Home » Mathematics » College Calculus: Level II
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Duration
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23
12:09

# College Calculus 2 Online CourseDr. William Murray, Ph.D. Facebook Twitter More

4.4
582 ratings • 46 reviews
• 23 Lessons (12hr : 09min)
• 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.

## 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
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
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
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
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
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
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
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

## 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
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
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
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

## 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
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

## 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
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
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
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
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
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
Power Series 38:36
Intro 0:00
Main Definitions and Pattern 0:07
What Is The Point 0:22
Interval of Convergence 2:42
Lecture Example 1 3:24
Lecture Example 2 10:55
Lecture Example 3 14:44

## 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
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

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.

• Free Sample Lessons
• Closed Captioning (CC)
• Practice Questions
• Study Guides

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

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By Acme WangDecember 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 KeSeptember 4, 2016
Yea I meant A/(x-3)^2 + B/(x-3).

Thank You!
By Silvia GonzalezJune 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.
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 AlibrahimFebruary 25, 2016
Dr Murray,

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

Thanks for the wonderful lecture

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