MATH 366, Honours Complex Analysis, Fall 2007

Course web page: http://www.math.mcgill.ca/jakobson/courses/math366.html

Lectures: MWF 11:30-12:30, Burnside 920
Tuesday, October 9, 11:30-12:30, Burnside 920
Instructor: D. Jakobson
Office: BH1212, Office Hours: M 13:00-14:00, W 12:30-13:30 (may be adjusted), or by appointment
Tel: 398-3828
E-mail: jakobson AT math.mcgill.ca
Web Page: www.math.mcgill.ca/jakobson
Prerequisite: Math 248. Co-requisite: Math 354
Marker: Tayeb Aissiou
Email: aissiou@math.mcgill.ca
Text
  • Required: T. Gamelin. Complex analysis. Undergraduate Texts in Mathematics. Springer-Verlag
  • Recommended: Ahlfors, Complex Analysis (on reserve in the library).
    • Syllabus: Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouche's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.

    Tests
  • The midterm will be held on Monday, Ocotber 29, 16:30-18:00, Burnside 1B39
  • Midterm solutions: pdf and ps
  • Take-home midterm, due Friday, November 9, by 5pm: pdf and ps.
  • Your midterm grade will be the best of the 2 grades: for in-class or for take-home midterm.
  • There will be a final exam on December 10, 2-5pm, Room 1B24.
  • Practice problems for the final: pdf and ps.
  • A summary of things to review: pdf and ps.
    • Grading: Your final mark will be the largest of the following: [20% Assignments + 30% Midterm + 50% Final]; OR [20% Assignments + 80% Final].
    WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT
    Supplemental There will be a supplemental exam, counting for 100% of the supplemental grade. No additional work will be accepted for D, F or J.
    Homework will be assigned in class and will be due by 5pm by the specified deadline. There will be a 50% deduction for late homework.

    Various math announcements

  • PUTNAM - contact Jim Loveys (loveys@math)

    Handouts

  • Point set topology and metric spaces handout (for math 466): postscript and pdf.
  • Differentiation under the integral sign handout (for math 466) (postscript, pdf)
  • Pages about simply-connected domains in Wikipedia and in Wolfram Mathworld
  • Pages about path homotopy (continuous deformation) in Wikipedia
  • Conservative vector fields, notes by L. Laayouni for Math 264. Note that conservative vector fields in the plane are the same thing as exact differentials, and a necessary condition for the vector field to be conservative is that the corresponding differential is closed.
  • Line Integrals, notes by L. Laayouni for Math 264.
  • Green's theorem, notes by L. Laayouni for Math 264.

    • Assignments

  • Problem Set 1 (due Monday, September 17 by 5pm): ps and pdf.
    Do any 10 problems:
  • Gamelin, section I.1, # 5, 7. section I.2, # 2abc, 5. section I.4, # 1ade, 3. section I.5, # 2ace. section I.6, # 1cd, 2bd.
  • Prove that the mapping z->(az+b)/(cz+d), ad-bc>0, maps the complex upper half-plane to itself.
  • Prove that all circles passing through the points a and 1/\bar{a} intersect the unit circle at right angles.
  • Problem 12 (iterations of the square function).
  • Extra credit: section I.3, #5.
  • Solutions to Problem Set 1: ps and pdf
  • Problem Set 2 (due Friday, September 28 by 5pm): ps and pdf.
  • Solutions to Problem Set 2: pdf
  • Problem Set 3, due Wednesday, October 17, by 5pm: ps and pdf.
  • Solutions to Problem Set 3: ps and pdf
  • Problem Set 4, due Monday, November 12, by 5pm: ps and pdf.
  • Solutions to Problem Set 4, part I: ps and pdf; and part II: ps and pdf
  • Problem Set 5, due date to be announced: ps and pdf.
  • Solutions to Problem Set 5: ps and pdf
  • Problem Set 6, due date to be announced: ps and pdf.
  • Solutions to Problem Set 6: ps and pdf

    • Web Links

    Complex Analysis:
  • McGill Analysis Seminar
  • Function viewers: an applet
  • Stereographic projection.
  • Spirographs: applet 1 and applet 2.
  • A nice links page.
  • Douglas Arnold's Graphics for Complex Analysis: java or non-java.
  • Curt McMullen's gallery.
  • Minnesota Geometry Center graphics page.
  • A web page on quaternions etc
  • Descriptions of the Mandelbrot and Julia sets.
  • Java applets for drawing the Mandelbrot set: applet 1 and applet 2.
  • Java applets for drawing Julia sets: applet 1, applet 2 and applet 3.
  • Computer code for drawing the Mandelbrot and Julia sets: Java You can also download programs from some of the sites above and from this list.
    • Functional Intro to Analysis and Topology (bottom of the page), this is my old math 354 page
    Calculus, Algebra, Geometry and Differential Equations
    HELPDESK and their email: helpdesk@math.mcgill.ca
    NOTICE: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).