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.

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I. 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 

II. 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 

III. 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 

IV. 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 

V. 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, 9 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.

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