midtermmaterial

# midtermmaterial - harmonic functions, harmonic conjugates,...

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ACM 95a/ACM 100a Midterm Information Topics Introduction to complex numbers, polar form, Euler's formula, the complex exponential, trigonometric functions, deMoivre's formula, integer powers and roots, the complex logarithm, multiple-valuedness, periodicity, complex exponents, inverse trigonometric functions, one-to-one mappings, Riemann surfaces, the point at infinity, the stereographic projection, branch points and branch cuts, branch point at infinity, regions of the complex plane, limits and continuity, the complex derivative, analyticity, the Cauchy-Riemann equations, complex integration, parameterization, contours, fundamental theorem for contour integration, equivalence between existence of antiderivatives, vanishing of closed contour integrals and independence of path, the Cauchy-Goursat theorem, extensions to self-intersecting contours and multiply-connected domains, deformation of contours, Cauchy integral formula, derivatives of analytic functions, generalized Cauchy integral formula, Morera's theorem, Cauchy's inequality, Liouville's theorem,
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Unformatted text preview: harmonic functions, harmonic conjugates, potential flow applications. Midterm review session Friday 10/31 at standard lecture time and location Exam Available online at 3pm on Friday 10/31 Due at 3pm on Tuesday 11/4 in the slot of Firestone 303 Exams should be completed in a single sitting (number of hours TBA) Closed-book: with the exception of official lecture handouts and problem set questions, only material written in your own hand or typed by your own hand may be used during the exam Calculators are not permitted Be sure to photocopy Problem Set 4 before you turn it in so that you will have it available during the exam Please use standard blue books and write your name and grading section number on each booklet. Grading section numbers are automatically assigned to you after you create a login account on the ACM95a/100a Underground web site. This can be reached at: https://secure.acm.caltech.edu/underground/ Extensions only with permission of the Dean...
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## This note was uploaded on 01/14/2010 for the course ACM 1 taught by Professor Prof during the Fall '09 term at Caltech.

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