Instructor: Vera Serganova
Email address: serganov@math.berkeley.edu
  • webpage:/~serganov
  • Phone Number: 642-2150
  • Office hours: Tu 1:00-2:00, W 2:00-3:00 in 709 Evans
  • Text: Brown, Churchill, Complex Variables and Applications
  • Homework: Each Thursday a problem assignment will be posted. The homework will be collected the next Thursday. Late homework will not be accepted.

    • Course outline

  • Review of complex numbers (Chapter 1)
  • Analytic functions: continuity, Cauchy- Riemann condition (Chapter 2)
  • Elementary functions of complex variable (Chapter 3)
  • Contour integrals, Cauchy-Goursat theorem, Cauchy integral formula, Liouville's theorem, maximum principle (Chapter 4)
  • Taylor and Laurent series (Chapter 5)
  • Residues and poles, Cauchy's Residue Theorem, singular points of an analytic function (Chapter 6)
  • Application of residues to improper integrals, argument principle (Chapter 7)
  • Conformal mappings, Riemann surfaces, some applications (Selected material from Chapters 8-12)

    • Homework assignment

  • Week 1 (Due 9/2) Read chapter 1. Problems: 4.4, 4.5, 5.2, 5.9, 5.14, 8.5, 8.9, 8.10, 10.3, 10.6, 10.7, 11.1, 11.5, 11.10.
  • Week 2 (Due 9/9) Read sections 12-18. Problems: 12.1, 12.2, 12.4, 14.1, 14.3, 14.5, 14.7, 18.1, 18.9, 18.10, 18.12, 18.13.
  • Week 3 (Due 9/16) Read sections 19-28. Problems: 20.2, 20.4, 20.8, 20.9, 23.1, 23.3, 23.4, 23.6, 25.4, 25.6, 26.3, 26.6, 28.1, 28.5.
  • Week 4 (Due 9/23) Read sections 29-45. Problems: 31.2, 31.3, 31.9, 32.1, 33.1, 33.8, 34.10, 34.11, 35.7, 36.3, 38.3, 39.5, 39.6, 42.4, 43.3.
  • Week 5 (Due 9/30) Read sections 46-49. Problems: 43.6, 43.8, 45.2, 45.4, 49.1, 49.2, 49.3, 49.4, 49.5, 49.7, 49.8,49.9.
  • Week 7 (Due 10/14) Read sections 50-54. Problems: 52.1, 52.2, 52.3, 52.4, 52.5, 52.6, 52.9, 52.10, 54.1, 54.3, 52.4, 54.5, 54.7, 54.8.
  • Week 8 (Due 10/21) Read sections 55-59. Problems: 56.2, 56.3, 56.6, 56.7, 56.8, 59.1, 59.2, 59.3, 59.6, 59.7, 59.8, 59.9, 59.10, 59.12, 59.13.
  • Week 9 (Due 10/28) Read sections 60-67. Problems: 62.1, 62.3, 62.5, 62.6, 62.8, 62.9, 66.3, 66.5, 66.6, 66.8, 66.11, 67.4, 67.7, 67.8.
  • Week 10 (Due 11/4) Read sections 68-74. Problems: 71.1, 71.2, 71.3, 71.6, 72.1, 72.2, 72.3, 72.4, 74.1, 74.2, 74.3, 74.4, 74.5, 74.6.
  • Week 11 (Due 11/16) Read sections 75-84. Problems: 76.2, 76.5, 76.6, 79.3, 79.4, 79.5, 79.6, 79.8, 81.1, 81.3, 81.6, 81.7, 81.11, 84.2, 84.3, 84.6, 84.7.
  • Week 12 (Due 11/23) Read sections 85-87. Problems: 85.1, 85.2, 85.3, 85.4, 85.6, 87.1, 87.3, 87.4, 87.5, 87.7, 87.8, 87.9.
  • Week 13 (Due 12/2) Read sections 90-95. Problems: 92.8, 92.12, 94.6, 94.11, 95.4, 95.5.
  • Practice exam
  • The final exam will take place in 155 Donner Lab on December 15 from 8 to 11 AM.
  • You can pick up your homework near the door of 709 Evans.
  • Review Session: December 9, 11-12:30, 71 Evans.
  • Office hours before Exam: December 14, 2:00-4:00 PM, 709 Evans.
  • All extra credit problems except the last two are due on December 2. The last two problems are due on December 9.
  • Old midterm for practice
  • Sample final
  • Extra credit problems
  • Elliptic functions exercises