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
- 12.1 Lecture Notes on 3-dimensional coordinate systems,
distance formula, spheres, etc (brief intro /
review by reading section)
- 12.2a Lecture Notes on Vectors
- 12.2b Lecture Notes on Vectors: 2d trig approach
- 12.3a Lecture Notes on The Dot Product
- 12.3b Lecture Notes on The Dot Product: projection along a direction
- 12.4 Lecture Notes on Cross Products
- 10.1 Lecture Notes on Curves Defined by Parametric Equations - Review
for straight lines
- 12.5a Lecture Notes on Equations of Lines and Planes
- 12.5b Lecture Notes on Equations of Lines and Planes: distances between
points, lines, planes [12-5c
clarification on skew lines]
Vector Calculus (curves)
- 13.1 Vector Functions and Space Curves
- 13.2a Derivatives and Integrals of Vector Functions
- 13.2b Derivatives and Integrals of Vector Functions
- 13.3 Arc Length and Curvature
(arclength)
- 13.3 Arc Length and Curvature
(curvature)
- 13.4 Motion in Space: Velocity and Acceleration
Multivariable Calculus (partial derivatives and surfaces)
- 14.1 Functions of Several Variables
- 14.2 Limits and Continuity
- 14.3 Partial Derivatives
(first order)
- 14.3 Partial Derivatives
(higher order)
- 14.4 Tangent Planes and Linear Approximations
- 14.4 Tangent Planes and Linear Approximations (differentials)
- 14.5a The Chain Rule
- 14.5b The Chain Rule (etc)
- 14.6a Directional Derivatives and the Gradient
- 14.6b Directional Derivatives and the Gradient
- 14.7a Maximum and Minimum Values
- 14.7b Maximum and Minimum Values
Multivariable Integration
- 15.1a
Lecture Notes on iterated and Riemann integrals
- 15.1b
Lecture Notes on iterated integrals on rectangle,
average value
- 15.2 Lecture
Notes on double
integrals, nonrectangular regions
- 10.3
Lecture Notes on polar coordinate grid
- 15.3 Lecture Notes on polar
coordinate integration
- 15.4a
Lecture Notes on centers of mass/centroids
- 15.4b Lecture Notes on probability
- 15.6a
Lecture Notes on triple integrals
- 15.6b Lecture Notes on deconstructing
triple integrals [15.6.34]
- 15.6c
Lecture Notes on center of mass
- 15.7 Lecture
Notes on cylindrical coordinates
- 15.8 Lecture
Notes on spherical coordinates
old:
- 15.7-8a: Lecture
Notes on cylindrical/spherical coordinates
- 15.7-8b Lecture
Notes on cylindrical/spherical coordinates;
snow cone exercise
Vector fields
- 16.1 Lecture
Notes on vector fields
- 16.2a
Lecture Notes on scalar line integrals
- 16.2b
Lecture Notes on vector line integrals
- 16.3 Lecture Notes on conservative vector fields;
- 16.4 Lecture Notes on Green's theorem
- 16.5 Lecture Notes on
grad, div, curl
- 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]