Vector Calculus - Introduction to Vectors, Vector Functions, and Vector Fields

Vector Calculus - Introduction to Vectors, Vector Functions, and Vector Fields

Krista King via YouTube Direct link

Plotting points in three dimensions (KristaKingMath)

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Plotting points in three dimensions (KristaKingMath)

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Classroom Contents

Vector Calculus - Introduction to Vectors, Vector Functions, and Vector Fields

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  1. 1 Plotting points in three dimensions (KristaKingMath)
  2. 2 distance between two points in three dimensions (KristaKingMath)
  3. 3 Equation of a sphere, plus center and radius (KristaKingMath)
  4. 4 Describing a region in 3D space (KristaKingMath)
  5. 5 Using inequalities to describe a region in 3D space (KristaKingMath)
  6. 6 Finding a Vector From Two Points (KristaKingMath)
  7. 7 Vector addition and combinations of vectors (KristaKingMath)
  8. 8 Sum of Two Vectors (KristaKingMath)
  9. 9 Copying vectors to find combinations of vectors (KristaKingMath)
  10. 10 Unit vector in the direction of the given vector (KristaKingMath)
  11. 11 Angle between a vector and the x-axis (KristaKingMath)
  12. 12 Magnitude and angle of the resultant force (KristaKingMath)
  13. 13 Dot product of two vectors (KristaKingMath)
  14. 14 Angle between two vectors (KristaKingMath)
  15. 15 Orthogonal, parallel or neither (vectors) (KristaKingMath)
  16. 16 Acute angle between the lines (vectors) (KristaKingMath)
  17. 17 Acute angles between the curves (vectors) (KristaKingMath)
  18. 18 Direction cosines and direction angles (vectors) (KristaKingMath)
  19. 19 Scalar Equation of a Line (KristaKingMath)
  20. 20 Scalar Equation of a Plane (KristaKingMath)
  21. 21 Scalar and vector projections (KristaKingMath)
  22. 22 Cross Product (KristaKingMath)
  23. 23 Vector orthogonal to the plane (KristaKingMath)
  24. 24 Volume of the parallelepiped determined by vectors (KristaKingMath)
  25. 25 Volume of the parallelepiped with adjacent edges (KristaKingMath)
  26. 26 Scalar triple product to verify the vectors are coplanar (KristaKingMath)
  27. 27 Vector and parametric equations of the line (KristaKingMath)
  28. 28 Parametric and symmetric equations of the line (KristaKingMath)
  29. 29 Symmetric Equations of a Line (KristaKingMath)
  30. 30 Parallel, intersecting, skew and perpendicular lines (KristaKingMath)
  31. 31 Equation of the plane using vectors (KristaKingMath)
  32. 32 Point of intersection of a line and a plane (KristaKingMath)
  33. 33 Parallel, perpendicular, and angle between planes (KristaKingMath)
  34. 34 Parametric equations for the line of intersection of two planes (KristaKingMath)
  35. 35 Symmetric equations for the line of intersection of two planes (KristaKingMath)
  36. 36 Distance between a point and a line (vectors) (KristaKingMath)
  37. 37 Distance between a point and a plane (vectors) (KristaKingMath)
  38. 38 Distance between parallel planes (vectors) (KristaKingMath)
  39. 39 Sketching the quadric surface (KristaKingMath)
  40. 40 Reducing a quadric surface equation to standard form (KristaKingMath)
  41. 41 Domain of the vector function (KristaKingMath)
  42. 42 Limit of the vector function (KristaKingMath)
  43. 43 Sketching the vector equation (KristaKingMath)
  44. 44 Projections of the curve onto the coordinate axes (KristaKingMath)
  45. 45 Vector and parametric equations of the line segment (KristaKingMath)
  46. 46 Vector function for the curve of intersection of two surfaces (KristaKingMath)
  47. 47 Derivative of the vector function (KristaKingMath)
  48. 48 Unit tangent vector (KristaKingMath)
  49. 49 Parametric equations of the tangent line (vectors) (KristaKingMath)
  50. 50 Integral of the vector function (KristaKingMath)
  51. 51 arc length of a vector function (KristaKingMath)
  52. 52 reparametrizing the curve in terms of arc length (KristaKingMath)
  53. 53 unit tangent and unit normal vectors (KristaKingMath)
  54. 54 curvature of the vector function (KristaKingMath)
  55. 55 maximum curvature of the function (KristaKingMath)
  56. 56 normal and osculating planes (KristaKingMath)
  57. 57 Velocity & Acceleration Vectors (KristaKingMath)
  58. 58 velocity, acceleration and speed, given position (KristaKingMath)
  59. 59 velocity and position given acceleration and initial conditions (KristaKingMath)
  60. 60 tangential and normal components of the acceleration vector (KristaKingMath)
  61. 61 line integral of a curve (KristaKingMath)
  62. 62 line integral of a vector function (KristaKingMath)
  63. 63 potential function of a conservative vector field (KristaKingMath)
  64. 64 potential function of the conservative vector field to evaluate a line integral (KristaKingMath)
  65. 65 independence of path (KristaKingMath)
  66. 66 work done by the force field (KristaKingMath)
  67. 67 Green's Theorem One Region (KristaKingMath)
  68. 68 Green's Theorem Two Regions (KristaKingMath)
  69. 69 curl and divergence (KristaKingMath)
  70. 70 potential function of the conservative vector field, three dimensions (KristaKingMath)
  71. 71 points on the surface (KristaKingMath)
  72. 72 surface of the vector equation (KristaKingMath)
  73. 73 parametric representation of the surface (KristaKingMath)
  74. 74 tangent plane to the parametric surface (KristaKingMath)
  75. 75 area of the surface (KristaKingMath)
  76. 76 surface integral (KristaKingMath)
  77. 77 surface integral, example 2 (KristaKingMath)
  78. 78 What is Stokes theorem? - Formula and examples

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