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 TaklooBighash, 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, 19961997; 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 mid90s. 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).

Writeup 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