Complex variables: MATH3410

Winter 2014


General Information:

  • Instructor: Dr. Youness Lamzouri.
                           Office: N515 Ross Building.
                           Email: lamzouri@mathstat.yorku.ca.
                           Website: www.math.yorku.ca/~lamzouri.
  • Lectures: Tuesdays and Thursdays, 1:00-2:30 pm, in in Ross S205.
  • Office hours: Tuesdays and Thursdays 2:30-3:30 pm.
  • Textbook: "Fundamentals of Complex Analysis with Applications to Engineering and Science" by E. B. Saff and A. D. Snider. Pearson, Third Edition, 2003.

  • Course Description :

    This course is an introduction to the powerful theory of complex analysis. We will essentially cover Chapters 1-6 of the textbook. Covered topics include: complex numbers, analytic functions, the Cauchy-Riemann equations, elementary functions, complex integration, Cauchy's integral theorem, Liouville's theorem, Taylor and Laurent series, Analytic continuation of functions, the Residue theorem, the Argument principle and Rouche's Theorem.


    List of practice problems:

  • Week 1 (Jan 6-10): Section 1.1 : 8, 15, 20, 24, 27. Section 1.2 : 5, 7 c) and i), 8, 15, 17.

  • Week 2 and 3 (Jan 13-24): Section 1.3 : 5, 7, 10, 16, 18, 20. Section 1.4 : 2, 6, 10, 12, 17, 23. Section 1.5 : 4, 5, 7, 12, 14, 16, 18. Section 1.6 : 2, 3, 4, 5, 6, 7, 8, 13, 14, 20.

  • Weeks 4 and 5 (Jan 27 - Feb 7): Section 2.1 : 1, 2, 7, 8, 9, 12. Section 2.2 : 7, 11, 12, 15, 25. Section 2.3 : 2, 3, 4, 7, 11. Section 2.4 : 2, 4, 5, 6, 9, 12. Section 2.5: 2, 3, 4, 5, 6.

  • Week 6 (Feb 10-14): Section 3.1 : 1, 2, 3, 6, 11, 16. Section 3.2 : 1, 5, 6, 12, 16, 17, 23. Section 3.3 : 1, 3, 5, 9, 10, 13.

  • Weeks 7 and 8 (Feb 24 - Mar 7): Section 3.5 : 1, 3, 4, 5, 7. Section 4.1: 1, 2, 6, 7, 8, 11. Section 4.2: 5, 6, 8, 11, 13, 14, 18. Section 4.3: 1, 2, 3, 11, 12.

  • Weeks 9 and 10 (Mar 10-21): Section 4.4 : 3, 5, 10, 13, 15. Section 4.5 : 1, 3, 6, 8, 10. Section 4.6: 2, 5, 7, 8, 14, 16. Section 5.1: 2, 5, 7, 11, 14. Section 5.3: 1, 3, 6, 7, 10.

  • Weeks 11 and 12 (Mar 24 - Apr 3): Section 5.2 : 1, 2, 4, 5, 14, 15. Section 5.5 : 1, 3, 5, 7, 9. Section 5.6: 1, 2, 6, 12, 17. Section 6.1: 2, 3, 4, 5, 6, 7. Section 6.2: 1, 2, 3, 4, 5, 6, 7. Section 6.3: 1, 2, 3, 4, 5, 6, 7.


    Course Evaluation:

  • 20% Assignments : There will be two assignments counting for 10% each. Late assignments will not be accepted.

    Assignment 1 (Due Thursday February 27, at the beginning of class).
    Solution to Assignment 1.

    Assignment 2 (Due Saturday April 19, 2014).

  • 30% Midterm exam: The tentative date for the midterm exam is: Thursday, February 27, 2014.
    Midterm syllabus: Chapter 1: sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6. Chapter 2: sections 2.1, 2.2, 2.3, 2.4, 2.5. Chapter 3: sections 3.1, 3.2, 3.3.
    There will be no makeup exam. If you miss the midterm exam and have a valid excuse (with an acceptable documentation), the exam weight will be transferred to the final exam.

    Here is the solution and marking scheme of the midterm exam.

  • 50% Final Exam: The final exam will be comprehensive. It will be held on Saturday April 19 from 2:00 pm to 5:00 pm in ACE 005. Here is the syllabus of the final exam. I will hold extra office hours on Thursday April 17 from 11:00 am to 1:00 pm.