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Protected: Complex Variables: Study Guides for Spring 2014

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Complex Variables: Homework information for Spring 2014

The assignments are organized according to their due date. Please report any issues back to Iva.

  • Assignments for Monday 1/27 and Tuesday 1/28:
      Based on 1/21 lecture: Please turn in Problems 2(g), 2(h), 2(i), 2(j), 4(1-17) and 4(1-18) from Section 1.2 of your textbook. Remarks: If you are not already fluent and fast in complex number arithmetic, you really need to first do Problem 1 or similar exercises. These are not due, but I expect you to be mature about this and practice the complex number arithmetic until you become fast at it. Also: If you find the problems which are due too elementary, feel free to do Problem 5(a) and Problem 9 of Section 1.2 instead.
      Based on 1/23 lecture: Please turn in Problem 6 from Section 1.3 and Problems 3, 5 from Section 1.4 of your textbook.
      Based on 1/24 lecture: Please turn in Problems 1 and 5 from Section 1.5 of your textbook.
  • Assignments for Monday 2/3 and Tuesday 2/4:
      Based on 1/28 lecture: Please turn in Problems 10 and 13 from Section 2.1 of your textbook, as well as the supplemental problems from this homework sheet.
      Based on 1/30 lecture: Please turn in Problems 1, 5, 7, 8, 10 and 12 from Section 2.2 of your textbook.
      Based on 1/31 lecture: Please turn in the two problems at the end of the lecture notes. Remarks: The material we covered in class corresponds to the Section 2.3 and the beginning of the Section 4.1. If you have a background in advanced calculus / topology or just a very strong background in set theory, you may benefit from reading Sections 2.3 and 4.1 of your textbook.
  • Assignments for Monday 2/10 and Tuesday 2/11:
      Based on 2/4 AND 2/6 lectures: Please turn in the problems from this homework sheet. Note: the problems on the sheet are modifications of problems from Section 2.4 of your textbook. Also note: it is very likely that you will want to refer to examples from class on Thursday, 2/6.
  • Assignments for Monday 2/17 and Tuesday 2/18:
      Based on 2/13 lecture: Please turn in Problems 1b), 1d), 1f), 1h), 5, 14, 15, 16 from Section 3.2 of your textbook.
      Based on 2/14 lecture: Please turn in Problem 3 from Section 4.4 of your textbook.
  • Assignments for Monday 2/24 and Tuesday 2/25:
      Based on 2/18 lecture: Please turn in Problems 4b), 4d), 4f) and 5 from Section 5.1 of your textbook.
      Based on 2/21 lecture: Please turn in Problems 1, 2 and 8 from Section 5.3 of your textbook.
  • Assignment for FRIDAY 2/28:
  • Assignments for Monday 3/10 and Tuesday 3/11:
      Based on 3/3 and 3/6 lectures: Please turn in Problems 7a), 7b), 7c), 7d), 9 and 14 from Section 6.2 along with Problems 1, 2, 3, 4, 5 from Section 6.4 of your textbook. Remarks: Students may find it helpful to start the homework by going over Problems 1 and 2 from Section 6.2 of the textbook. These problems are optional, but recommended for those who may be rusty on parametric curves.
  • Assignments for Monday 3/17 and Tuesday 3/18:
      Based on 3/11 lecture: Please turn in Problems 1, 3, 4, 5, 7 and 13 from Section 6.3 of your textbook.
      Based on 3/13 lecture: Please turn in Problems 2, 4, 6, 11, 12, 13, 15 and 18 from Section 6.5 of your textbook.
  • Assignments for March 3/31 and Tuesday 4/1:
      Based on 3/20 lecture: Please turn in Problems 3, 5 and 7 from Section 7.3 of your textbook, along with a supplemental problem.
      Based on 3/21 lecture: Please turn in Problems 1b), 1d), 1f), 1h) and 1j) from Section 7.4 of your textbook.
  • Assignments for Monday 4/7 and Tuesday 4/8:
      Based on 4/1 lecture: Please turn in Problems 2d), 2e), 2g), 2h), 2i), 3e), 3f), 8 and 9 from Section 7.4, Problems 1b), 1d), 1f), 1h), 1j) and 10 from Section 8.1 of your textbook, along with this supplemental problem.
      Based on 4/3 lecture: Please turn in Problems 2, 4, 6, 8, 10 from Section 8.2 of your textbook.
      Based on 4/4 lecture: Justify the formulas on the top of page 4 of this handout.
  • Assignments for Monday 4/14 and Tuesday 4/15:
      Based on 4/8 lecture: Please turn in Problems 2, 3, 6, 9, 10, 12 from Section 8.3 of your textbook, along with this supplemental problem.
      Based on 4/10 lecture: Please turn in Problems 1, 2, 3, 4, 5, 9, 10 from Section 8.4 of your textbook.
      Based on 4/11 lecture: Please turn in Problems 4, 6, 8, 14 from Section 8.5 of your textbook.
  • Assignment for FRIDAY 4/18:
      Based on 4/15 lecture: Please turn in Problems 1, 2, 9, 11, 13, 14, 15, 18, 21 from Section 8.6 of your textbook.

