Lecture 04

• Objectives

  • Form the equation of a plane using a point and a normal vector.
  • Extract the latter from the former.
  • Specify lines and planes based on relationships to other points/lines/planes.
  • Measure distances among points/lines/planes using projections.
  • Sketch traces of quadric surfaces
  • Match contour plots to graphs.

• Resources

  • Content
    • Stewart: §12.5–6
    • New Strang: §2.5 §2.6
    • Slides via JupyterHub
  • Practice
    • Mooculus: Lines Planes *not everything is relevant
  • Extras
    • CalcBLUE: Lines & Planes Quadric surfaces

 

Lecture 05

• Objectives

  • Connect the formula of space curves with their graphs.
  • Compute limits, derivatives, and integrals of vector-valued functions.
  • Interpret first and second derivatives.
  • Compute arc length of curves.

• Resources

  • Content
    • Stewart: §13.1–3
    • New Strang: §3.1 §3.2
    • Slides via JupyterHub
  • Visualization
    • CalcPlot3D
  • Practice
    • Mooculus: Lines and Curves Calculus of Vector-valued Functions
  • Extras
    • CalcBLUE: Derivatives of Curves Arc Length

 

Lecture 06

• Objectives

  • Describe motion of objects using calculus of curves.
  • Compute arc length of curves.
  • Explain thquantity 𝜅$\kappa$, the curvature.

• Resources

  • Content
    • Stewart: §13.3-4
    • New Strang: §3.3 §3.4
    • Slides via JupyterHub
  • Visualization
    • CalcPlot3D
  • Practice
    • Mooculus: Motion and Paths in Space
  • Extras
    • CalcBLUE:
    • Vector Calculus and Motion

 

Lecture 07

• Objectives

  • Sketch contour plot of a function of 2 variables
  • Relate level sets to a graph
  • Explore limits and continuity of 𝑓(𝑥,𝑦)$f(x,y)$.
  • Define partial derivatives

• Resources

  • Content
    • Stewart: §14.1–2
    • New Strang: §4.1 §4.2
    • Slides via JupyterHub
  • Visualization
    • CalcPlot3D
  • Practice
    • Mooculus: Functions of Several Variables Level Sets Continuity
  • Extras
    • CalcBLUE: Multivariate Functions

Lecture 08

• Objectives

  • Explore limits and continuity of 𝑓(𝑥,𝑦)$f(x,y)$.
  • Define partial derivatives
  • Estimate partial derivatives from contour maps and tables.

• Resources

  • Content
    • Stewart: §14.2—3
    • New Strang: §4.2
    • Slides via JupyterHub
  • Visualization
    • CalcPlot3D
  • Practice
    • Mooculus: Continuity Partial Derivatives
  • Extras
    • CalcBLUE: Partial Derivatives

Lecture 09

• Objectives

  • Relate "differentiability" to linear functions.
  • Find the tangent plane to the graph of a function of two variables.
  • Use linearization and/or differentials to estimate quantities.

• Resources

  • Content
    • Stewart: §14.4
    • New Strang: §4.4
    • Slides via JupyterHub
  • Practice
    • Mooculus: Tangent Planes
  • Extras
    • CalcBLUE: Tangent Spaces Linearization

Lecture 10

• Objectives

  • Compute derivatives of compositions.
  • Compute derivatives from implicit relations.
  • Review for midterm.

• Resources

  • Content
    • Stewart: §14.5
    • New Strang: §4.5
    • Slides via JupyterHub
  • Practice
    • Mooculus: Chain Rule
  • Extras
    • CalcBLUE: WARNING! This is very matrix-dependent (and thus extra) The Chain Rule

Lecture 11

• Objectives

  • Define directional derivatives.
  • Compute 𝐷𝐮𝑓$D_{\mathbf{u}}f$ using the gradient.
  • Use the properties of ∇𝑓$\mathrm{\nabla }f$ to compute tangent spaces and the like.

• Resources

  • Content
    • Stewart: §14.6
    • New Strang: §4.6
    • Slides via JupyterHub
  • Practice
    • Mooculus: The Gradient
  • Extras
    • CalcBLUE: Gradients

Lecture 12

• Objectives

  • Define local minima/maxima.
  • Classify critical points using the second derivative test.
  • Solve unconstrained optimization problems

• Resources

  • Content
    • Stewart: §14.7
    • New Strang: §4.7
    • Slides via JupyterHub
  • Practice
    • Mooculus: Minima and Maxima
  • Extras
    • CalcBLUE: Critical Points

 

Slide Type - Slide Sub-Slide Fragment Skip Notes

Lecture 13

• Objectives
  • Identify open and closed sets
  • Solve unconstrained optimization problems
  • Solve constrained optimization problems (Lagrange Multipliers)

• Resources
  • Content
    • Stewart: §14.8
    • New Strang: §4.8
    • Slides via JupyterHub
  • Practice
    • Mooculus: Constrained Optimization Lagrange Multipliers
  • Extras
    • CalcBLUE: Optimization

 

Lecture 14

• Objectives

  • Integration.
    • Define the double integral
    • Compute using iterated integrals
    • Convert from rectangular to polar coordinates.

