Professor David Blecher
Welcome to Advanced Multivariable Calculus
Class time and place: MoWeFr 12:00PM - 1:00PM in PGH 348
Office Hours Mo-We 11-12 (or by
appointment)
Students in this course should keep monitering this website,
particularly just before tests
(for example if there is a last minute change in a test date)
Last day to drop the class and get a full refund is January 28, at 5pm.
After that date there are no refunds.
Please review 1.1-1.4 in the text on your own.
(Note from Feb 20:) The students main job right now towards preparing for Test 1 is to be reading all
notes thoroughly, and assimilating and understanding everything.
Memorize all definitions and the statements (not proofs yet)
of all facts, theorems, propositions, corollaries, lemmas etc.
The test will be shortly after I return, and if you do not start the
memorization/assimilation process now, you will have a very hard time doing
it just before the test. And of course complete homework assignments
(I distributed HW 5 which will keep you going for quite a while, as well
as a key to HW 3). Go carefully through all keys, learning from them.
Homework 5: Shortened list to be turned in Wednesday March 12 :
Q 1: 5a, 8b, 10c,12c,16b,18,25, 26. Q2. Q3. Q5: 4b,d from 2.3; 2c, 3c, 10,
25,26 from 2.5.
Test 1 is on Monday March 24 in class.
To study for Test 1: Test 1 will cover up till
and including the chain rule. Read classnotes several times,
assimilating and understanding everything.
Memorize all definitions
and statements of Facts, Theorems, Propositions, Corollaries, etc.
Carefully review all homework,
and their keys,
learning from your mistakes. Understand how the concepts fit together.
Memorize proofs from the list in the next paragraph.
Do mock exam below after you have
finished studying, as a reality check, then as a guide to what you
should spend more time studying.
List of proofs from classnotes
to study for Test 1:
Cauchy-Schwarz inequality, the triangle inequality, B(x,r) is open, the Heine-Borel
theorem, Bolzano-Weierstrass theorem, the fact that a sequence in R^n converges
to x iff each `coordinate' converges to the matching `coordinate' of x,
the characterization of the closure and of closed sets in terms of sequences (2/6/08),
(i) iff (ii) in the `main' theorem about limits, (i) iff (ii) in
the `main' theorem about continuity, limits and continuity for
f + g, f . g , f/g, f o g$ (2/13/08), f(K) is compact if K compact and f
continuous, the Min-Max theorem. Then from the typed notes while I was away:
Prop 2.2, Prop 2.3, Theorem 2.4, Theorem 2.5 (see classnotes from 3/10 and HW 5).
-
The key for HW 5 (except the last question or so)
List of proofs from classnotes
to study for Test 2 (on Final):
the fact that the derivative of A x + b is A (a matrix), the mean value
theorem proved in class (involving a line segment in n-space), Corollary 3.4 and 3.5,
from the typed notes while I was away, proof of the Calc 3 first and second derivative tests
(not including the lemma about when a 2x2 matrix is positive definite), the
proof that `Riemann's condifion' is equivalent to f being integrable,
a continuous function on a compact set is uniformly continuous,
a continuous function on a compact box is integrable, Properties of
the integral (except parts (6) and (8)), Fubini's theorem, Calc 1 integration
by substitution and integration
by parts. You also need to refresh yourself on the list
of proofs for test 1. Again, first read through to understand these proofs. Then memorize them by writing them down
each many times until you can write them quickly and accurately. I require this
memorization of proofs in large
part to force the students to `internalize' the subject.
Please turn in Homework 7 by Wednesday or so, and get it back before the final.
Note that this mock exam together with the mock exam for test 1,
should be taken as a mock exam for the final.
More information, mock exams, etc will be added to constantly here below.
For example I hope to say how many quizzes/homework will
be dropped.