  • Assignments for Monday 4/28 and Tuesday 4/29:
      Based on 4/17 lecture: Please turn in Problems 15, 16, 17, 18 from Section 12.9 of your textbook.
      Based on 4/22 lecture: Please follow the guidelines from the following homework sheet.
      Based on 4/24 and 4/25 lectures: Please follow the guidelines from the following homework sheet. Enjoy!!
  • Complex Variables: Course information for Spring 2014

    Textbook
    We will use the 6th edition of Complex analysis for mathematics and engineering by John H. Mathews and Russell W. Howell. Do note that some of the course content will not be directly based on the textbook material. At times, you will be expected to rely on the lecture notes I provide or your own lecture notes.

    Homework
    Most lectures will be followed by a homework assignment, which will be posted online. Homework will be due once a week; most often at class time on Tuesdays. The class meeting prior to the day the homework is due (Monday, in most cases) will be dedicated to answering homework questions or doing extra examples. You are expected to have a draft of your homework completed and with you at that time, and ask homework questions either in class or during subsequent office hours. In particular, I reserve the right to refuse to answer homework questions on the day the homework is due. Each homework assignment will contribute to the course grade through the letter grade for the relevant educational goal.

    Late or missed assignments
    I understand that you might find yourself in a situation where you cannot complete a homework assignment on time. You will nevertheless be expected to turn in what you have by the due date and immediately inform me about your situation. Assuming you are making a good faith effort to stay current in the class, you will be given an opportunity to make up an incomplete assignment.

    Exams and such
    There will be two in-class exams, and a partly take-home final exam, each of which will contribute to the course grade through the letter grade for the relevant educational goal. In-class exams will take place on Monday, March 3rd and Monday, April 21st; the time of the in-class portion of the final exam is Wednesday, May 7th, from 1pm to 4pm.

    Grading scheme
    For each rubric under Educational Goals you will receive a letter grade determined by your performance on the corresponding portion(s) of exams, homework assignments etc. In addition, a certain portion of your grade will correspond to the effort you put into participating and staying current in the class; students with a substantial number of class absences and/or late assignments can expect a slightly lowered course grade. The final course grade will be a weighted average of the above:

      Goal 1: 25%
      Goal 2: 15%
      Goal 3: 25%
      Goal 4: 25%
      Goal 5: 5%
      Participation: 5%

    For the description of letter grades and their numerical equivalents please refer to our College Catalog. Please note that a professor has a right to withdraw a student for the reasons of non-attendence.

    Complex Variables: Educational Goals for Spring 2014

  • Goal 1:
    To develop basic literacy involving (functions of) complex variables. This includes:

      – Reaching a degree of fluency with complex number arithmetic and geometry;
      – Developing a solid understanding of elementary functions of complex variable.

    The extent to which this goal is achieved will be determined by student performance on the corresponding in-class exam and homework.

  • Goal 2:
    To become aware of basic ideas of complex analysis. The extent to which this goal is achieved will be determined by student performance on the corresponding homework.
  • Goal 3:
    To develop a computational ability within the context of calculus of residues. The extent to which this goal is achieved will be determined by student performance on the corresponding in-class exam and homework.
  • Goal 4:
    To gain independence in reading and understanding mathematical material which uses complex variables. The corresponding assessment will be based solely on the take-home final exam.
  • Goal 5:
    To situate the practice of complex analysis within its larger mathematical and social context, primarily by understanding the kind of role complex analysis plays in certain currently open problem(s). The corresponding assessment will be based solely on the matching homework assignment.