# Multivariable Calculus Tutorials from Khan Academy

### 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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### Video Lectures & Study Materials

Visit the official course website for more study materials: https://www.khanacademy.org/math/multivariable-calculus

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