Mathematics 39 - Complex Variables - Spring 2004
Professor Dan Sloughter

March
MondayTuesdayWednesdayThursday Friday
8
Section 1
Complex numbers
9
Section 2: 1, 2, 4, 10
Section 3: 1, 8
Algebra of complex numbers
10
Section 4: 1, 3, 4, 5
Section 5: 1, 2, 3, 7, 10, 14, 16
Moduli and conjugates
11
Section 6
Section 7: 1, 5, 6, 9, 10, 11
Polar coordinates
12
Section 8
Section 9: 1, 2, 5, 6, 7, 8
Roots of complex numbers
15
Section 10: 1, 2, 3, 4, 7, 9, 10
Some topology
16
Section 11: 1, 2, 3, 4
Functions of a complex variable
17
Section 12
Section 13: 1, 2, 3, 4, 7
Mappings
18
Sections 14 - 15
Limits
19
Section 16
The point at infinity
HW # 1: 4.3, 5.10, 5.14, 7.5, 9.5
22
Section 17: 1, 3, 5, 7, 9, 10, 11
Continuity
23
Sections 17 (cont'd)
HW # 2: 10.4, 10.10, 11.3, 13.2, 13.3
24
Section 18
Section 19: 1, 2, 3, 4, 7, 8, 9
Derivatives
25
Review for Exam # 1
26
Exam # 1
29
Sections 20 - 21
The Cauchy-Riemann equations
30
Section 22: 1, 2, 3, 4, 5, 6, 7, 8
Cauchy-Riemann equations: polar form
31
Section 23
Section 24: 1, 2, 4, 7
Analytic functions

April
MondayTuesdayWednesdayThursdayFriday

1
Section 25: 1, 2, 3, 4
Harmonic functions
2
Section 28: 1, 2, 3, 4, 6, 11, 12
Section 29
Exponentials and logarithms
5
Section 30: 1, 2, 3, 4, 5, 8, 9, 10, 11
Section 31: 1, 4
Properties of Logarithms
6
Section 32: 1, 2, 3, 7
Complex exponents
7
Section 33: 2, 7, 8, 9, 10, 12, 13, 15
Trigonometric functions
HW # 3: 22.4, 22.6, 24.2, 24.7, 25.1
8
Section 34: 7, 10, 14
Hyperbolic functions
9
Good Friday
12
Easter Monday
13
Section 35: 1, 5, 6, 7
Inverse functions
HW # 4: 28.3, 30.3, 30.11, 31.4, 32.2
14
Section 36
Section 37: 1, 2, 3, 4, 7
Complex functions of a real variable
15
Review for Exam # 2
16
Exam # 2
19
Section 38: 1, 4, 5, 6
Contours
20
Section 39
Contour integrals
21
Section 40: 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12
22
Section 41: 1, 2, 4, 5, 6, 7
The modulus of an integral
23
Sections 42
Section 43: 1, 2, 3, 4
Antiderivatives
26
Sections 44 - 45
The Cauchy-Goursat theorem
27
Section 46: 1, 2, 3, 4, 5, 8, 9
Simply connected domains
28
Section 47
The Cauchy integral formula
29
Section 48: 1, 2, 3, 4, 7, 8
Derivatives of analytic functions
30
Section 49
Liouville's theorem
HW # 5: 40.2, 40.10, 41.4, 43.3, 43.4
May
MondayTuesdayWednesdayThursdayFriday
3
Section 50: 1, 2, 4, 5, 7, 10
The maximum modulus principle
4
Section 51
Section 52: 1, 2, 3, 4, 6, 7
Sequences and series
5
Section 53
Taylor series
6
Section 54: 1, 3, 5, 6, 11, 12, 13
Examples of Taylor series
HW # 6: 46.2, 46.4, 48.3, 48.7, 48.8
7
Beach weekend
10
Section 55
Laurent series
11
Review for Exam # 3
12
Exam # 3
13
Section 56: 1, 2, 3, 4, 5, 9
Examples of Laurent series
14
Section 57
Uniform convergence
17
Section 58
Continuity of power series
18
Section 59
Integration of power series
19
Section 60: 1, 2, 3, 4, 6, 8, 9, 10
Uniqueness of series representations
20
Section 61: 1 , 2, 3, 4
Multiplication and division of power series
21
Section 62
Residues
24
Section 63
Section 64: 1, 2, 3, 4, 5
Cauchy's residue theorem
25
Section 65: 1, 2, 3
Poles
26
Review for Final
27
28

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Last modified: Tuesday 07 March 14:00 UTC