Math 227
Advanced Calculus II (Honours Vector Calculus)


Information on final exam

Solutions to Practice Final Exam

Practice Final Exam

Review of Differential Forms

Review of Green, Gauss and Stokes

Review material from Midterm 2 (revised)

Review material from Midterm 1 (revised)

Lecture 36

Lecture 35

Lecture 34

Lecture 33

Midterm 2 and Solutions

Lecture 32

Lecture 31

Lecture 30: Midterm 2

Lecture 29

Lecture 28

Lecture 27

Midterm 2: Wednesday, March 22, in class.
Review session on Monday, Feb. 20, 2:30 - 4:00. Location TBA.

Solutions to Sample Midterm 2

Sample Midterm 2

A bit of review for Midterm 2

Lecture 26

Lecture 25

Lecture 24

Lecture 23

Lecture 22

Lecture 21

Lecture 20

Lecture 19

Lecture 18

Lecture 17

Lecture 16: Midterm 1

Lecture 15

Lecture 14

Lecture 13

Lecture 12


Midterm 1: Wednesday, Feb. 8, in class.
Closed Book. No Notes. No calculators. Midterm 1 will cover chapter 11, emphasizing the topics that we have covered in class and in homework. This means all sections, except for 11.2. You should know how to compute the Frenet frame, curvature and torsion given arclength and general parameterization, ideas in proof of Kepler's first law and statements of other laws. Review session on Monday, Feb. 6, 2:30 - 4:00. Location TBA.

Midterm 1 and Solutions

A bit of review for Midterm 1

Solutions to Practice Midterm

Practice Midterm. Will post solutions by Monday, Feb. 6.

Lecture 11

Lecture 10

Lecture 9

Lecture 8

Lecture 7

Lecture 6

Lecture 5

Lecture 4

Lecture 3

Proof of product rule for cross product

Lecture 2

Lecture 1

Questions regarding registration for this class should be addressed to the Mathematics Department office staff.

Homework assignments will be posted weekly and due at the beginning of class on Wednesdays. First homework will be due on Wednesday, January 11. For information on homework policy, see below.

Midterm 1: Wednesday, Feb. 8

Midterm 2: Wednesday, March 22
For information on midterm policy, see below..

For other important dates:
See the calendar below.

Instructor Information

Instructor: Brian Marcus
Email : marcus[at]math[dot]ubc[dot]ca
Office: Math Building, Room 218
Office Hours:  Monday, Friday 2:00-3:00, Tuesday 1:30-3:00, and by appointment.
Phone: 822-1369

Course Information

Section: 201
Class time:  MWF 12:00 - 12:50
Class location:  Mathematics 203

Course web page:
will be updated throughout the term.

Textbook:  Calculus: A Comnplete Course, R. Adams and C. Essex, 8th edition (or Calculus of Several Variables, R. Adams and C. Essex, 8th edition)

A score of 68% or higher in Math 226, or permission of department head.

Course Description :
This is an honours course on vector calculus, which bridges the gap between classical physics and modern differential geometry. We plan to cover Chapters 11, 15, 16 and part of 17 of the textbook. Topics include paramatrized curves, Frenet frames, complete invariants of space curves, Kepler's laws, vector fields, line integrals, surface integrals, classical theorems of Green, Stokes and Gauss, and an introduction to higher-dimensional generalizations via differential forms.


Your course mark will be based on homework, the midterms and the final exam:

Homework (15%) + Midterms (35%) + Final Exam (50%)

Homework is an essential part of the course. Homework will be assigned every week and collected in class on Wednesdays. A portion of each assignment will be graded by the course marker. Late homework will not be accepted. The lowest homework grade will be dropped. Students are allowed to consult one another concerning homework problems, but solutions submitted for credit must be written by the student in his or her own words. Copying solutions from another student, from the web or from any other source, and turning them in as your own is a violation of the Academic Code.

Missed Exam Policy: Please make sure you do not make travel plans, work plans, etc., without regard to the examination schedule in this class. There will be no make-up or alternate exams.

If you miss a midterm, your score will be recorded as 0, unless you have a serious documented reason (an illness, a death in the family, etc.), in which case you must discuss your circumstances with the Instructor as soon as possible, and well in advance of the test.

Missed finals are not handled by the Instructo or the Mathematics Department. Students with legitimate reasons for missing the final exam should request a "Standing Deferred" status through their Faculty.

Academic Integrity: The Mathematics Department strictly enforces UBC's Academic Integrity Code.

Students with Disabilities

Please see the Instructor as soon as possible if you need any special accommodations.

Homework #1 due Wednesday, January 11

Homework #2 due Wednesday, January 18

Solutions to problems not in textbook.

Homework #3 due Wednesday, January 25

Solutions to problems not in textbook.

Homework #4 due Wednesday, February 2

Solutions to problems not in textbook.

Solutions to all problems in Chapter 11

Homework #5, due Wednesday, February 15

Solution to problem not in textbook

Homework #6, due Wednesday, March 1

Solutions to problems not in textbook

Homework #7, due Wednesday, March 8

Solutions to problems not in textbook.

Homework #8, due Wednesday, March 15

Solutions to all problems in Chapter 15

Solutions to all problems in Chapter 16

Homework #9, due Wednesday, March 29

Solutions to problem not in textbook.

Homework #10, due Friday, April 7 by 5PM in my office, Math 218 (under the door if I'm not there).

Solutions to all problems in Chapter 17


Wednesday, Jan 4
First lecture
Wednesday, February 8
Midterm 1
Monday, February 13
Family Day, no class
Monday, Feb 20 - Friday, Feb 24
Break (no classes)
Wednesday, March 22
Midterm 2
Wednesday, April 5 Last lecture
Final exam