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Readings

The readings below were found in the textbook: Saff, Edward B., and Arthur David Snider. Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 2002. ISBN: 0139078746. The problems bold-faced below seemed especially well suited for the students' practice and for discussion at the recitations.

lec #	TOPICS	readings	reading assignments
I. Complex Algebra and Functions
1	Algebra of Complex Numbers Complex Plane Polar Form	Read 1.1 - 1.3	p5: 8, 9,24 p12: 6, 7fq,16 p22: 6, 7eq, 8, 11, 17
2	cis(y) = exp(iy) Powers Geometric Series	Read 1.4, 1.5	p31: 1, 3, 4, 11, 12a,14 p37: 4, 5d, 9, 10, 11, 21b
3	Functions of Complex Variable Analyticity	Read 2.1 - 2.3	p56: 4, 5 p63: 6, 7, 11cd p70: 4, 7c, 13, 15
4	Cauchy-Riemann Conditions Harmonic Functions	Read 2.4, 2.5	p77: 1, 3, 6, 8, 11 p84: 2, 3bc, 6, 9, 12, 18
5	Simple Mappings: az+b, z², √z Idea of Conformality	Skim pp. 377-79, 383-87	p57: 7, 8, 9, 11,13 p71: 8 p392: 1, 3ae
6	Complex Exponential	Reread 1.4 Begin 3.2	p32: 20a, 23a p115: 3, 5ab, 9a, 14a, 17ab, 20
7	Complex Trigonometric and Hyperbolic Functions	Finish 3.2	p115: 5cdef, 11, 14bcd, 17c, 18b, 23
8	Complex Logarithm	Read 3.3	p123: 1, 4, 5, 6, 8, 11, 12, 19
9	Complex Powers Inverse Trig. Functions	Read 3.5	p136: 1, 4, 5, 7, 9, 11, 19
10	Broad Review ... Probably focusing on sin^-1z
II. Complex Integration
11	Contour Integrals	Read 4.1, 4.2	p160: 2, 4, 5, 13 p171: 3b, 6c, 9, 10, 11, 14
12	Path Independence	Read 4.3 Skim 4.4a	p178: 1aeh, 2, 5, 6, 7, 11
	Exam 1
13	Cauchy's Integral Theorem	Read 4.4b	p200: 6, 9, 10, 13, 15, 17, 18, 20
14	Cauchy's Integral Formula Higher Derivatives	Read 4.5	p212: 1, 3abd, 5, 6, 8, 13
15	Bounds Liouville's Theorem Maximum Modulus Principle	Read 4.6	p219: 1, 7, 10, 14, 15, 16, 18
16	Mean-value Theorems Fundamental Theorem of Algebra	Skim 4.7	p225: 4, 6, 7, 11 + 14?!
17	Radius of Convergence of Taylor Series	Read 5.2, 5.3	p249: 1ad, 4, 5be, 11ab, 18a p259: 7, 13a
III. Residue Calculus
18	Laurent Series	Read 5.5	p276: 3, 5, 6, 7a, 10
19	Poles Essential Singularities Point at Infinity	Read 5.6, 5.7	p285: 1, 2, 3, 5, 8, 12 p117: 25 p290: 1, 4, 6
20	Residue Theorem Integrals around Unit Circle	Read 6.1, 6.2	p313: 1adq, 3abce, 5, 7 p317: 2, 6, 9
21	Real Integrals From -∞ to +∞ Conversion to cx Contours	Read 6.3	p325: 1, 4, 6, 10, 11, 13
22	Ditto ... Including Trig. Functions Jordan's Lemma	Read 6.4	p336: 1, 3, 7, 11, 12
	Exam 2
23	Singularity on Path of Integration Principal Values	Read 6.5	p344: 1a, 3, 5, 10, 12
24	Integrals involving Multivalued Functions	Read 6.6 Skim 6.7	p354: 1, 2, 4, 8, 10, 13 p364: 7, 8, 9 (all 3 w/o Rouche!)
IV. Conformal Mapping
25	Invariance of Laplace's Equation	Read 7.1	p374: 1, 3, 4
26	Conformality again Inversion Mappings	Read 7.2+3 to p389	p382: 1b, 3, 7, 11, 13 ( see also p57: 6 + p85: 11)
27	Bilinear/Mobius Transformations	Finish 7.3 Skim 7.4	p392: 3cd, 6, 7b, 8, 11 p405: 18
28	Applications I	Read 7.6	430: 1, 2, 3, 6, 10 p416: 4(!)
29	Applications II	Read 7.7	p440: 3, 5, 6
V. Fourier Series and Transforms
30	Complex Fourier Series	Read 8.1 to p453	p459: 1a, 2ac, 5, 7ac
31	Oscillating Systems Periodic Functions	Skim 3.6	p143: 1b, 3, 5 p393: 13(!) p461: 9, 10
32	Questions of Convergence Scanning Function Gibbs Phenomenon	Finish 8.1	p460: 3, 6, 8, 11
33	Toward Fourier Transforms	Read 8.2	p473: 1abd, 2, 3abc
34	Applications of FTs	Read 8.2 again	p473: 6abc, 7, 8
	Exam 3
35	Special Topic: The Magic of FFTs I	Reread pp. 457-59	p462: 12(!)
36	Special Topic: The Magic of FFTs II
	Final Exam