Math 263 - Multivariable and Vector Calculus - Fall 2008

Section 101

Instructor: Daniel Coombs
E-mail: coombs at math dot ubc dot ca

Section Webpage: For office location, office hours, and other section specific information, see

Section 102

Instructor: Malabika Pramanik
E-mail: malabika at math dot ubc dot ca

Section Webpage: For office location, office hours, and other section specific information, see

Additional Resources (TA office hours, Drop-in help etc.)

Putnam Exam Information

The practice sessions for the 2008 Putnam Examination will be held on Tuesdays from 12:30-2:00 pm in Math 104, Mathematics building. The organizational meeting is on Tuesday September 16 at 12:30. Anyone interested intaking the Putnam exam or working on the practice problems is welcome to attend. Pizza and pop will be provided for participants starting September 23. For more information, see Greg Martin's webpage .

Course information

Homework and Midterm

Lesson plan

The table below shows the tentative lesson plan for the semester. There may be modifications to this later.

Date Day Note Topics (Mon, Wed, Fri) Topics (Friday second hour) Book sections
03-Sep Wed   Intro, coordinates, vectors, lengths, addition/scalar multiplication 13.1, 13.2  
05-Sep Fri   Dot product, angles, projection, cross product Eqns of lines and planes, examples 13.3, 13.4 13.5
08-Sep Mon   Vector functions and space curves, parametrization    14.1  
10-Sep Wed Derivatives and integrals of vector functions 14.2  
12-Sep Fri   Arc length, speed, velocity and acceleration Examples and applications 14.3, 14.4 14.4
15-Sep Mon   Functions of several variables   15.1  
17-Sep Wed Limits 15.2  
19-Sep Fri Partial derivatives, higher order derivatives Tangent planes and linear approximations 15.3 15.4
22-Sep Mon Chain rule, directional derivatives, gradient 15.5, 15.6  
24-Sep Wed Quadratic approximation, examples page 969  
26-Sep Fri Local maxima and minima Examples and catch-up 15.7 15.1-15.7
29-Sep Mon   Lagrange multipliers,    15.8  
01-Oct Wed   Double integrals   16.1  
03-Oct Fri Iterated integrals Integrals over non-rectangular shapes 16.2 16.3
06-Oct Mon Polar coordinates 16.4  
08-Oct Wed Applications of double integrals 16.5  
10-Oct Fri Applications of double integrals Review for test 16.5 up to 16.4
13-Oct Mon NO CLASS  
15-Oct Wed TEST 1 on Chapter 13, 14, 15, 16.1-16.4  
17-Oct Fri Triple integrals Changing order of integration 16.6 16.6
20-Oct Mon Cylindrical coordinate integrals 16.7  
22-Oct Wed   Spherical coordinate integrals   16.8  
24-Oct Fri   Vector fields conservative fields, potentials, examples 17.1 17.1
27-Oct Mon line integrals 17.2  
29-Oct Wed applications of line integrals 17.2  
31-Oct Fri fundamental theorem of line integrals Green's theorem 17.3 17.4
03-Nov Mon Div and curl 17.5  
05-Nov Wed Div and curl, examples and identities 17.5  
07-Nov Fri Examples and applications Review for test 17.5  
10-Nov Mon Review for test up to 17.5  
12-Nov Wed TEST 2 Up to 17.5  
14-Nov Fri Parametric surfaces Parametric surfaces 17.6 17.6
17-Nov Mon Surface integrals 17.7  
19-Nov Wed examples and applications 17.7  
21-Nov Fri divergence theorem Examples and applications 17.9 17.9
24-Nov Mon Stokes' theorem 17.8  
26-Nov Wed Examples and applications 17.8  
28-Nov Fri   Review Review    

Sample tests

The files below are tests and solutions from some earlier semesters. These are being provided only to help you in practice and as a study guide. You should not expect the exams in this semester to contain problems identical to these. Moreover, the lesson plans in earlier semesters could have been different from the one this semester - hence you should not assume the same topic coverage for the tests as in these files. (Even course numbers have changed over the years) . All the files below are in PDF format. Last updated on Sept 6 2008.