MAT2500 [Jantzen] homework and daily class log

These hand written notes were developed for remote teaching during the pandemic but are too long to cover in person. Parts will be extracted for white board presentation step by step, so derivations or new concepts discussed in class can be consulted here if desired, or previewed briefly before class to see what notes are worth taking as they are presented, depending on your learning style.

These hand written lecture notes have been scanned to PDF files. Our textbook Stewart Calculus 9e section numbers name the lecture files. Supplementary details from PDF notes and Maple worksheets are found at the homework log page.

There are occasional "typos" in these notes done under the pandemic stress. Please inform bob when you think you found one.

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 (partial derivatives and 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. 14.5a The Chain Rule
  8. 14.5b The Chain Rule (etc)
  9. 14.6a Directional Derivatives and the Gradient
  10. 14.6b Directional Derivatives and the Gradient
  11. 14.7a Maximum and Minimum Values
  12. 14.7b Maximum and Minimum Values

Multivariable Integration

  1. 15.1a Lecture Notes on iterated and Riemann integrals
  2. 15.1b Lecture Notes on iterated integrals on rectangle, average value
  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 Lecture Notes on cylindrical coordinates
  12. 15.8 Lecture Notes on spherical coordinates
    old:
  13. 15.7-8a: Lecture Notes on cylindrical/spherical coordinates
  14. 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. 16.5b Lecture Notes on 2d vector field patterns and div/curl properties
    16.6-9 Lecture Notes on surface integrals and Gauss and Stokes [optional]