# 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.