Multivariable functions 
Multivariable functions
by Khan
Video Lecture 1 of 86
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Date Added: August 14, 2016

Lecture Description

An introduction to multivariable functions, and a welcome to the multivariable calculus content as a whole.

Course Index

  1. Multivariable functions
  2. Representing points in 3d
  3. Introduction to 3d graphs
  4. Interpreting graphs with slices
  5. Contour plots
  6. Parametric curves
  7. Parametric surfaces
  8. Vector fields, introduction
  9. Fluid flow and vector fields
  10. 3d vector fields, introduction
  11. 3d vector field example
  12. Transformations, part 1
  13. Transformations, part 2
  14. Transformations, part 3
  15. Partial derivatives, introduction
  16. Partial derivatives and graphs
  17. Formal definition of partial derivatives
  18. Symmetry of second partial derivatives
  19. Gradient
  20. Gradient and graphs
  21. Directional derivative
  22. Directional derivative, formal definition
  23. Directional derivatives and slope
  24. Why the gradient is the direction of steepest ascent
  25. Gradient and contour maps
  26. Position vector valued functions | Multivariable Calculus | Khan Academy
  27. Derivative of a position vector valued function | Multivariable Calculus | Khan Academy
  28. Differential of a vector valued function | Multivariable Calculus | Khan Academy
  29. Vector valued function derivative example | Multivariable Calculus | Khan Academy
  30. Multivariable chain rule
  31. Multivariable chain rule intuition
  32. Vector form of the multivariable chain rule
  33. Multivariable chain rule and directional derivatives
  34. More formal treatment of multivariable chain rule
  35. Curvature intuition
  36. Curvature formula, part 1
  37. Curvature formula, part 2
  38. Curvature formula, part 3
  39. Curvature formula, part 4
  40. Curvature formula, part 5
  41. Curvature of a helix, part 1
  42. Curvature of a helix, part 2
  43. Curvature of a cycloid
  44. Computing the partial derivative of a vector-valued function
  45. Partial derivative of a parametric surface, part 1
  46. Partial derivative of a parametric surface, part 2
  47. Partial derivatives of vector fields
  48. Partial derivatives of vector fields, component by component
  49. Divergence intuition, part 1
  50. Divergence intuition, part 2
  51. Divergence formula, part 1
  52. Divergence formula, part 2
  53. Divergence example
  54. Divergence notation
  55. 2d curl intuition
  56. 2d curl formula
  57. 2d curl example
  58. 2d curl nuance
  59. Describing rotation in 3d with a vector
  60. 3d curl intuition, part 1
  61. 3d curl intuition, part 2
  62. 3d curl formula, part 1
  63. 3d curl formula, part 2
  64. 3d curl computation example
  65. Laplacian intuition
  66. Laplacian computation example
  67. Explicit Laplacian formula
  68. Harmonic Functions
  69. What is a tangent plane
  70. Controlling a plane in space
  71. Computing a tangent plane
  72. Local linearization
  73. What do quadratic approximations look like
  74. Quadratic approximation formula, part 1
  75. Quadratic approximation formula, part 2
  76. Quadratic approximation example
  77. The Hessian matrix
  78. Expressing a quadratic form with a matrix
  79. Vector form of multivariable quadratic approximation
  80. Multivariable maxima and minima
  81. Saddle points
  82. Warm up to the second partial derivative test
  83. Second partial derivative test
  84. Second partial derivative test intuition
  85. Second partial derivative test example, part 1
  86. Second partial derivative test example, part 2

Course Description

In multivariable calculus, we progress from working with numbers on a line to points in space. It gives us the tools to break free from the constraints of one-dimension, using functions to describe space, and space to describe functions.

The only thing separating multivariable calculus from ordinary calculus is this newfangled word "multivariable". It means we will deal with functions whose inputs or outputs live in two or more dimensions. Here we lay the foundations for thinking about and visualizing multivariable functions.
Introduction to multivariable calculus

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