MAT2500 21S [Jantzen] homework and daily class log

2020 brought us into the age of Zoom delivery of classes to protect participants during a serious health crisis poorly addressed by our nation.

These hand written lecture notes have been scanned using the mobile phone app Adobe Scan. The textbook Stewart Calculus 8e section numbers name the lecture files. Supplementary details from PDF notes and Maple worksheets are found at the homework log page.

Vector operations

  1. 12.1 Lecture Notes on 3-dimensional coordinate systems, distance formula, spheres, etc (brief intro / review by reading section)
  2. 12.2a Lecture Notes on Vectors
  3. 12.2b Lecture Notes on Vectors: 2d trig approach
  4. 12.3a Lecture Notes on The Dot Product
  5. 12.3b Lecture Notes on The Dot Product: projection along a direction
  6. 12.4 Lecture Notes on Cross Products
  7. 10.1 Lecture Notes on Curves Defined by Parametric Equations - Review for straight lines
  8. 12.5a Lecture Notes on Equations of Lines and Planes
  9. 12.5b Lecture Notes on Equations of Lines and Planes: distances between points, lines, planes [12-5c clarification on skew lines]

Vector Calculus (curves)

  1. 13.1 Vector Functions and Space Curves
  2. 13.2a Derivatives and Integrals of Vector Functions
  3. 13.2b Derivatives and Integrals of Vector Functions 
  4. 13.3 Arc Length and Curvature (arclength)
  5. 13.3 Arc Length and Curvature (curvature)
  6. 13.4 Motion in Space: Velocity and Acceleration

Multivariable Calculus (surfaces)

  1. 14.1 Functions of Several Variables
  2. 14.2 Limits and Continuity
  3. 14.3 Partial Derivatives (first order)
  4. 14.3 Partial Derivatives (higher order)
  5. 14.4 Tangent Planes and Linear Approximations
  6. 14.4 Tangent Planes and Linear Approximations (differentials)
  7. 14.5 The Chain Rule
  8. 14.6a Directional Derivatives and the Gradient
  9. 14.6b Directional Derivatives and the Gradient
  10. 14.7a Maximum and Minimum Values
  11. 14.7b Maximum and Minimum Values

Multivariable Integration

  1. 15.1a Lecture Notes in two parts: the geometrical interpretation of nested (iterated) calc I integrals comes from the Riemann integration approach
  2. 15.1b Lecture Notes on iterated integrals on rectangles, average values)  1
  3. 15.2 Lecture Notes on double integrals, nonrectangular regions
  4. 10.3 Lecture Notes on polar coordinate grid
  5. 15.3 Lecture Notes on polar coordinate integration
  6. 15.4a Lecture Notes on centers of mass/centroids
  7. 15.4b Lecture Notes on probability
  8. 15.6a Lecture Notes on triple integrals
  9. 15.6b Lecture Notes on deconstructing triple integrals [15.6.34]
  10. 15.6c Lecture Notes on center of mass
  11. 15.7-8a: Lecture Notes on cylindrical/spherical coordinates
  12. 15.7-8b Lecture Notes on cylindrical/spherical coordinates; snow cone exercise

Vector fields

  1. 16.1 Lecture Notes on Vector fields!
  2. 16.2a Lecture Notes on scalar line integrals
  3. 16.2b Lecture Notes on vector line integrals
  4. 16.3 Lecture Notes on conservative vector fields;
  5. 16.4 Lecture Notes on Green's theorem
  6. 16.5 Lecture Notes on grad, div, curl
  7. 16.6-9  Lecture Notes on surface integrals and Gauss and Stokes