Written Exam Workshop
Fall 2009
Will Perkins
perkins@cims.nyu.edu
office 1111
office hours: Mondays, 7 - 8 pm (note
the change)
schedule
practical information
links
references
schedule
Week 1 (9/17) - Calculus
Topics: Limits and Series; tests of convergence
Worksheet
Week 2 (9/24) - Calculus
(there will be a subsitute instructor this week)
Topics: Multivariable calc; Green's / Stokes' / Divergence
Theorem. Polar / spherical coordinates. Tangents, normals,
Implicit Function Theorem. Optimization Problems.
Worksheet
Homework (for today): S07 #2, S06 #3, S05 #4, J05#4, S03 #5,
S03 #4
Week 3 (10/1) - Linear Algebra
Topics: Solving Linear Equations; Det, Trace, Characteristic
Poly; Diagonalizing; Block Matrices; Projections
Worksheet
Homework: S98 #5, J00 #3, J02 #1, S02 #2, S03 # 1, J07 #1
Week 4 (10/8) - Advanced Calculus
Topics: Improper Integrals, Limits of Integrals,
Infinite Products.
90-second student presentations on special types of matrices
Worksheet
Homework: S03 #1, J07 #2, J04 #2, J99 #2, S98 #4, S98 #3, S96 #1
Week 5 (10/15) - Complex
Topics: Conformal Maps; Liouville's Theorem; Schwartz's
Lemma; Rouche's Theorem
Worksheet
Homework: S07 #3, S07 #4, S07 #5, J07 #4, J06 #5, S05 #5
Week 6 (10/22) - Linear Algebra
Topics: Decompositions; Graham Schmidt; Rayleigh Quotient
Worksheet
Homework: J07 #4, J07 #5, S04 #3, J04 #3, J01 #4, J98 #5
Week 7 (10/29) - Advanced Calculus
Topics: Optimization, Functional Equations, Fourier Stuff,
Worksheet
Homework:
Week 8 (11/5) - Complex
Topics: Analytic continuation, branch cuts,
Schwartz-Christoffel mapping,
Worksheet
Homework: J98 #4, S98 #5, S99 #4, J01 #1, J02 #5, J02 #1
Week 9 (11/12) - Advanced Calculus
Topics: More Multivariable Calculus
Worksheet
Homework: No specific problems assigned - we'll be going over the basic
methods. But look through the past problems and come in with any
that you have questions about.
Week 10 (11/19) - Linear Algebra
Topics: Jordan form, least squares, + assorted
problems
Worksheet
Homework: J 98 #2, J 96 #4, S 96 #3, J 97 #2, J 99 #5, J 02
#2, J 06 #5
Thanksgiving (11/26) 
Week 11 (12/3) - Complex
Topics: Harmonic functions, Poisson Integral Formula,
Infinite Products,
Worksheet
Homework: S95 #4, S99 #5, J03 #4, J05 #5, S05 #4, J07 #2
Week 12 (12/10) - Review
Topics: Review of all 3 subjects + practice problems
of crucial types.
REVIEW SHEET
Homework: Prepare and bring to class an outline of each subject,
dividing it into different categories and types of problems.
For the types of problems you still need to review, add references and
practice problems.
practical information
- The most important thing for you to do is pick up a copy of the
past written exams from Tamar's office!
- Each week I'll assign 6 or so past written exam problems to do
for the next week. I strongly enocurage you to do/try them.
We'll go over the key points of the solutions in class , but if you'd
like to see the details flushed out, just stop by my office.
- Please print out the worksheet and any handouts before each
class. I'll bring a few copies in case you forget, but not enough
for the whole class.
- Give me lots of feedback about what you want covered, how fast
we're going, etc. The mix of the topics covered should depend on
what you guys want to learn.
- The best advice I can give you? Do lots and lots of
problems!
links
- Evan Chou's Writtens
Wiki
- Andrew Suk's Writtens
Solutions
- Miranda Holmes' Fall 07 Written
Workshop page
references
General
Calculus
- Advanced
Calculus
,
Buck. Spells out some of the more difficult techniques of taking
limits of integrals.
- Differential
and Integral Calculus (2 Volume Set)
, Courant. Besides writing this
excellent book,
the author also founded this school.
- Div,
Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth
Edition
,
Schey. Useful if, like me, you are completely lost when calculus
and vectors meet.
Linear Algebra
Complex
,
De Souza & Silva. A ton of collected problems from Berkeley's
version of the written exams, with solutions. Not quite the same
topics as we have, but a good place to see a lot of useful
techniques. 
, Polya & Szego. Sort of
old-timey and more
difficult than the problems you'll see, this does contain some problems
that have appeared before and is written by the master problem solver.
,
Strang. Thorough and readable of the basics.
,
Lax. Good on the abstract stuff. You can also get your copy
autographed here if you're lucky.
,
Trefethen & Bau. Very good on some of the stuff you won't see
in the introductory class: the different decompositions, like SVD,
Choelesky, etc. Very useful!
, Churchill & Brown. The
complex analogue
of Strang.
,
Conway. My personal favorite.