Lecture 
Date 
Topics covered 
Sections fromText and Section(Assigned
problem numbers parts)

1 
0120 
Discussion of complex plane,
algebra of complex numbers, functions of a complex variable

21.121.2(6,9,11ab) (AEM) 
2 
0122

Elementary functions. Polar form
of complex numbers

21.3 (7,8)21.4 (1,2,3,4,5) 
3 
0127

More on elementary functions.
Multivaluedness and branch cuts. 
21.3 (12,13,16abc) 21.4 (11) 
4 
0129

More on branch cuts. Regions.
Differentiability. CR equations.

21.5
21.3(18d );
21.4 (11) 
5 
0203 
More
on CR equations. Analyticity.

21.5(2,5ab) 
6 
0205

Analyticity (cont).

21.5(9,10abc,11ab,13)

7 
0210 
Introduction to conformal mapping.

22.122.2
21.5(10fg,15ad)

8 
0212 
Conformal mapping (cont).
Bilinear transformations. 
22.3 22.2(1,4,5) 
9 
0217 
Bilinear
transformations (cont). Separation of variables. Laplace's equation.
Polar coordinates. 
22.422.6 22.3(10ac,12,14) 
10 
0219 
Multivalued function,
applications. Dirichlet, Neumann boundary conditions. Applications. 
22.4(4a) 22.5(3b) 22.6(2a) 
11 
0224 
More
discussions


12 
0226 
Review
for exam 1.


13 
0302

Exam
1.

Through 22.3 (AEM) 
14 
0304

Brief discussion of exam.
Introduction to complex integration. Cauchy's theorem. 
23.123.3 23.2(3dg) 23.3(4ag,9b) 
15 
0309 
Fundamental theorem of complex
integral calculus. Cauchy's integral formula. 
23.423.5 23.4(3d) 23.5(1ae,2,4a)

16 
0311 
Generalized Cauchy
integral formula. Complex power series. Taylor series.

24.124.2 24.2(5acfh, 6aceh) 23.5(1ae,2,4a)

17 
0323 
Complex Taylor series
(cont). Laurent series.

24.3 24.2(8ac, 9ab,10,11be,13a,16acdg) 
18 
0325 
Taylor and Laurent series (cont).

24.3(4adeh,5ae,6) 
19 
0330

Classification of singularities
of functions of a complex variable. Residue theorem

24.424.5 24.4(2acde,3adg,5acd) 24.5(1a) 
20 
0401 
More discussions


21 
0406 
Applications
of residue theorem.

24.5(1d,2d,3j,5c,6b) 
22 
0408 
Residue
theorem and applications (cont). Review for secon exam


23 
0413 
Second
midterm.

Through 24.3 (AEM)

24 
0415 
Brief discussion of exam 2.
Introduction to calculus of variations. Lagrange multipliers.

2.2 (MAM)
(Ch2, p195 :8,9)

25 
0420 
Stationary functions. Euler's
equation.

2.22.3 Ch2, p1956 :10,15) 
26 
0422 
Variational notation. Constraints
and Lagrange multipliers.

2.42.9

27 
0427 
Hamilton's prnciple. Lagrange's
equations

2.102.11

28 
0429 
Final
review.

