| Lecture |
Date |
Topics covered |
Sections fromText and Section(Assigned
problem numbers parts)
|
| 1 |
01-20 |
Discussion of complex plane,
algebra of complex numbers, functions of a complex variable
|
21.1-21.2(6,9,11ab) (AEM) |
| 2 |
01-22
|
Elementary functions. Polar form
of complex numbers
|
21.3 (7,8)-21.4 (1,2,3,4,5) |
| 3 |
01-27
|
More on elementary functions.
Multivaluedness and branch cuts. |
21.3 (12,13,16abc) 21.4 (11) |
| 4 |
01-29
|
More on branch cuts. Regions.
Differentiability. C-R equations.
|
21.5
21.3(18d );
21.4 (11) |
| 5 |
02-03 |
More
on C-R equations. Analyticity.
|
21.5(2,5ab) |
| 6 |
02-05
|
Analyticity (cont).
|
21.5(9,10abc,11ab,13)
|
| 7 |
02-10 |
Introduction to conformal mapping.
|
22.1-22.2
21.5(10fg,15ad)
|
| 8 |
02-12 |
Conformal mapping (cont).
Bilinear transformations. |
22.3 22.2(1,4,5) |
| 9 |
02-17 |
Bilinear
transformations (cont). Separation of variables. Laplace's equation.
Polar coordinates. |
22.4-22.6 22.3(10ac,12,14) |
| 10 |
02-19 |
Multivalued function,
applications. Dirichlet, Neumann boundary conditions. Applications. |
22.4(4a) 22.5(3b) 22.6(2a) |
| 11 |
02-24 |
More
discussions
|
|
| 12 |
02-26 |
Review
for exam 1.
|
|
| 13 |
03-02
|
Exam
1.
|
Through 22.3 (AEM) |
| 14 |
03-04
|
Brief discussion of exam.
Introduction to complex integration. Cauchy's theorem. |
23.1-23.3 23.2-(3dg) 23.3(4ag,9b) |
| 15 |
03-09 |
Fundamental theorem of complex
integral calculus. Cauchy's integral formula. |
23.4-23.5 23.4(3d) 23.5(1ae,2,4a)
|
| 16 |
03-11 |
Generalized Cauchy
integral formula. Complex power series. Taylor series.
|
24.1-24.2 24.2(5acfh, 6aceh) 23.5(1ae,2,4a)
|
| 17 |
03-23 |
Complex Taylor series
(cont). Laurent series.
|
24.3 24.2(8ac, 9ab,10,11be,13a,16acdg) |
| 18 |
03-25 |
Taylor and Laurent series (cont).
|
24.3(4adeh,5ae,6) |
| 19 |
03-30
|
Classification of singularities
of functions of a complex variable. Residue theorem
|
24.4-24.5 24.4(2acde,3adg,5acd) 24.5(1a) |
| 20 |
04-01 |
More discussions
|
|
| 21 |
04-06 |
Applications
of residue theorem.
|
24.5(1d,2d,3j,5c,6b) |
| 22 |
04-08 |
Residue
theorem and applications (cont). Review for secon exam
|
|
| 23 |
04-13 |
Second
midterm.
|
Through 24.3 (AEM)
|
| 24 |
04-15 |
Brief discussion of exam 2.
Introduction to calculus of variations. Lagrange multipliers.
|
2.2 (MAM)
(Ch2, p195 :8,9)
|
| 25 |
04-20 |
Stationary functions. Euler's
equation.
|
2.2-2.3 Ch2, p195-6 :10,15) |
| 26 |
04-22 |
Variational notation. Constraints
and Lagrange multipliers.
|
2.4-2.9
|
| 27 |
04-27 |
Hamilton's prnciple. Lagrange's
equations
|
2.10-2.11
|
| 28 |
04-29 |
Final
review.
|
|