Textbook? You are not required to buy a specific textbook for this course,
but I am aware that many students will find it convenient to have a
textbook, and so I usually would recommend having one.
If you come from M148 or M142 in Spring 2015, you may already have
Rogawski. This book covers most of what I do in the course, but (as most Calc
1-3 textbooks) has a few mismatches for the purpose of this course; namely
it is a bit skimpy in its use of matrix formalism and simplifies the 2nd
derivative test for minimax problems in a way that obfuscates conceptual
clarity. If you can live with this mismatch and rely on notes I am handing out,
Rogawski (or similar books like eg Stewart) will work.
The book that is the closest match to the philosophy of the course is by
Marsden and Tromba: the title is `Vector Calculus' (also published by Freeman).
There is no need to get the latest edition; rather I recommend to get an older
edition for cheap. As I am writing this, I find the 4th and 5th editions (1993
and 1996) on amazon used with sufficient supply in the 5-30 dollar range.
The purpose of the textbook is that it should be a reference for you; preferably one that you'd like to keep for later and that should not bind so much capital such as to dissuade you from keeping it.
I will hand out some notes of my own (in a terser style than the standard textbooks), and I am making up my own homework.
M247 and M251/M257: According to our catalog, neither is MV Calculus (241 or 247) a prerequisite for Linear Algebra (251 or 257), nor is Linear Algebra a prerequisite for MV Calculus. I think this is unfortunate, but we have to live with it. I will start out with maybe a week's worth of vector and matrix material for use in MV calculus, to make the logical connection to linear algebra as needed by the material. Many of the MV textbooks will not use matrices, but this can be fixed in the lecture quickly. If you can schedule it and have not taken 251 or 257 yet, you may gain some synergetic effects by taking Linear Algebra (also called Matrix Algebra) along with MV Calculus; but you are not required to do so, as I will cover the needed material independently.
Syllabus --- Also refer to the Campus Syllabus for general info.
The Class Diary will tell what was covered each day, and what homework was assigned.
Some notes for the first few class meetings of
the semester (Vectors and points and their use for MV functions.
Coordinate transformations. Continuity. Open, closed, boundary)
Derivatives for multi-variable functions (handing out up to page 18 by Sep 14; more to be handed out later)
For graphing in polar coordinates, you may want to print out this sheet of polar coordinate paper (pdf) (you do need a ruler, though) --- same in PostScript
For precise graphics in cartesian coordinates, you find here files that
print a decimal grid on
a sheet of paper, with the small square 1mm, 2mm or 3mm sidelength.
I tested the postscript version of the files on one laser printer.
The quality of the actual outcome may be hardware dependent.
| size | PostScript | |
|---|---|---|
| 1mm | 1mm:ps | 1mm:pdf |
| 2mm | 2mm:ps | 2mm:pdf |
| 3mm | 3mm:ps | 3mm:pdf |
Homework assignments (as of 10/27: until number 42)
What is assigned with what due date will be mentioned in the class diary or announced to class by blackboard e-mail.
Here I will gradually gather a list of sample solutions:
Solutions to Hwk 1-5
Solutions to Hwk 6-9
Solutions to Hwk 10-13
Solutions to Hwk 14-18
Solutions to Hwk 19-22
cumulative sols to all hwk up to 30
Solutions to Hwk 31-39
Solutions to Hwk 40-47
More material coming in due time