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Applications of Calculus

Applications of Calculus

Eddie Woo via YouTube Direct link

Second Derivative: Notation

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Second Derivative: Notation

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Classroom Contents

Applications of Calculus

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  1. 1 Maximum & Minimum
  2. 2 Turning Points
  3. 3 Stationary Points
  4. 4 Non-Stationary Turning Points (1 of 2)
  5. 5 Non-Stationary Turning Points (2 of 2)
  6. 6 Introduction to Points of Inflexion
  7. 7 The Special Case of x^4
  8. 8 Horizontal Points of Inflexion
  9. 9 Overview of Critical Points (1 of 2)
  10. 10 Overview of Critical Points (2 of 2)
  11. 11 Overview of Critical Points: Examples (1 of 2)
  12. 12 Overview of Critical Points: Examples (2 of 2)
  13. 13 Finding and Confirming Turning Points
  14. 14 Curve Sketching: Locating Stationary Points
  15. 15 Curve Sketching: Determining Nature of SPs
  16. 16 Curve Sketching: Drawing the Graph
  17. 17 Sign of the First Derivative
  18. 18 Second Derivative: A Physical Analogy
  19. 19 Second Derivative: Concavity
  20. 20 Second Derivative: Notation
  21. 21 Second Derivative: Relationship w/ First Derivative
  22. 22 Graphing w/ the First Derivative
  23. 23 Graphing w/ the Second Derivative
  24. 24 Choosing First or Second Derivative
  25. 25 Graph Behaviour Chart
  26. 26 Implicit Differentiation
  27. 27 Implicit Differentiation - example question
  28. 28 Visual Approach to Derivatives (1 of 2)
  29. 29 Visual Approach to Derivatives (2 of 2)
  30. 30 Y11 Mathematics Ext 1 Quiz (1 of 2: Curve sketching with calculus)
  31. 31 Introduction to Solids of Revolution
  32. 32 Verifying Formulae for Cylinder, Cone & Sphere
  33. 33 Compound Volumes (1 of 2)
  34. 34 Compound Volumes (2 of 2)
  35. 35 Volumes: Examples around x-axis & y-axis
  36. 36 Subtraction of Volumes
  37. 37 Subtraction of Volumes: Class Discussion
  38. 38 Volume within a Cone (1 of 3: Separating variables and constants for differentiation)
  39. 39 Volume within a Cone (2 of 3: Finding Volume in terms of a single variable to differentiate)
  40. 40 Volume within a Cone (3 of 3: Finding the Stationary Points to determine the maximum volume)
  41. 41 Solids of Revolution (1 of 3: What happens when you rotate an area around an axis?)
  42. 42 Solid of Revolution (2 of 3: Finding Volume of the Solid of Revolution using Volume of a cylinder)
  43. 43 Solids of Revolution (3 of 3: Finding the Volume of an area rotated around the y axis)
  44. 44 Conical Volume (1 of 2: Derivation of the Volume of a Cone through Solids of Revolution)
  45. 45 Spherical Volume (2 of 2: Derivation of the Volume of a Sphere through Solids of Revolution)
  46. 46 Difference between Volumes (1 of 2: Method to finding the difference between volumes)
  47. 47 Difference Between Volumes (2 of 2: Investigating the relationship between Parabolas & Cylinders)
  48. 48 Intro to Solids of Revolution (1 of 3: Establishing the formula)
  49. 49 Intro to Solids of Revolution (2 of 3: Simple worked example)
  50. 50 Intro to Solids of Revolution (3 of 3: Other axes, volume of a sphere)
  51. 51 Solids of Revolution - Subtracting Volumes
  52. 52 Non-Standard Integrals: "Differentiate, hence integrate" (1 of 2)
  53. 53 Non-Standard Integrals: "Differentiate, hence integrate" (2 of 2)
  54. 54 Areas Under Curves: Logarithmic Functions
  55. 55 Integration & Logarithmic Functions: Log Integrands (1 of 2)
  56. 56 Integration & Logarithmic Functions: Log Integrands (2 of 2)
  57. 57 Integration & Logarithmic Functions: Non-Log Integrands (1 of 3)
  58. 58 Integration & Logarithmic Functions: Non-Log Integrands (2 of 3)
  59. 59 Integration & Logarithmic Functions: Non-Log Integrands (3 of 3)
  60. 60 Areas Under Curves: Logarithmic Functions (Alternative Approach)
  61. 61 Applications & Implications of d/dx(½v²): Concrete Example
  62. 62 Motion Exam Question (1 of 2: Finding v(x) from a(x))
  63. 63 Motion Exam Question (2 of 2: Finding x(t) from v(x))
  64. 64 Differentiating x^x (3 of 3: Implicit Differentiation)
  65. 65 Implicit Differentiation (Differentiating a function without needing to rearrange for x or y)
  66. 66 Rates of Change (1 of 4: Finding the Volume of an unknown height of water with a diagram)
  67. 67 Maximum/Minimum with Quadratics (1 of 2: Axis of symmetry)
  68. 68 Maximum/Minimum with Quadratics (2 of 2: Completing the square)
  69. 69 Max/Min Question: Cutting a Wire in Two (1 of 2: Setting up the equations)
  70. 70 Max/Min Question: Cutting a Wire in Two (2 of 2: Finding the minimum)
  71. 71 Challenging Max/Min Exam Question
  72. 72 Graphing Logarithmic Function with Calculus (1 of 2: Identifying features)
  73. 73 Graphing Logarithmic Function with Calculus (2 of 2: Constructing the sketch)
  74. 74 Differential Equation in terms of Dependent Variable (1 of 2: Partial Fractions)
  75. 75 Differential Equation in terms of Dependent Variable (2 of 2: Integration)

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