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Visualizations for Multivariable & Vector Calculus

Left-click and drag to rotate pictures. Right-click and drag to pan. Use the scroll wheel (or zoom gesture on touch screen) to zoom.

 Chapter 12

Section 12.1: 3D Coordinate Systems

• octants
• a point in 3D space
• a point in 3D space (user input)
• planes of the form variable = constant
• coordinates of the corners of a box
• circle vs. cylinder
• circle vs. cylinder + line vs. plane

Section 12.2: Vectors

• a vector in 3D space
• vector addition
• vector components
• unit vectors & normalization
• commutivity of vector addition

Section 12.3: The Dot Product

• dot product in 3D space
• direction angles
• vector and scalar projections

Section 12.4: The Cross Product

• cross product
• volume of a parallelepiped

Section 12.5:  Equations of Lines & Planes

• a line in 3D space (static)
• a line in 3D space (variable)
• a plane in 3D space
• intercepts of a plane

Section 12.6:  Cylinders & Quadric Surfaces

• quadric surfaces

 Chapter 13

Section 13.1: Vector Functions & Space Curves

• a space curve
• another space curve (helix)
• line segment
• gallery of examples

Section 13.3: Arc Length & Curvature

• linear approximation of arc length
• problem set

 Chapter 14

Section 14.1: Functions of Several Variables

• gallery of examples
• level curves of a paraboloid
• level curves of a Gaussian surface

Section 14.3: Partial Derivatives

• cross sections

Section 14.4: Tangent Planes & Linear Approximations

• linear approximation

Section 14.6: Directional Derivatives & the Gradient Vector

• directional derivatives

Section 14.7: Maximum & Minimum Values

• varieties of extrema

 Chapter 15

Section 15.1: Double Integrals over Rectangles

• Riemann sum in 2D
• Riemann sum in 3D

Section 15.7: Triple Integrals in Cylindrical Coordinates

• cylindrical coordinates

Section 15.8: Triple Integrals in Spherical Coordinates

• spherical coordinates
• basic shapes in spherical coordinates

 Chapter 16

Section 16.1: Vector Fields

• simple 2D vector field
• interesting 2D vector field
• simple 3D vector field
• interesting 3D vector field

Section 16.2: Line Integrals

• introduction to line integrals
• ds vs. dx vs. dy (reverse orientation) (on a half-circle)

Section 16.6: Parametric Surfaces & Their Areas

• gallery of examples
• problem set

 Old Materials (Spring 2016)

Older course materials can be found here.

 

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