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) turkey

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
  1. The most important thing for you to do is pick up a copy of the past written exams from Tamar's office!
  2. 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. 
  3. 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.
  4. 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.
  5. The best advice I can give you?  Do lots and lots of problems! 
just do it


links
  1. Evan Chou's Writtens Wiki
  2. Andrew Suk's Writtens Solutions
  3. Miranda Holmes' Fall 07 Written Workshop page



references

General
Calculus

Linear Algebra

Complex