| Date | Topics |
Book |
| Wed 1/19 |
Basic properties of complex numbers, Part I
| § 1, 2, 3, 4, 5 |
| Fri 1/21 |
Basic properties of complex numbers, Part II
| § 6, 7, 8, 9, 10 |
| Mon 1/24 |
Stereographic projection, functions of a complex variable
| § 11, 12, 13, 14 |
| Wed 1/26 |
Limits and differentiation
| § 15, 16, 17, 18, 19, 20 |
| Fri 1/28 |
Chain rule, Cauchy-Riemann equations
| § 21, 22, 23 |
| Mon 1/31 |
Analytic functions, curves in the complex plane
| § 24, 25 |
| Wed 2/2 |
Conformality, harmonic functions, e^z revisited
| § 101, 26, 29 |
| Fri 2/4 |
log, Log, complex exponents, trig functions
| § 30, 31, 32, 33, 34 |
| Mon 2/7 |
trig/hyp functions and their inverses, Mobius transf.s
| § 34, 35, 36, 90, 91, 92 |
| Wed 2/9 |
Mobius transformations
| § 93, 94, 95 |
| Fri 2/11 |
Contour integrals
| § 37, 38, 39, 40 |
| Mon 2/14 |
Path independence and equivalent things
| § 41, 42, 43, 44, 45 |
| Wed 2/16 |
MIDTERM 1
| |
| Fri 2/18 |
The Cauchy-Goursat Theorem, Part I
| § 46, 47 |
| Mon 2/21 |
NO CLASS (Presidents' Day)
| |
| Wed 2/23 |
The Cauchy-Goursat Theorem, Part II
| § 48, 49 |
| Fri 2/25 |
Cauchy's Integral Formula, Part I
| § 50, 51 |
| Mon 2/28 |
Cauchy's Integral Formula, Part II: Higher Derivatives
| § 52 |
| Wed 3/2 |
Morera, Cauchy's Ineq.s, Liouville, Fund. Thm. of Alg.
| § 53 |
| Fri 3/4 |
Mean Value Property, Maximum Principle
| § 54 |
| Mon 3/7 |
Review of Complex Integration, I
| |
| Wed 3/9 |
Review of Complex Integration, II
| |
| Fri 3/11 |
Basic facts about infinite series, Taylor's Theorem
| § 55, 56, 57, 58 |
| Mon 3/14 |
Laurent series and Laurent's Theorem, Part I
| § 59, 60, 61, 62 |
| Wed 3/16 |
Laurent series and Laurent's Theorem, Part II
| § 59, 60, 61, 62 |
| Fri 3/18 |
Laurent series and Laurent's Theorem, Part III
| § 59, 60, 61, 62 |
| Mon 3/21-25 |
NO CLASS (Spring Break)
| |
| Mon 3/28 |
Integration and Differentiation of Power Series
| § 63, 64, 65 |
| Wed 3/30 |
Review
| |
| Fri 4/1 |
MIDTERM 2 ***in 70 Evans***
| Covers Lectures 1--24 |
| Mon 4/4 |
Rad. of Conv., Taylor Series with Remainder
| § 63, 64, 65 |
| Wed 4/6 |
Midterm Results, Zeros of Analytic Functions
| § 75 |
| Fri 4/8 |
Zeros of Analytic Functions, Begin Isolated Sing.s
| § 75, 68, 69 |
| Mon 4/11 |
Three Types of Isolated Sing.s, Local Behavior
| § 72, 76, 77 |
| Wed 4/13 |
Casorati-Weierstrass Theorem, Residue Theorem
| § 77, 70, 71 |
| Fri 4/15 |
Calculating certain integrals by residues, Part I
| § 78-85 |
| Mon 4/18 |
Calculating certain integrals by residues, Part II
| § 78-85 |
| Wed 4/20 |
Calculating certain integrals by residues, Part III
| § 78-85 |
| Fri 4/22 |
Calculating certain integrals by residues, Part IV
| § 78-85 |
| Mon 4/25 |
Calculating certain integrals by residues, Part V
| § 78-85 |
| Wed 4/27 |
Calculating certain integrals by residues, Part VI
| § 78-85 |
| Fri 4/29 |
Calculating certain integrals by residues, Part VII
| § 78-85 |
| RRR Week |
We will have reviews from 4-5pm, MWF, in our regular classroom.
| |
| Friday 5/13 |
FINAL EXAM (8-11am) in 106 Stanley Hall
| |