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Complex Variables with Applications >> Content Detail



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The readings below were found in the textbook: Amazon logo 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 #TOPICSreadingsreading assignments
I. Complex Algebra and Functions
1Algebra 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
2cis(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
3Functions of Complex Variable

Analyticity
Read 2.1 - 2.3p56: 4, 5

p63: 6, 7, 11cd

p70: 4, 7c, 13, 15
4Cauchy-Riemann Conditions

Harmonic Functions
Read 2.4, 2.5
p77: 1, 3, 6, 8, 11

p84: 2, 3bc, 6, 9, 12, 18
5Simple Mappings: az+b, z2, √z

Idea of Conformality
Skim pp. 377-79, 383-87p57: 7, 8, 9, 11,13

p71: 8

p392: 1, 3ae
6Complex ExponentialReread 1.4

Begin 3.2
p32: 20a, 23a

p115: 3, 5ab, 9a, 14a, 17ab, 20
7Complex Trigonometric and Hyperbolic FunctionsFinish 3.2p115: 5cdef, 11, 14bcd, 17c, 18b, 23
8Complex LogarithmRead 3.3p123: 1, 4, 5, 6, 8, 11, 12, 19
9Complex Powers

Inverse Trig. Functions
Read 3.5p136: 1, 4, 5, 7, 9, 11, 19
10Broad Review ... Probably focusing on sin-1z
II. Complex Integration
11Contour IntegralsRead 4.1, 4.2p160: 2, 4, 5, 13

p171: 3b, 6c, 9, 10, 11, 14
12Path IndependenceRead 4.3

Skim 4.4a
p178: 1aeh, 2, 5, 6, 7, 11
Exam 1
13Cauchy's Integral TheoremRead 4.4bp200: 6, 9, 10, 13, 15, 17, 18, 20
14Cauchy's Integral Formula

Higher Derivatives
Read 4.5p212: 1, 3abd, 5, 6, 8, 13
15Bounds

Liouville's Theorem

Maximum Modulus Principle
Read 4.6p219: 1, 7, 10, 14, 15, 16, 18
16Mean-value Theorems

Fundamental Theorem of Algebra
Skim 4.7p225: 4, 6, 7, 11 + 14?!
17Radius of Convergence of Taylor SeriesRead 5.2, 5.3p249: 1ad, 4, 5be, 11ab, 18a

p259: 7, 13a
III. Residue Calculus
18Laurent SeriesRead 5.5p276: 3, 5, 6, 7a, 10
19Poles

Essential Singularities

Point at Infinity
Read 5.6, 5.7p285: 1, 2, 3, 5, 8, 12

p117: 25

p290: 1, 4, 6
20Residue Theorem

Integrals around Unit Circle
Read 6.1, 6.2p313: 1adq, 3abce, 5, 7

p317: 2, 6, 9
21Real Integrals From -∞ to +∞

Conversion to cx Contours
Read 6.3p325: 1, 4, 6, 10, 11, 13
22Ditto ... Including Trig. Functions

Jordan's Lemma
Read 6.4p336: 1, 3, 7, 11, 12
Exam 2
23Singularity on Path of Integration

Principal Values
Read 6.5p344: 1a, 3, 5, 10, 12
24Integrals involving Multivalued FunctionsRead 6.6

Skim 6.7
p354: 1, 2, 4, 8, 10, 13

p364: 7, 8, 9 (all 3 w/o Rouche!)
IV. Conformal Mapping
25Invariance of Laplace's EquationRead 7.1p374: 1, 3, 4
26Conformality again

Inversion Mappings
Read 7.2+3 to p389p382: 1b, 3, 7*, 11, 13 (* see also p57: 6 + p85: 11)
27Bilinear/Mobius TransformationsFinish 7.3

Skim 7.4
p392: 3cd, 6, 7b, 8, 11

p405: 18
28Applications IRead 7.6430: 1, 2, 3, 6, 10

p416: 4(!)
29Applications IIRead 7.7p440: 3, 5, 6
V. Fourier Series and Transforms
30Complex Fourier SeriesRead 8.1 to p453p459: 1a, 2ac, 5, 7ac
31Oscillating Systems

Periodic Functions
Skim 3.6p143: 1b, 3, 5

p393: 13(!)

p461: 9, 10
32Questions of Convergence

Scanning Function

Gibbs Phenomenon
Finish 8.1p460: 3, 6, 8, 11
33Toward Fourier TransformsRead 8.2p473: 1abd, 2, 3abc
34Applications of FTsRead 8.2 againp473: 6abc, 7, 8
Exam 3
35Special Topic: The Magic of FFTs IReread pp. 457-59p462: 12(!)
36Special Topic: The Magic of FFTs II
Final Exam

 








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