S24MATH519_Info.html

Spring 2024 MATH 519 (Section 1, CRN 12026)
Complex Variables

Class Time & Room (Jan.16 -- May 03) MWF 10:00--10:50am, Engrg E106
Instructor: Prof. Jiangguo (James) Liu
Office: Weber 127 Phone: (970)491-3067 Email: liu@math.colostate.edu
URL: https://www.math.colostate.edu/~liu/
Office Hours: MWF 1--2pm and by appointments

Textbook
J.Brown, R.Churchill, "Complex Variables and Applications", McGraw Hill, 8th ed.(2004)

Schedule (for 15 weeks)

#1, #2: Complex numbers; Paths and domains on the complex plane; Continuity
#3: Differentiation, Cauchy-Riemann equations, Analytical functions
#4: Elementary functions
#5, #6: Path integrals, Cauchy-Goursat Theorem, Cauchy integral formulas
#7, #8: Taylor series, Laurent series; Uniform convergence
#9,#10: Poles, residues, and applications
#11, #12: Mappings by elementary functions; Conformal mappings and applications
#13: Gamma and Zeta functions
#14: More applications: Dirichlet BVPs; Planar flow
#15: Prime Number Theorem; Review

Homeworks and Class Participation (75%)
There will be six (6) regular homework assignments.
HW1 Due Wed.01/31 HW2 Due Fri.02/16 HW3 Due Mon.03/04
HW4 Due Mon.04/01 HW5 Due Mon.04/15 HW6 Due Wed.05/01

Final Exam (25%)
Thu. May 9, 2024, 7:30-9:30am (as scheduled by the University).
This exam may be used as a QE for math students.

Last modified by J.Liu on Sat. 2024/03/16