Math 46: Resources
- SPRING 2011
Theory
- Your main resource will be practising solving as many problems
as you can. This includes the old practise exams which are on the
Schedule page.
- ERRATA for our textbook,
Logan's Applied Mathematics, 3rd Edition (2006).
- At the library:
- J. David Logan, Applied Partial Differential Equations (2004).
This nice book
goes into more detail than chapter 6 of our book, at a slightly more leisurely
pace. I nearly chose this book as our text, but preferred a more
broad coverage of applied math.
- F. B. Hildebrand, Methods of Applied Mathematics, 2nd edition
(1965). Although old-looking, Chapter 3 on integral equations is a very clear
coverage of the same material we'll do from Logan.
- Bender & Orszag, ``Advanced Mathematical Methods for
Scientists and Engineers'' (1999). This is the bible on asymptotics
and boundary layers, and is graduate-level.
- Daw's nice 13-page lecture notes on dimensional analysis.
-
Course with lecture notes, homeworks, using our textbook,
at U. Alberta, Canada.
Another course using our book (2nd Ed.) at Montana, with HW and exams.
- Linear methods in
applied mathematics by Harrell and Herod, from Georgia Tech,
covers most of our course,
esp. Ch.4 and 6, including much more material.
- Linear PDEs course from MIT, with lecture notes and HW.
Math 4348
course with lecture notes on integral equations, PDEs and Greens functions,
from Georgia Tech.
- Principles of Applied Mathematics course at MIT,
just HW and exams.
Also Introduction to Modeling and Simulation,
has lecture notes and HW.
- General notes on exam and study
technique (geared mainly towards final exams in intermediate-level math courses).
Tools
-
Java applet versions of
dfield and pplane
that let you numerically explore 1-variable and 2-variable ODEs.
- my Matlab demo of 2nd-order singularly-perturbed 2-point BVPs,
showing boundary layer behavior:
bdrylayerdemo.m
- Matlab demo of relative accuracy of WKB approximations to
eigenvalues converging as O(1/n2):
wkb_acc.m and shooting.m (it would be probably better to recode this using bvp4c; somebudy have a try...)
- MAPLE tutorials;
MAPLE is useful for symbolic calculation and is free to use on campus,
download here.
