Math 200 -- Multivariable Calculus
Winter 2016-2017 Term 2

Common Course Website



Here is the FORMULA SHEET (ALL SECTIONS) that you will be provided during the final exam.

MATERIAL:  The exam will based on all the material and textbook sections covered in the course with the following exceptions: Limits and continuity (section 12.2) and the formal definition of differentiability (appearing in 12.4) will not be examined. See the course outline below for the precise list of sections that are covered. You are encouraged to review your class, quizzes, midterms and past final exams in preparing for the final exam. You are also encouraged to look at other sections quizzes and midterms for review as well. Also, check out the UBC Math Wiki Math Exam Resources for two past final exams with solutions.

MATH200 201 (SHEN)           APR 24 2017 03:30 PM OSBO A
MATH200 202 (YILMAZ)      APR 24 2017 03:30 PM OSBO A
MATH200 203 (MURUGAN) APR 24 2017 03:30 PM OSBO A

Mar 07  End of term scaling policy: In assigning the grades at the end of the term, our responsibility is to assign a grade that reflects each student's level of mastery of the course material. Individual assessments throughout the term may vary in their grade distributions (sometimes by large amounts) between sections and also between various assignments and tests. To ensure fairness and consistency across all sections, we will use the final exam results (common to all sections) to normalize grades. In practice, this normally means that the term grades (i.e., everything but the final exam) of a section are scaled so that the median scaled term grade is matched to the median of that section's final exam grades.

Jan 27  Here is some additional practice material (past midterms) for the midterm: 2012 MT1, 2013 MT1, 2015 MT1, 2013 MT2 (only 1, 3), 2015 MT2 , solutions (only 1d, 2)

Jan 04   Piazza is now ready to use. Please sign up here using your UBC email address.

This is the common course website for Math 200 (Winter Term 2, 2016-17). For section-specific information, please refer to resources provided by individual sections' instructors:

Section 201(
MWF 9-10 am, LSK 201, Shen)
Section 202 (MWF 11am-12 pm, MATH 100, Yilmaz)
Section 203 (TTH 12:30-2 pm, MATH 100, Murugan)


Primary textbook: For most of the course, we will be using APEX Calculus, which you can download for free. We will be using "Version 3.0, Volume 3 (Chapters 9 - 13)" as listed on the APEX Calculus Download page:

At times, especially in the last few weeks of the course, we will also refer to the following secondary online textbooks:
    Secondary textbook #1: Single and Multivariable Calculus (Whitman College)
    Secondary textbook #2: Calculus (Strang)

Our reference and use of these free online textbooks will be in accordance with the creative commons license. In addition to these, any standard textbook in multivariable calculus will also serve as a reference for most of the topics in this course. This includes the textbook by Stewart, used for this course in recent past years.


  • weekly webwork assignments (worth 10% of overall grade)
  • 5 in class quizes (worth 15% of overall grade)
  • 1 midterm exam (worth 25% of overall grade)
  • 1 final exam (worth 50% of overall grade)

  • MORE 


    The weekly WeBWork assignments can be reached at:  
    The due dates are Fridays at 11:59pm (see webwork site).

    There will be 5 quizzes. These will be short 10 minute quizes that will take place in class on the dates listed below. The information for each quiz below will be updated closer to the time of the quiz -- please check your section's website for up-to-date information. The solutions to these will be posted on the individual sections' websites. The Friday dates below are for MWF sections, and the Thursdays are for TT sections.
    1. Date: Thursday, Feb 9 in class (for T-TH sections); Friday. Feb 10 in class (for MWF sections)
    2. Time/Place: During regular class time in the regular classroom
    3. Duration: 50 minutes
    4. What is covered: Check your section's website for specific information on test material. It may differ for different sections.
    5. IMPORTANT: Check the common course website and your individual section's website for further announcements regarding the midterm.


    The following is an outline of the topics to be covered in the course. The section numbers below correspond to the primary textbook unless otherwise stated. See also below some suggested problems from past final exams (which you can find here).

    Part I: 3-Dimensional Geometry
    Introduction, three dimensional coordinate systems, vectors, dot product, cross product, equations of lines and planes, cylinders and quadratic surfaces

    Suggested problems from the primary textbook:

    Section 10.1, problems 1-3, 7, 9, 12, 16
    Section 10.2, problems 1-5, 8, 11, 15, 20, 23, 27, 31
    Section 10.3, problems 1-3, 11, 15, 19, 31, 39
    Section 10.4, problems 1-5, 9, 15, 27, 30, 31, 35, 39, 41
    Section 10.5, problems 7, 11, 21, 27, 31
    Section 10.6, problems 1, 2, 9, 11, 14, 15, 17, 19, 25, 29, 32
    Section 10.1, problems 15, 17, 23-26, 27, 32

    Suggested problems from past final exams (mostly involving lines and planes in space):

    2015WT1 #1a, b
    2013WT2 #1a, b, c
    2013WT1 #1a (i, ii)
    2012WT1 #1
    2011WT2 #1

