Paul Bryan

UCSD Mathematics


Vector Calculus
Credit Hours
Math 20C (or Math 21C) or Math 31BH with a grade of C– or better.
Catalog Description
Change of variable in multiple integrals, Jacobian, Line integrals, Green’s theorem. Vector fields, gradient fields, divergence, curl. Spherical/cylindrical coordinates. Taylor series in several variables. Surface integrals, Stoke’s theorem. Gauss’ theorem. Conservative fields.
Vector Calculus, sixth edition, by Jerrold E. Marsden and Anthony J. Tromba; published by W. H. Freeman and Company; 2012
Subect Material
We will cover parts of chapters 2, 3, 4, 5, 6, 7, and 8 of the text
Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment; you are responsible for material in the assigned reading whether or not it is discussed in the lecture. It will be expected that you read the assigned material in advance of each lecture.
There will weekly homework projects, due in the drop-off box in AP&M by 4pm on the due date. I strongly encourage you to discuss the homework with other students in the class and to attend the sections. However, doing the homework exercises and understanding them is your best preparation for the exams. You must write up the solutions yourself and mention any sources used and students with whom you collaborated. See UCSD's policy on Academic Integrity.

Please observe the following neatness guidelines for homework that you turn in to be graded; homework not conforming to these guidelines will not receive full credit and may not be graded at all.

  • Use clean, white notebook paper that is not torn from a spiral notebook.
  • Write your Name, PID, and Section clearly on the front page of your completed assignment.
  • Write clearly and legibly.
  • Clearly number each solution and present them in numerical order.
There will be one midterm exams and one final exam. You may bring one 8.5 by 11 inch handwritten sheet of notes - written on both sides - with you to the midterm exam and two sheets - written on both sides - to the final. No other materials are permitted. See the calendar for dates. There will be no makeup exams.
Grade Composition
  • Homework: 25%. Midterm 1: 25%. Final: 50%.
Grading Scale
A+ A A- B+ B B- C+ C C- D
97 93 90 87 83 80 77 73 70 60

We may adjust the scale to be more lenient, but we guarantee that the grade corresponding to a given percentage will not be lower than specified by the above scale. In addition, you must pass the final examination in order to pass the course.

Electronic Devices
For homework, you may use whatever electronic devices you like, e.g. calculators, PC's, smartphones… No such devices will be permitted in the exams.