Calendar: MAT 421-01 Fall 2009

• 1st Week: Aug. 31 - Sept. 4
  • Monday: Read sec I.1, I.2 in the text. Homework: do problems sec. I.1 #1a,b,d,j, 3, 6, 8, 9.
  • Wednesday: Do problems Sec. I.2 1f, 2b, 3, 7, 8. Start reading sec. I.3
• 2nd Week: Sept. 7 - 11
  • Monday Sept. 7: Labor Day holiday. No classes.
  • Wednesday:
• 3rd Week: Sept. 14 - 18
  • Monday: I.3 #1, 2, 4 Due next Monday.
  • Wednesday: I.4 #1, 2 Due next Monday.
• 4th Week: Sept. 21 - 25
  • Monday: I.5 #1c-f, 2 and I.6 #1a,d, 2, 4. Due Wednesday Sept 30.
  • Wednesday: Read sect I.7 through Phase Change Lemma (pg. 26). We'll finish this on Monday. On Monday I will assign problems from I.7 so if you have time you may want to start on them now.
• 5th Week: Sept. 28 - Oct 2
  • Monday: I.7 #1-6. Due Monday Oct. 5
  • Wednesday: Today we went to the computer lab in WH F154 and practiced making plots using the Mathematica computer package. Click this complexPlots.pdf to obtain a copy of the notes in *.pdf format which you may read with Adobe Acrobat reader, or click here complexPlots.nb to obtain a file that you read with Mathematica and also run the commands or change them to see what happens. The sliders only work when you are running Mathematica, the *.pdf document is not dynamic.

    CSU Dominguez students may obtain a free copy of Mathematica by following the instructions in the notes, or look on my website for MAT 153 and follow the link. Mathematica is not required for this course, but it is available if you want to use it.

• 6th Week: Oct. 5 - 9
  • Monday: Complex derivatives and their relation to functions on R^2. Cauchy-Riemann equations.
  • Wednesday: Review calculus III. Functions on R^2
• 7th Week: Oct. 12 - 16
  • Monday: Calculus III review cont. functions on R^2, their derivatives, derivatives of functions on C, Cauchy-Riemann equations again.
  • Wednesday: Calculus III review cont. gradient, divergence, harmonic functions and potentials. Sec II.2 Analytic functions.
• 8th Week: Oct. 19 - 23
  • Monday: Section II.3 Cauchy-Riemann equations, mainly theorem on p. 49: if f'(z)=0 on a domain then f is constant there. Begin sec. II.4: example plotting gradient fields. If f=u+iv is analytic then grad(u) is perpendicular to grad(v), level curves of u are streamlines of grad(v) and vice-versa. . Homework: II.3 #3-7 (additional hint on #4: use result from #3). Also II.4 #1
  • Wednesday:
• 9th Week: Oct. 26 - 30
  • Monday: Section II.6 Conformal mappings
  • Wednesday: Meet in WH C-155 computer lab to plot some level curves from the exercises in sect. II.6. Here are some notes. If you want to see the commands that produced the graphs download the Mathematica notebook version of the notes and open it with Mathematica.
  • Homework II.6 #6,7.
• 10th Week: Nov. 2 - 6
  • Monday: II.7 Fractional Linear Transformations. Homework: II.7 #1a,b, 2, 3
  • Wednesday: III.1 Line integrals and Green's theorem. Start III.2 Independence of path. (These sections are more calculus III review.). Homework III.1 #1-6. Due Monday Nov. 30.
• 11th Week: Nov. 9 - 13
  • Monday: More on Green's theorem.
  • Wednesday Nov. 11. Veterans' Day Holiday. No classes.
• 12th Week: Nov. 16 - 20
  • Monday: Green's theorem again.
  • Wednesday: Green's theorem again. Homework III.2 #1c,d. Due Monday Nov. 30.
  • There is a test Monday! Test review
• 13th Week: Nov. 23 - 27
  • Monday: Test.
  • Wednesday:
• 14th Week: Nov. 30 - Dec. 4
  • Monday:
  • Wednesday:
• 15th Week: Dec. 7 - Dec. 22
  • Monday:
  • Wednesday:
• 16th Week: Dec. 14 - Dec. 18
  • Final Exam Monday Dec 14 4-6pm