• Resources

  • Content
    • Stewart: §15.1
    • New Strang: §5.1 §5.2 §5.3
    • Slides via JupyterHub
  • Practice
    • Mooculus: Multiple Integrals Polar Coordinnates
  • Extras
    • CalcBLUE: Integrals

Lecture 15

• Objectives

  • Integration
    • See examples using polar coordinates.
    • Applications of integration:
      • Center of mass
      • Moment of intertia
      • Probability
    • Preview triple integrals.

• Resources

  • Content
    • Stewart: §15.3–4
    • New Strang: §5.3 §5.6
    • Slides via JupyterHub
  • Practice
    • Mooculus: Polar Coordinates Mass and Moments
  • Extras
    • CalcBLUE: Integrals

Lecture 16

• Objectives
  • Triple Integration
    • Change order of integration for nonrectangular domains.
    • Cylindrical Coordinates.
    • Spherical Coordinates.
• Resources
  • Content
    • Stewart: §15.5–7
    • New Strang:
      • §5.4 Some good practice on changing order of integration here, Particularly, nos. 203–206, 211, 212, 215–220, 235, 240
      • §5.5
    • Slides via JupyterHub
  • Practice
    • Mooculus: Cylindrical Coordinates Spherical
  • Extras
    • CalcBLUE: Cylindrical Coordinates Spherical Coordinates

 

Lecture 17¶

• Objectives
  • Triple Integration
    • Integrals in Spherical and Cylindrical Coords
    • Integration Review
    • Midterm 2 review.
• Resources
  • Content
    • Stewart: §15.5–7
    • New Strang:
      • §5.4 Some good practice on changing order of integration here, Particularly, nos. 203–206, 211, 212, 215–220, 235, 240
      • §5.5
    • Slides via JupyterHub
  • Practice
    • Mooculus: Cylindrical Coordinates Spherical
  • Extras
    • CalcBLUE: Cylindrical Coordinates Spherical Coordinates

 

Lecture 18

• Objectives
  • Vector Fields
    • examples, plots
    • examples from physics
  • Conservative vector fields and potentials
• Resources
  • Content
    • Stewart: §16.1–2
    • New Strang:
      • §6.1
    • Slides via JupyterHub
  • Practice
    • Mooculus: Vector Fields
  • Extras
    • CalcBLUE: Fields

 

Lecture 19

• Objectives
  • Line Integrals
    • examples, plots
    • examples from physics
  • Conservative vector fields and potentials
• Resources
  • Content
    • Stewart: §16.1–3
    • New Strang:
      • §6.2
    • Slides via JupyterHub
  • Practice
    • Mooculus: Line Integrals
  • Extras
    • CalcBLUE: Path Integrals

Lecture 20

• Objectives
  • Fundamental Theorem of Line Integrals
    • Relation to path-independence
    • Why "conservative"?
  • Green's Theorem (if time)
• Resources
  • Content
    • Stewart: §16.4
    • New Strang:
      • §6.3
      • §6.4
    • Slides via JupyterHub
  • Practice
    • Mooculus: Line Integrals Green's Theorem
  • Extras
    • CalcBLUE: Path Independence

Lecture 21

• Objectives
  • Green's Theorem
    • Know the statement.
    • Know the ingredients.
    • Scalar curl
    • Divergence in 2D
• Resources
  • Content
    • Stewart: §16.5
    • New Strang:
      • §6.4
    • Slides via JupyterHub
  • Practice
    • Mooculus: Green's Theorem
  • Extras
    • CalcBLUE: Green's

Slide Type - Slide Sub-Slide Fragment Skip Notes

Lecture 22

• Objectives
  • Find parametrizations for the following surfaces in ℝ3${\mathbb{R}}^3$:
    • graphs of functions (of 2 variables)
    • parts of spheres
    • surfaces of revolution
  • Compute surface integrals
    • with respect to surface area
    • of a vector field (flux integrals)
• Resources
  • Content
    • Stewart: §16.6-7
    • New Strang:
      • §6.6
    • Slides via JupyterHub
    • Screencast
  • Practice
    • CalcPlot3D
    • Mooculus: Surface Integrals
  • Extras
    • CalcBLUE: 2-Form Fields *Use with caution. This is a different and more general formulation of surface integrals.

Lecture 23

• Objectives
  • Compute surface integrals
    • of a vector field (flux integrals)
  • Divergence Theorem
    • know what divergence measures
    • describe it as a conservation law
    • use it to compute flux
• Resources
  • Content
    • Stewart: §16.6-9
    • New Strang:
      • §6.5 §6.6 §6.8
    • Slides via JupyterHub
    • CalcPlot3D
    • Mooculus: Surface Integrals Divergence Theorem

Lecture 24

• Objectives
  • Curl
    • compute the curl of a vector field
    • interpret direction and magtitude of curl vector
    • relate to grad and div
  • Stokes' Theorem
    • orient a surface and its boundary
    • recognize when it applies
    • relate to divergence theorem
• Resources
  • Content
    • Stewart: §16.6-9
    • New Strang:
      • §6.7
    • Slides via JupyterHub
    • CalcPlot3D
    • Mooculus: Surface Integrals Stokes' Theorem
  • Extras
    • CalcBLUE: Stokes' Theorem *Use with caution. This is a different and more general formulation of surface integrals.