Additional Comments on the lectures:
click here
Review
sheet for the course (definitions, theorems):
click here for a review sheet
for the course (summarizes main results, definitions, key steps in the
proofs, some examples)
Upcoming HW and reading: (previous HW)
(comments/solutions to the HW)
solutions to similar questions
Readings before class: click
here for a bullet point summary to help prepare you for class.
Takeaways for undergraduate classes:
summarizes key points from this and
other undergrad courses
Click here for Mathematica and LaTeX templates
SUPPLEMENTAL MATERIAL ON LECTURES
HANDOUTS: click
here for class notes
click here for a review sheet (click
here for the review sheet as a .ps file
version wi'out images)
-
click here for a review sheet
for the course (summarizes main results, definitions, key steps in the
proofs, some examples)
-
Summary of key points from this and
other undergrad courses
- REVIEW MATERIAL: Numerous worked
out calculus problems (differentiation, integration, statement of topics you
should know)
-
Notes on Induction, Calculus,
Convergence, the Pigeon Hole Principle and Lengths of Sets (from the first
appendix to
An Invitation to
Modern Number Theory, by myself and Ramin Takloo-Bighash, Princeton
University Press 2006). We will not need all the material there for this course,
but it is easier to just post the entire chapter.
-
Handout on Types of Proofs (from a
handout I wrote for math review sessions at Princeton, 1996-1997; this was
written for students from calculus to linear algebra).
-
Intermediate and Mean
Value Theorems and Taylor Series (you should know this material already; the
main results are stated and mostly proved, subject to some technical results
from analysis which we need to rigorously prove the IVT).
-
The chain rule:
this is a slight modification of a handout I wrote for a similar class at
Princeton in the mid-90s. Unfortunately it is in MSWord.
-
Expanded notes on
optimization, including the location of the military base or warehouse problem
-
My notes on the Method of Least
Squares.
-
Lancaster: The Mathematics of
Warfare
-
Equality of mixed derivatives: two articles on the web:
here and
here (the
second link is through JStor, and might only work when you are at Williams).
-
Write-up of the Change of Variable
Theorem, including the illustrative example, sketch of proof, and
formulations for the big three examples (polar, cylindrical and spherical).
- Sequences and series:
-
Notes on Vector Calculus.
These are by
Frank
Benford (grandson of the Frank Benford whom
Benford's law is
named after, a subject I love and have written numerous papers on). He does
applied math work and consulting (see
his homepage here) for more on opportunities and services.
-
Free textbooks:
-
click here for Mathematica and LaTeX templates
- Isaac Asimov: The
Relativity of Wrong
MIT Open Courseware