    Part II: Differentiation of Multivariable Functions (12.1, 12.3-12.8 (primary text) & 14.8 (secondary text #1))

    Functions of several variables, limits and continuity, Partial derivatives, Tangent planes and linear approximations, chain rule, directional derivatives and gradient vector, Maximum and minimum values, Lagrange multipliers

    Suggested problems from the primary textbook:

    Section 12.1, problems 1-6, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31
    Section 12.3, problems 1-4, 5, 13, 19, 29, 33
    Section 12.4, problems 7, 10, (find equation of tangent plane to z=f(x, y) at given point for 11, 12) , 13, 15, (find linear approximation for 17, 18 at the given point)
    Section 12.5, problems 1-5, 9, 17, 21, 29
    Section 12.6, problems 1-6, 13, 15, 21, 23, 25, 27
    Section 12.7, problems 17, 19, 21, 23
    Section 12.8, problems 1-4, 5, 7, 11, 13, 15, 17 (also 11, 13, 15, 19 from 14.7 in secondary text #1)
    Section 14.8 (from secondary text #1) 5, 10, 11, 12, 13, 15, 17

    Suggested problems from past final exams (mostly involves linear approximation, tangent plane to graphs):

    2015 #2 ii
    2014 #3
    2011WT2 #2a
    2011WT2 #2b
    2011WT1 #1b, c

    Suggested problems from past final exams (mostly involves chain rule and/or implicit diff.):

    2015 #3
    2014 #2
    2013WT2 #2a
    2013WT1 #1b(ii, iii)
    2013WT1 #1c
    2013WT1 #1d
    2012WT1 #2, 3
    2011WT2 #3
    2011WT1 #2

    Suggested problems from past final exams (involves gradient vectors and relations to directional derivatives, and level sets):

    2015 #1(iii)
    2015 #2(i, iii)
    2014 #1, 4
    2013WT1 #1b(i)
    2013WT2 #2 b, c
    2013WT1 #1e
    2013WT1 #1f
    2013WT1 #2
    2011WT2 #4
    2011WT1 #3

    Suggested problems from past final exams (involves classifying local extrema, absolute extrema, Lagrange Multipliers):

    2015 #4, 5
    2014 #5
    2013WT2 #3, 4
    2013WT1 #3, 4
    2012WT1 #4, 6
    2011WT2 #5
    2011WT1 #4

    Part III: Integration of Multivariable Functions (13.1-13.4, 13.6 (primary text), and 14.4 (secondary text #2))

    Double integrals over rectangles, Iterated integrals, double integrals over general regions, Double integrals in polar coordinates, applications of double integrals, triple integral, Triple integrals in cylindrical and spherical coordinates

    Suggested problems from the primary textbook:

    13.1 PROBLEMS: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 17.1 secondary text #1)
    13.2 PROBLEMS: 1-4, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 secondary text #1)
    13.3 PROBLEMS: 3, 4, 8, 13, 15
    13.4 PROBLEMS: 1, 5, 6, 13, 24
    13.6 PROBLEMS: 5, 7, 9, 11, 13, 15, 19, 23
    14.4 (from secondary text #2) PROBLEMS: 11, 13, 15, 19, 22, 23

    Suggested problems from past final exams (double integrals):

    2015 #6
    2014 #6
    2013WT2 #5, 6a
    2013WT1 #6
    2012WT1 #7,8
    2011WT2 #6, 7
    2011WT1 #5, 6

    Suggested problems from past final exams (triple integrals in rectangular, cylindrical and spherical coord):

    2015 #7, 8
    2014 #8, 9
    2013WT2 #7,8
    2013WT1 #7, 8, 9
    2012WT1 #9,10
    2011WT2 #8, 9, 10
    2011WT1 #7, 8


    1. No electronic devices will be allowed at the midterm and final exam. This includes calculators, cell phones, music players, and all other such devices. Formula sheets and other memory aids will not be allowed.
    2. Missing a homework, a quiz, or a midterm normally results in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be notified within 48 hours of the missed test, and presented with a doctor's note immediately upon the student's return to UBC. Failure to comply results in a 0 mark. If a midterm was missed for legitimate reasons, the weight of the missed midterm will be transferred to the final. Make-up midterms will not be provided. Please note that a student may NOT have 100% of their assessment based on the final examination. A student who has not completed a substantial portion of the term work normally shall not be admitted to the final examination.
    3. Missing the Final Exam: You will need to present your situation to the Dean's Office of your Faculty to be considered for a deferred exam. See the Calendar for detailed regulations. Your performance in a course up to the exam is taken into consideration in granting a deferred exam status (e.g. failing badly generally means you won't be granted a deferred exam). In Mathematics, generally students sit the next available exam for the course they are taking, which could be several months after the original exam was scheduled.
    4. UBC takes cheating incidents very seriously. After due investigation, students found guilty of cheating on tests and examinations are usually given a final grade of 0 in the course and suspended from UBC for one year. More information.
    5. Note that academic misconduct includes misrepresenting a medical excuse or other personal situation for the purposes of postponing an examination or quiz or otherwise obtaining an academic concession.