Calculus does not have to be difficult. Dr. William Murray knows what it takes to excel in math and will show you everything you need to know about calculus. Dr. Murray demonstrates his extensive teaching experience by clarifying complicated topics with a wide array of examples, helpful tips, and time-saving tricks. Topics range from Advanced Integration Techniques and Applications of Integrals to Sequences/Series. Dr. Murray received his Ph.D from UC Berkeley, B.S. from Georgetown University, and has been teaching in the university setting for 10+ years.

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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