COURSE OUTLINE
The following is an outline of the topics to be covered in the course. The suggested problems from
the reference #1 listed below roughly 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 (Chapter 1 (CLPIII)); (10.1-10.6 (reference #1))
Coordinate systems, equations and surfaces, vectors. Think of this section as pre-multivariable Calculus.
TOPICS:
-three dimensional coordinate systems
-equations and surfaces in space
-vectors; arithmetic, dot product, cross product
-lines and planes
suggested problems from reference #1:
Section 10.1, problems 1-3, 7, 9, 12, 16, 15, 17, 27, 32
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
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 (Chapter 2 (CLPIII)); (12.1-12.8 (reference #1) & 14.8 (reference #2))
The differentiability of a two variable function ƒ(x, y) at a fixed point (x, y) =(a, b) is symbolically expressed by the equation
dƒ=Adx+Bdy
asserting that: for some fixed numbers A and B, any infinitessimal(tiny) changes dx, dy in the variables produce a corresponding change df in the function satisfying the symbolic equation. A very similar equation is used in the case of a function of 3 or more variables. We will learn the precise meaning of the above symbolic equation, how to use it, and how it encodes almost all the important formulas from multivariable Calculus.
TOPICS:
-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 reference #1:
Section 12.1, problems 1-6, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31
Section 12.2, problems 17, 18, 19
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 reference #2)
Section 14.8 (from reference #2) 5, 10, 11, 12, 13, 15, 17
suggested problesm from past final exams (mostly involves linear approximation, tangent plane to graphs):
2016 #3 a)
2015 #2 ii
2011WT2 #2a
2011WT2 #2b
2011WT1 #1b, c
suggested problesm from past final exams (mostly involves chain rule and/or implicit diff.):
2016 #4 a)
2015 #3
2014 #2, #3
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):
2016 2(i,iv); 3(b,c);
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 (Chapter 3 (CLPIII)); (13.1-13.6 (reference #1) and 14.4 (reference #3))
The double integral of a two variable function ƒ(x, y) over a region R in the plane is denoted symbolically as
∫ ∫R ƒ(p) dA
and represents an area-weighted continuous summation of ƒ over R where in particular: p represents a point in R, dA the area of an infinitessimal(tiny) patch around p, and ∫ ∫R a continuous summation over all points p in R. We will give a more precise definition of double integrals, interpret them in various different contexts, and learn to calculate them explicitly. We will then similarly define and treat triple integrals of three variable functions over regions in space.
TOPICS:
-double integrals over rectangles
-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 reference #1:
13.1 PROBLEMS: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 15.1 reference #2)
13.2 PROBLEMS: 1-4, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 reference #2)
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 reference #3) PROBLEMS: 11, 13, 15, 19, 22, 23
suggested problems from past final exams (double integrals):
2015 #6
2014 #6
2013WT2 #5, 6a
2013WT1 #5, #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
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 tests: If a student misses a test, 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.
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