Math 136: Complex Variables and Integral Transforms
Fall 2004
Prof Lesley Ward

Welcome to the Math 136 Homepage!

Course hand-out with contact info, grading policy, etc.
Course schedule with day-by-day list of topics.
Math Dept guidelines on homework format. Please follow these.

Office hours with Prof Ward in Olin 1281. Please stop by often.
  • Mondays 1:15 - 2:30pm
  • Tuesdays 3 - 5pm
  • By appointment
To contact Prof Ward: ward@math.hmc.edu, x76019, Olin 1281.

Tutor/grader Carl Yerger. Carl's office hours:
  • Tuesdays 7:30 - 8:30pm, Mathematics Department Library.
    (It's in the basement of the Olin building.) TO BE CONFIRMED.
To contact Carl: Carl_Yerger@hmc.edu, x74741, Case 207.
Homework assignments.

Our textbook is Fundamentals of Complex Analysis for Mathematics, Science, and Engineering, 3rd edition, E.B. Saff and A.D. Snider, Prentice Hall, 2003. (New edition.)

Solutions to the previous homework assignments are available online. Also, here is a link to the front page of ERes: Electronic Reservations.
Hard copies are also on reserve in a binder at Sprague Library; ask for the Math 136 binder.

  • Homework 1 Due Fri 3 Sept, by 2:45pm, in my office (Olin 1281). Complex arithmetic.
  • Homework 2 Due Wed 8 Sept. Powers and roots, the Riemann sphere, complex functions, limits and continuity, analyticity.
  • Homework 3 Due Wed 15 Sept. The Cauchy-Riemann equations, harmonic functions, polynomials and rational functions, exponential, trig, and hyperbolic functions.
  • Homework 4 Due Wed 22 Sept. Logarithms, 'washers, wedges, and walls', complex powers, inverse trig and hyperbolic functions, contours.
  • Homework 5 Due Wed 29 Sept. Contour integrals, path-independence, Cauchy's Theorem (via Section 4.4b, not 4.4a).
  • No homework due Wed 6 Oct because of midterm.
    Midterm will be handed out in class on Wed 29 Sept, and is due in class on Monday 4 Oct.
    Here is a practice test.
  • Homework 6 Due Wed 13 Oct. Cauchy's Integral Formula and its consequences: bounds on analytic functions, harmonic functions.
  • Homework 7 Due Fri 22 Oct. (Extension to Friday because of fall break.)
    Sequences and series, Taylor series.
  • Homework 8 Due Wed 27 Oct. Power series, Laurent series.
  • Homework 9 Due Wed 3 Nov. Zeroes and singularities, the point at infinity, the Residue Theorem.
  • No homework due Wed 10 Nov because of midterm. Read Sections 6.2, 6.3.
    Midterm will be handed out in class on Wed 3 Nov, and is due in class on Monday 8 Nov. You may use Saff and Snider during the test, and you may also prepare one page of notes (both sides ok) to use during the test.
    If you need an extension (for instance because of the Subject GRE), please see Prof Ward.
    Here is a list of topics to study.
    Here is a practice test.
  • Homework 10 Due Wed 17 Nov. Trigonometric integrals, improper integrals of certain functions.
  • Homework 11 Due Wed 24 Nov by 2:45pm at my office. Improper integrals, Jordan's Lemma, indented contours, multiple-valued integrands.
    Note: We will not have class on Wed 24 Nov, because of the impending holiday. Happy Thanksgiving!
  • Homework 12 Due Wed 1 Dec. Conformal mapping, Moebius transformations.
  • Homework 13 Due Wed 8 Dec. Last one!! The Schwarz-Christoffel Transformation, conformal mapping applied to electrostatics, heat flow, and fluid mechanics, the Fourier transform.

    The final exam will be handed out in class on Wed 8 Dec, and is due in the Math Office by 5:30pm on Monday 13 Dec. (Note corrected date!)
    Here is a practice test.

Grading:
  • 25% for Homework: weekly, due in class on Wednesdays. (Except HW 1 due on Friday 3 September.)
  • 25% for first Midterm: distributed in class on Wednesday 29 September. Two-hour closed-book take-home test. Due in class, Mon 4 Oct.
  • 25% for second Midterm: distributed in class on Wednesday 3 November. Two-hour closed-book take-home test. Due in class, Mon 8 Nov.
  • 25% for Final: Three-hour closed-book take-home test. Due by 5:30pm on Monday 13 December.

Course Outline: Monday-Wednesday lectures
  1. Complex Numbers (1 lecture)
  2. Analytic Functions (2 lectures)
  3. Elementary Functions (2 lectures)
  4. Complex Integration (5 lectures)
  5. Taylor and Laurent Series (5 lectures)
  6. Residue Theory (4 lectures)
  7. Conformal Mapping (4 lectures)
  8. Integral Transforms (4 lectures)
+ 1 lecture for lag time = 28 lectures in all
Fun Links:
  • For some tips from students on how to succeed at Mudd,
    visit the `Wisdom from ... ' section of the Teaching and Learning Committee's webpage.
  • Don Marshall's home page Click on the Software by Graduate Students link, then on Pictures of Analytic Functions, for some great colour pictures. The Numerical Conformal Mapping link has material we'll be studying later in the course. Have a look at the airfoil.
  • Colour pictures of complex functions This page has graphs in C^2 (or R^4) of complex functions, using colour to indicate the fourth dimension. Developed by Thomas Banchoff and Davide Cervone.

Last modified December, 2004, by Ward.

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