MATH 217 and 263
Math 217/263
Multivariable and Vector Calculus
Latest AnnouncementsInstructor Information
Instructor: Dr Codina Cotar
Email: c.cotaratmathdotubcdotca
Office: Math Annex 1215
Hours: 12:0013:00 Tuesday, 12:0013:00 Wednesday, 12:0013:00 Thursday, and by appointment
Drop in tutorial: hours in the MSRC (mouldy building behind the Math Annex): Tuesday, Thursday 14:0016:00.
Phone: 8223783
Homework Assignments
 Homework 1 (Due Thursday 18th May) Solutions
 Homework 2 (Due Thursday 25th May) Solutions
 Homework 3 (Due Tuesday 30th May) Solutions
 Homework 4 (Due Thursday 8th June) Solutions
 Homework 5 (Due Thursday 15th June) Solutions
 Homework 6 (Due Friday 23rd June 5pm) Solutions
 Homework 7 (NOT to be handed in)
 Homework 8 (Due Tuesday 11th July) Solutions
 Homework 9 (Due Thursday 20th July) Solutions
 Homework 10 (Due Wednesday 26th July)
Practice Problems
 Lines and planes (Solutions)
 Week 1 Practice
 Chapter 13 Practice
 Chapter 14 Practice
 Chapter 15 Practice(I)
 263 Midterm 1 (2004) (Solutions)
 263 Midterm 1 (2005)
 263 Mock Midterm 1 (2005)
 217 Midterm 1 (2005)
 217 Mock Midterm 1 (2005) (Solutions)
 217/263 Mock Midterm 1
 217/263 Midterm 1 Soln
 Chapter 15 Practice(II)
 Chapter 16 Practice(I)
 263 Midterm 2 (2004)
 263 Midterm 2 (2005)
 217 Mock Midterm 2 (2005)
 217 Midterm 2 (2005)
 263 Mock Midterm 2 (2005)
 217/263 Midterm 2 Soln
 Chapter 16 Practice(II)
 Chapter 17 Practice
 Chapter 17 Mock Exam
 217 Final Exam (Winter 2005)
 263 Final Exam (Winter 2004)
 263 Final Exam (Winter 2005)
 217/263 Final Exam (Summer 2005)
 317 Final Exam (19992004)
Resources
Table of derivatives and integrals
Graphs of useful curves
Notes on Cylindrical and Spherical Coordinates
Examples on Cylindrical and Spherical Coordinates
More Examples on Cylindrical and Spherical Coordinates
Examples on the Jacobian
Integrals over curves and surfaces (from Prof Loewen)
Announcements
Sunday 16th July 2006
The material for the final exam is as follows:

vectors and the geometry of space;

the dot product and the cross product;

equations for lines and planes; graphs for cylinders and quadratic surfaces;

vector functions, space curves, derivatives and integrals of vector functions, arc length and curvature;

applications to velocity and acceleration, tangential and normal components of acceleration;

