Calculus IV

Course Overview


Instructor: Dave Feldman
Email: dave@hornacek.coa.edu
Office: Second floor, Turrets Annex
Phone: x249, 276-5284
Mailing List: calc4 at hornacek dot coa dot edu
Office Hours: By appointment
Help Sessions: Wednesdays, 6:30 -- 8:00 pm

Goals

  1. I want to help you improve your quantitative literacy, problem solving skills, and mathematical confidence.
  2. I want you to understand and know how to use the main elements of vector calculus: the divergence, gradient, and curl; line and surface integrals; and Greens Theorem, Stokes Theorem, and the Divergence Theorem. We will also cover multidimensional integrals in Cartesian, Polar, Cylindrical, and Spherical Coordinates.
  3. I want to help you get ready for more advanced math and physics classes by doing some challenging problems that will "stretch" you some.
  4. I want to have fun while working hard and learning a lot.

I hope to cover chapters 16-20 of our textbook. This is similar to the material covered in most other Calc IV courses at colleges and universities with trimesters or quarters. At some schools such a course would be called vector analysis or vector calculus instead of Calculus IV.

Evaluation


Your evaluation will be based roughly on the following: I recommend against grades; I believe they are more likely than not to interfere with genuine, reflective learning. However, I will assign grades (for those who so opt) by following the guidelines in the COA Course Catalog. I do not have any quota of A's, B's, etc.


Policies, Advice, and Stuff:

  1. Our textbook will be McCallum, Hughes-Hallett, et al., Calculus: Multivariable. 4th edition. J. Wiley. 2005. ISBN: 0-471-48480-6.
  2. Homework will be due Fridays at the end of the day. More than one unexcused late homework assignment will result in me mentioning this in your narrative evaluation and may result in a lowering of your grade.
  3. You are strongly encouraged to work together on homework. You can also consult me, class tutors, other faculty, friends, and family. However, the homework you hand in should represent your own understanding. This means that if your friends get a homework problem and you don't understand how they did it, you shouldn't photocopy their solution and turn it in.
  4. Since this is a tutorial, in some cases you will be correcting your own homework.
  5. In addition to the regular homework assignments, I'd like to do three in-depth assignments: one that is a challenging set of Maple problems, one that is a challenging theory problem or a by-hand calculation, and one that is an interesting application of vector calculus.
  6. Unless students prefer otherwise, I do not plan on giving any exams in this class.
  7. You'll want a calculator that can handle scientific notation, trigonometry, and logarithms. There's no need to buy an expensive graphing calculator.
  8. The first half of this course, when we focus on multivariable integration, will be a little "messy". The second half of the course will be more elegant and less algebra-intensive.
  9. We will be making use of Maple for this class. Maple is an extremely powerful mathematics package that can do graphical, numerical, and symbolic computations.
  10. I will be sending out class info via email. Thus, it's important that you check your email.
  11. Academic misconduct -- cheating, plagarizing, etc. -- is bad. Any cases of academic misconduct will result in a judicial hearing, as per pp. 14-15 of the COA handbook. Possible consequences range from failure of the assignment to expulsion. For more, see the revised statement on academic integrity passed by the faculty winter term, 1999.