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Home » Mathematics » College Calculus: Level II
No. of
Lectures
Duration
(hrs:min)
23
12:09

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

4.4
582 ratings • 46 reviews
  • Level Advanced
  • 23 Lessons (12hr : 09min)
  • 13,142 already enrolled!
  • 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

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%
48%
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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.
By Gautham PadmakumarApril 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 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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