MATH 200
Multivariable Calculus
Winter 2016
COURSE PAGE
This is the common page for the seven sections (linked below) of MATH 200 in
Term 2 of the 2016W session (September to December 2016). Your grade in the course will be determined by your grades in
weekly webwork assignments (worth 10% of overall grade)
6 in class quizes (worth 15% of overall grade)
1 midterm exam (worth 25% of overall grade)
1 final exam (worth 50% of overall grade)
All the basic information on these can be found below. The midterm and quizes will be held during regular class time.
It is your own responsibility to also check your own section website for any section specific instructions regarding these and for other announcements in general. In particular, different sections will have different quizes and midterms and your grades in these assesments may be scaled to ensure fairness across the different sections of the course. The final exam however will be the same for all sections.
FINAL EXAM
Below are the exam dates, times and locations for all sections of the course. The SRC is a big gymnasium which will be partitioned into three spaces (A, B, C) on the day of the exam. There is very little signage indicating which space is A, B, C, and it will be extremely crowded on exam day so know in advance which side of the building your section is in ( LOOK HERE).
MATH200 101 DEC 12 2016 03:30-6:00 PM SRC A
MATH200 102 DEC 12 2016 03:30-6:00 PM SRC A
MATH200 103 DEC 12 2016 03:30-6:00 PM SRC B
MATH200 104 DEC 12 2016 03:30-6:00 PM SRC B
MATH200 105 DEC 12 2016 03:30-6:00 PM SRC C
MATH200 106 DEC 12 2016 03:30-6:00 PM SRC C
MATH200 107 DEC 12 2016 03:30-6:00 PM BUCH A101
FORMULA SHEET: You will be given a formula sheet on the exam, which will be the exactly the same as the one appearing at the end of the 2015 final exam.
MATERIAL: The exam will be 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) were both discussed in the course, but will not be examined.
REVIEW MATERIAL: You are encouraged to review your class notes, webwork sets, quizes, midterms and past final exams in preparing for the final exam. You are also encouraged to look at other sections quizes and midterms for review as well. Solutions to the past finals can be purchased from the UBC MATH CLUB (solution package only covers 2007-2011 exams). Solutions to the 2015, 2014 finals can be found on the section 101 site linked below. Solutions to the Dec 2006 finals are
HERE and the 2006 april solutions are HERE (thanks to Warren Code for writing these)
INDIVIDUAL SECTION LINKS
Section 101 (MWF 9:00am-10:00am, LSK 201, Chau)
Section 102 (MWF 11:00am-12:00pm, LSK 201, Chau)
Section 103 (MWF 11:00am-12:00pm, MATX 1100, Nguyen)
Section 104 (MWF 1:00pm-2:00pm, Buchanan A104, Nguyen)
Section 105 (TT 9:30am-11:00am, Buchanan A201, Jamieson-Lane)
Section 106 (MWF 3:00pm-4:00pm, LSK 200, Code)
Section 107 (TT 3:30pm-5:00pm, Buchanan A104, Shen)
TEXTBOOK
Our primary reference for the course will be the following online textbook
PRIMARY TEXTBOOK
At times, especially in the last few weeks of the course, I will also refer to the following secondary online textbooks.
SECONDARY TEXTBOOK #1
SECONDARY TEXTBOOK #2
Our reference and use of these free online textbooks will be in accordance with the creative commons liscence. 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.
COURSE OUTLINE
The following is an outline of the topics to be covered in the course. The suggested problems from
the Primary textbook listed below represent the order in which we will be covering the topics. These will not be collected or graded. You are strongly advised to work out the problems in detail before looking at the solutions as they will give
you practice in the techniques learned in class and provide essential help in
preparing for the WebWorK homework, midterms, and final exam. Suggested problems from PAST FINALS are also listed below. Note that you can also search the Math 200 resource wiki for past exam problems basedo n their topics. Finally, you are encouraged to learn how to use Wolfram Alpha (the syntax you need to know for this is similar to using Webwork, which you will have to use anyways) although there will not be specific reference to it in the course. You can even check some of your homework answers wich Wolfram Alpha.
