Multivariable Calculus, with Michael Hutchings

Video Lectures

Displaying all 40 video lectures.
Lecture 1
Areas and Lengths in Polar Coordinates
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Areas and Lengths in Polar Coordinates
Lecture 2
Vectors, Dot Product
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Vectors, Dot Product
Lecture 3
Cross Product, Determinant
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Cross Product, Determinant
Lecture 4
Lines and Planes
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Lines and Planes
Lecture 5
Cylinders and Quadric Surfaces
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Cylinders and Quadric Surfaces
Lecture 6
Vector-Valued Functions and Space Curves
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Vector-Valued Functions and Space Curves
Lecture 7
Functions of Several Variables
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Functions of Several Variables
Lecture 8
Limits and Continuity
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Limits and Continuity
Lecture 9
Partial Derivatives
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Partial Derivatives
Lecture 10
Tangent Planes and Linear Approximations
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Tangent Planes and Linear Approximations
Lecture 11
The Chain Rule
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The Chain Rule
Lecture 12
Directional Derivatives and the Gradient Vector
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Directional Derivatives and the Gradient Vector
Lecture 13
Maxima and Minima
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Maxima and Minima
Lecture 14
More Maxima and Minima; Lagrange Multipliers
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More Maxima and Minima; Lagrange Multipliers
Lecture 15
Midterm Review
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Midterm Review
Lecture 16
More Lagrange Multipliers
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More Lagrange Multipliers
Lecture 17
Double Integrals Over Rectangles
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Double Integrals Over Rectangles
Lecture 18
Double Integrals over General Regions
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Double Integrals over General Regions
Lecture 19
Double Integrals in Polar Coordinates
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Double Integrals in Polar Coordinates
Lecture 20
Applications of Double Integrals
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Applications of Double Integrals
Lecture 21
Triple Integrals
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Triple Integrals
Lecture 22
Triple Integrals in Cylindrical Coordinates
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Triple Integrals in Cylindrical Coordinates
Lecture 23
Triple Integrals in Spherical Coordinates
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Triple Integrals in Spherical Coordinates
Lecture 24
Change of Variables, Jacobians
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Change of Variables, Jacobians
Lecture 25
More change of variables and Jacobians
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More change of variables and Jacobians
Lecture 26
Vector Fields
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Vector Fields
Lecture 27
Line Integrals
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Line Integrals
Lecture 28
Green's Theorem I
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Green's Theorem I
Lecture 29
Green's Theorem II
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Green's Theorem II
Lecture 30
Curl and Divergence
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Curl and Divergence
Lecture 31
Parametric Surfaces
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Parametric Surfaces
Lecture 32
More Parametric Surfaces; Surface Integrals (Part I)
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More Parametric Surfaces; Surface Integrals (Part I)
Lecture 33
More Parametric Surfaces; Surface Integrals (Part II)
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More Parametric Surfaces; Surface Integrals (Part II)
Lecture 34
More Parametric Surfaces; Surface Integrals (Part III)
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More Parametric Surfaces; Surface Integrals (Part III)
Lecture 35
Stokes' Theorem I
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Stokes' Theorem I
Lecture 36
Stokes' Theorem II
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Stokes' Theorem II
Lecture 37
Divergence Theorem I
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Divergence Theorem I
Lecture 38
Divergence Theorem II
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Divergence Theorem II
Lecture 39
Review I
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Review I
Lecture 40
Review II
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Review II