functions of 2 variables: limits and continuity, partial derivatives, tangent planes, linear approximations, differentiation;
 The chain rule;
 Directional derivatives and the gradient vector;
 Minimum and maximum values;
 Multiple integrals: double integrals over rectangles, average value, iterated integral (Fubini theorem), double integrals over general regions,double integrals in polar coordinates;
 Applications of double integrals (density and mass, center of mass); Surface area;
 Triple integrals. Applications to volume, mass and center of mass. Cylindrical coordinates. Spherical coordinates. Change of variables in integrals. Jacobian;
 Line integral along a curve C. Line integrals of vector fields. Path independence and conservative fields. Green’s Theorem;
 Curl and Divergence. Parametric surfaces and their area. Surface integrals;
 Stokes’ Theorem. The divergence Theorem.
Sunday 16th July 2006
Homework 9 has been posponed until Thursday 20th July. Note that Homework 10 will now become Bonus Homework, so it will be optional. Homework 10 will be due on Tuesday the 25th July. Even though Homework 10 will now be optional, the material in it is part of the material for the Final Exam.
Thursday 13th July 2006
The FINAL EXAM will take place on Friday the 28th July, at 8:30 am in LSK 201.
Thursday 22nd June 2006
The average for the second midterm was 68/100 and the median was also 68/100. WELL DONE.
Thursday 22nd June 2006
Here is a list of questions from previous Midterm 2 Exams which you wont be able to solve.
217 Mock Midterm 2 (2005): questions 1, 2, 3, 4, 9 and 10;
217 Midterm 2 (2005): questions 1, 4 and 5;
263 Mock Midterm 2 (2005): questions 7, 8, 14, 15, 16 and 17.
Also note that you can now solve the following problems from previous Midterm 1 exams, which were from Chapters included in our Midterm 2 exam material:
263 Midterm 1 (2004): question 4;
263 Mock Midterm 1 (2005): questions 5, 6, 12, 15, 16 and 17;
217 Mock Midterm 1 (2005): questions 4 and 7.
217 Midterm 1 (2005): question 4.
Wednesday 21th June 2006
Due to general demand, Midterm 2 will now take place on Wednesday 28th June, instead of Tuesday 27th June. Here is the material for Midterm 2:
 The chain rule;
 Directional derivatives and the gradient vector;
 Minimum and maximum values;
 Multiple integrals: double integrals over rectangles, average value, iterated integral (Fubini theorem), double integrals over general regions,double integrals in polar coordinates;
 Applications of double integrals (density and mass, center of mass); Surface area.
The exam will start at 10:00am. You are allowed to bring a double sided page of formulas; another double sided page containing derivations and integration formulas will be provided. No calculators are allowed. The exam will last 60 minutes.
Tuesday 20th June 2006
Here is a list of suggested practice problems from Chapters 15 and 16 in preparation for Midterm 2:
Chapter 15
 15.5: 716, 2134, 41, 4351;
 15.6: 417, 2127, 28,31, 33, 3944, 49, 50, 51, 53, 55, 56, 60;
 15:7: 522, 2734, 3749, 51.
 16.2: 320, 2330, 3334;
 16.3: 728, 3752;
 16.4: 916, 2127, 2935;
 16.5: 114;
 16.6: 112, 1721.
Thursday 15th June 2006
There was a mistake in the last example in today’ lecture (lecture 16). Here is the correct example.
Thursday 15th June 2006
I will also be in my office on Monday between 11:00am and 6:00pm. Please feel free to come and ask any questions you may have about the course. Also, if there are enough requests, I can do an additional problem session on Monday, to consist of problems covering this week’s lectures. Please email if you would like me to do a problem session on Monday and also let me know what time you would prefer.
Note that there will be a usual problem session during Thursday’s lecture.
Wednesday 14th June 2006
I have decided to postpone the handing in of Homework 5 until Friday, 16th June, 5pm; you may still hand it in during the lecture tomorrow, if you prefer. I will be in the office after 11am on Friday and will answer any questions you may have about this week’s lectures or the homework.
Monday 12th June 2006
Due to illness, the lectures this week will be given by another UBC maths instructor. I will still answer questions by email, so feel free to address any questions to me at the usual address. I will be back next week.
Tuesday 6th June 2006
Note that there was a typo in HWK4, question 5, part a). The typo has been corrected. Here is the new corrected Homework 4.
Sunday 4th June 2006
The first midterm average was 70/100 and the median was 71/100. Well done everybody. Email me if you want to know your grade before Tuesday’s lecture.
Friday 26th May 2006
Here is a list of suggested Practice Problems from Chapters 14 and 15:
Chapter 14
 14.2: 1720, 2326, 29, 31, 32, 47, 48, 49;
 14.3: 6, 911, 1316, 20, 21, 22, 2325, 29, 47, 56;
 14.4: 38, 916, 19, 3136, 37, 39.
Chapter 15
 15.2: 520, 2736;
 15.3: 1334, 5764, 44, 91, 82, 89;
 15.4: 16, 1116, 17, 18, 3940.
Thursday 25th May 2006
Here is the material for Midterm 1.

vectors and the geometry of space;

the dot product and the cross product;

equations for lines and planes; graphs for cylinders and quadratic surfaces;

vector functions, space curves, derivatives and integrals of vector functions, arc length and curvature;

applications to velocity and acceleration, tangential and normal components of acceleration;

functions of 2 variables: limits and continuity, partial derivatives, tangent planes, linear approximations, differentiation.
Tuesday 21st May 2006
Here is a list of questions from previous Midterm 1 exams, which you wont be able to solve as preparation for our Midterm 1 exam.
263 Midterm 1 (2004): question 2, part b) and question 4;
263 Mock Midterm 1 (2005): questions 5,6,12 and 15;
217 Midterm 1 (2005): questions 3 and 4;
217 Mock Midterm 1 (2005): questions 1, 6 and 7.
Tuesday 21st May 2006
Note that Homework 2 has been modified to make it easier. Namely, in question 3, part a), you have to calculate the curvature, but you dont have to find the point t, which maximized the curvature. Also, in question 3, part b), you no longer have to calculate N. In question 4, part b), v(0)=<1,1,1>. Here is the new version of Homework 2.
Sunday 21st May 2006
Here are Homework 2 and the solution to Homework 1. Let me know if you find any typos or mistakes in the solution to Homework 1.
Thursday 18th May 2006
Here is the derivatives/integrals formula sheet you are allowed to take to the midterms and the final exam .
Saturday 13th May 2006
Homework 1 has been posted on the website.
Monday 8th May 2006
Website Created