review for my calc finals

By Mohsin Alibrahim•February 25, 2016

Dr Murray,

In example 3, how come du = [3sec^2(x)] while u = 9sec^2(x) ?

Thanks for the wonderful lecture