The exam will cover the material in lectures 1 through 11 as supplemented by material in the textbook. A discussion of the principal themes of the course so far is below, along with some specific references and corresponding problems.
The exam is scheduled for 80 minutes, from 5:00 to 6:20 PM on Wednesday, March 3, in our usual classroom.
The cover sheet for your exam will state:
Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. |
Here are some previous exams and review material that I've given in this course, going backwards in time (most recent is first). The various instantiations of the course have varied in emphasis, and I will try to address the relevance of these references below.
Old problems in relation to our syllabus
Here is a list of problems from this material "keyed" to major themes
discussed so far in the course. This may be useful to you. Lectures
are available here.
| Themes | References | Specific problems |
|---|---|---|
| The algebraic preliminaries, Δ≤, and various definitions and novelties; mapping properties of elementary functions: DeMoivre, zn (n=2,3...,–1,...,½,...); {l|L}ogs and {a|A}rgs, exp, sin ... | Sections 1.1–5; lectures 1–5, 9, and 11. | A1,2,3,6; B1,2,5,6; C1,2,5,6,7,8; D1,2,4,6. |
| Line integrals: preliminaries and computation | Sections 1.6 and 2.3 (statement of Cauchy's Theorem); lectures 6–8. | A4; B7; C11; D8. |
| Estimating complex line integrals | Section 1.6; lecture 8. | A7; B8; C12; D8. |
| The Cauchy-Riemann equations and complex differentiability | Section 2.1; lectures 8–10. | B3; C9; D5. |
| Harmonic functions (an introduction) | Section 2.1; lecture 10. | A5; B4; C10; D3. |
| Power series (an introduction) | Sections 1.5 and 2.2; lectures 6 and 11. | A8; B9; C3,4; D7. |
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