Calculus IV Mathematics S1202D
Summer 2006 Section 001

The class is held Monday, Tuesday, Wednesday, and Thursday from 4:30 PM to 6:05 PM in the Mathematics Building room 417. The class is held during the first summer session, May 22nd through June 30th.

Links:

• Important Announcements (Check periodically)
  
• Course Information
  
• Course Details
  
• Schedule of Lectures and Homework
  
• My homepage

Announcements

June 15th, 2006:

• I have moved around the dates for the next two quizzes and updated the syllabus. Check out the answers I posted to the problems up through 16.2.
• I have finished grading your midterms. I can't give you them to take home, but if you want you can look at the midterms during my office hours. I can also make you a copy.
• I have changed the tentative grading scheme.

June 7th, 2006:

• I have now added the solutions to the problems from the book. See the Course Schedule below.

June 5th, 2006:

• As we discussed in class, we are moving the date of the midterm. In compensation, I have also moved around the dates of some of the quizzes.
• Because I forgot to upload this web page on Friday, I have cut out a few homework problems and moved the due date to Wednesday.

May 31st, 2006:

• As requested, I have moved the due date for the homework due June 1st to June 2nd.
• I am moving the quiz to Monday, as we discussed in class.
• For more information about spherical coordinates and spherical geometry, I highly recommend the notes at Geometry of the Sphere. This is a completely supplementary and extracurricular set of notes. However, I think that it is very interesting. For more along the lines of what I expect you to know about spherical, cylindrical, and polar coordinates, see Sections 10.3 and 12.7 of Stewart.

May 23rd, 2006:

• I have added the homework for the next couple of classes.
• I have added the quiz dates and noted that the lowest quiz grade will be dropped. The first quiz is Thursday.
• The help room will open on next Tuesday, May 30th.

May 22nd, 2006:

• I have updated the TA's office hours.
• I have posted the homework. Note that Monday's homework will be due on Wednesday (to give you a break), and Tuesday's and Wednesday's homework will be due on Thursday, as usual.

May 21st, 2006:

• Friday, June 9th will be the makeup class for the Memorial Day University holiday. Please make a note of this.
• The final exam will be given on Tuesday, June 27th. I am soliciting feedback from the students for the first few weeks of class. Let me know if you have any.

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Course Information

Instructor: Shaffiq Welji
My campus telephone number is x45881, and my office is in Mathematics Building room 408. You can also reach me via e-mail at welji@math.columbia.edu.
TA: Xinyi Yuan
Xinyi can be reached at yxy@math.columbia.edu. His office hours are 12:00 PM to 6:00 PM on Mondays and Thursdays in Mathematics Building 406.

Office Hours and Additional Help: Shaffiq's office hours are Mondays and Wednesdays from 3:45 PM to 4:30 PM in 408 Mathematics. Additional times are available by appointment.
Xinyi's office hours are 12:00 PM to 6:00 PM on Mondays and Thursdays in Mathematics Building 406.
As always, help is available (for free!) in the math department's Help Room, which is open pretty much all day, every day in Math 406. A more detailed schedule is available here.

Texts:

• J. Stewart. Calculus: Early Transcendentals. Fifth edition. Belmont, CA: Brooks/Cole, 2003.
  Note the "Early Transcendentals" part. If you buy the other fifth edition, you should check to make sure you are doing the proper homework. This text is on reserve in the Mathematics Library. Stewart's book is the main reference for this course.
• R. Friedman. Notes on Complex Analysis Written for Calc IV at Columbia.
  This set of notes should be the primary reference for studying complex analysis at the end of the course. The notes come in three parts: Complex Numbers, Complex Functions and the Cauchy-Riemann Equations, and Contour Integrals and Cauchy's Theorem. Additional resources should also be used when studying complex analysis. Some options are listed below.
• H. Jacquet. Notes on Complex Analysis Written for Calc IV at Columbia.
  Use this as an additional resource for studying complex analysis at the end of the course. The notes come in two parts: Complex Functions, and Complex Calculus.
• G. Cain. Complex Analysis.
  For a more detailed exposition of complex analysis, consider this reference. It is available on the Internet here.
• H. McIntosh. Complex Analysis.
  For a more detailed exposition of complex analysis, consider this reference. It is available on the Internet here.

Course Description: This course will focus on vector calculus and introduce complex analysis. The material for the former is covered in chapters fifteen and sixteen of the primary text. The primary topics are

1. multiple integrals,
2. change of variables--specifically using non-rectangular coordinate systems (polar, cylindrical, spherical),
3. areas,
4. vector fields (gradients, curl, divergence),
5. Fundamental Theorems (Theorem of Line Integrals, Green's Theorem, Stokes's Theorem, Divergence Theorem).

Complex Analysis is covered in a variety of sources, two of which are Internet books listed above. In addition, I will post some handouts on complex analysis is the Schedule of Lectures and Homework.

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Course Details

Homework: Homework will appear daily and will be collected on Tuesdays and Thursdays at 4:30 PM (that is just before class begins). You should submit homework outside of room 407 Mathematics Building to the box labeled "Shaffiq Welji / Calculus IV In" (look in the upper right corner of all the boxes). Homework will be returned to the box labeled "Shaffiq Welji / Calculus IV Out". Homework from Monday and Tuesday will be due on Tuesday, and homework from Wednesday and Thursday will be due on Thursday. Late homework will not be accepted under any circumstances. Although homework does not contribute to a large fraction of your grade, it is an essential component of learning the subject. Make sure your homework is stapled with clear, coherent, and organized solutions. No homework will be considered fully correct if it is not clear, coherent, and organized.

Tests: We will have quizzes regularly (about once a week), one midterm and one final. I have decided to give about five tests throughout the course. These quizzes should not be anything to worry about. They will just test to see how well you are keeping up with the work. In fact, I have decided to drop the lowest quiz grade. All test will be announced well ahead of time in the Schedule of Lectures and Homework. No calculators are allowed on any of these tests. In fact, make sure all electronic devices are completely put away during all tests. The final exam will be given on June 26th. If you let me know about any conflicts well ahead of time (at least a week), I might be able to make arrangements. However, there will be no make-up tests without a note from a doctor or a dean.

Grading: The following grading scheme is tentative.

• Homework: 15%
• Quizzes: 20%
• Midterm: 30%
• Final: 35%

Collaboration: Although collaboration is encouraged on homework and any more informal circumstances, any work you submit for homework must be your own write-up (which means taking the ideas and notes from the collaborative effort and turning those notes and ideas into coherent, clear explanations). Copying homework will not be tolerated. Any cheating on exams or quizzes will be handled severely.

Notes: The course is only six weeks long, so we will be moving quickly. This means that you will have to keep up because there will not be any time to catch up. In order to help you do this, I have a number of suggestions for how to study. Complex analysis is unlike anything most of you have probably seen. It will be a glimpse of more advanced mathematics classes, so you will probably have to learn a new study method. Active participation is encouraged. Please ask me any questions that you have. Mathematics is not a spectator sport, and you cannot learn without questioning and doing exercises. Your work for every class should consist of:

1. Read the appropriate section(s) before class.
2. Come to class.
3. Read the section(s) again after class.
4. Do the homework (even the problems that don't have to be turned in).
5. Come to the help room or office hours to answer any remaining questions.

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Schedule of Lectures and Homework

This schedule is tentative. It might change as the class progresses. Please check regularly for changes and updated homework information.

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