PART I: 3-DIMENSIONAL GEOMETRY (10.1-10.6): Introduction, three dimensional coordinate systems, vectors,
Dot product, cross product, equations of lines and planes, cylinders and quadric surfaces
suggested problems from text:
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 (12.1-12.8 & 14.8 from 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 primary text:
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 problesm 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 problesm 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 problesm 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 problesm 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 (13.1-13.6 and 14.1 from 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 text:
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
WEBWORK ONLINE HOMEWORK
- UBC Webwork site Link :
Use your CWL to login to
do your weekly on-line homework problem sets (some users have experienced
difficulties when using Firefox to access Webwork. If this happens to you,
please try to use another web browser) Due dates: Fridays at 11:59pm (see webwork site) Note that
the intent of homework is to help you learn the material, and therefore it
should be done as you are studying.
IN CLASS QUIZES
There will be 6 quizes. These will be short 10 minute quizes to 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. The solutions to these will be posted on your individual section links. The Friday dates below are for MWF sections, and the Thursdays are for TT sections.
- Quiz 1: (Fri Sept 16 and Thursday Sept 15)
- Quiz 2: (Fri Sept 30 and Thursday Sept 29)
- Quiz 3: (Fri Oct 28 and Thursday Oct 27)
- Quiz 4: (Wed Nov 9 and Thursday Nov 10)
- Quiz 5: (Fri Nov 18 and Thursday Nov 17)
- Quiz 6: (Fri Nov 25 and Thursday Nov 24)
MIDTERM EXAM INFORMATION
- TIME: Fri. Oct. 14th in class (for MWF sections); Thurs. Oct. 13th (for TT sections)
- PLACE: During regular class time
- DURATION: 50 minutes
- TOPIC LIST: CHECK YOUR SECTION WEBSITE FOR SPECIFIC INFORMATION ON TEST MATERIAL. IT MAY DIFFER FOR DIFFERENT SECTIONS. Note the past midterms below were from years when 2 midterms were held, which is why the second midterms below contain alot of material which we will not be covered on our midterm. In addition to these, you are also encouraged to look at relevant problems from the list of suggested past final exam problems.
- IMPORTANT: CHECK INDIVIDUAL WEBSITE FOR ANY FURTHER ANNOUNCEMENTS REGARDING YOUR MIDTERM. IT IS YOUR OWN RESPONSIBILITY TO DO SO.
- SOME PAST MIDTERMS
2012 MT1
2013 MT1
2015 MT1
2013 MT2
(only 1, 3)
2015 MT2 , solutions
(only 1b, 1d, 2)
GETTING HELP AND ADDITIONAL RESOURCES
- Math 200 resource wiki.
- In addition to your instructor's office hours, please take advantage of the
Math Learning Centre drop-in tutoring.
Do not wait till the exams -- if you feel uncomfortable with any of the
material, talk to your classmates, talk to the instructor, and come ask
questions at the Math Learning Centre.
- You can use Wolfram Alpha
-- it is a wonderful tool for calculations, plotting graphs of functions of two
variables, and various other tasks. If you want to visualize, for example, the
surface x^2+xy-y^2+3z=0, just type in "plot (x^2+xy-y^2+3z=0)".
Course policies
- No electronic devices will be allowed at the final examination. This
includes calculators, cell phones, music players, and all other such
devices. Formula sheets and other memory aids will not be allowed.
- Missing midterms: If a student misses a midterm, that student shall
provide a documented excuse or a mark of zero will be entered for that
midterm. Examples of valid excuses are an illness which has been
documented by a physician and Student Health Services, or an absence to
play a varsity sport (your coach will provide you with a letter). In
the case of illness, the physicians note must contain the statement that
``this student was/is physically unfit to attend the examination on the
scheduled date". There will be no make-up midterms, and the weight
of the missed midterm will be transferred to the final examination.
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.
- 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.
- 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.
- 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.