MATH200-253 ST1 2015
FINAL EXAM INFORMATION:
The final exam will be based on all the topics listed in the course
outline. The exam will last for exactly 150 minutes (2.5 hours). Use
of calculators, books, notes and formula sheets will NOT be allowed
during the test. Formula sheets will not be provided. Review by looking
over past final exams. The recent past final exams are a good indication
of the length and level of difficulty of our final exam. Also review
your notes, suggested problems from text, webwork problems, and our
midterms.
I. VECTORS, LINES, PLANES, QUADRIC SURFACES,
PARTIAL DERIVATIVES
(§12.1-12.6, 14.1, 14.3)
For a summary of these sections, see the Midterm1 information sheet
posted on the course website (link for the lazy http://www.math.ubc.
ca/~mtalpo/stuff/math2002015/MT1_INFO.pdf).
II. APPLICATIONS OF GRADIENT VECTOR,
MAXIMA/MINIMA, LAGRANGE MULTIPLIERS
(§14.4-14.8)
For a summary of these sections, see the Midterm2 information sheet
posted at http://www.math.ubc.ca/~chau/MATH200/MT2_INFO.pdf (from
last term’s course).
III. MULTIPLE INTEGRATION
(§15.1-15.9 (not including 15.6))
DOUBLE INTEGRAL
RR
D
f dA over general regions D:
-Know the basic idea behind the construction of the double integral
in terms of a limit of double Riemann sums.
-Know how, when possible, to express and calculate the double integral as an iterated integral either in Cartesian coordinates or polar
coordinates. Know how, when possible, to switch the order of integration in an iterated intetgral in Cartesian cooridnates (using either
dA = dxdy or dA = dydx). Recall that choosing such an order of integration corresponds to viewing D as either a type I or type II region
in the plane.
-You should be able to sketch a plane region D given a description of
the functions bounding it (provided it is not too complicated). Given
an iterated integral, you should know how to sketch the corresponding
domain of integration D (provided it is not too complicated).
-Given a mass density function ρ on D, know how to compute the
total mass and the coordinates of the center of mass. You will be given
the formulas for these in the exam, if they are needed.
TRIPLE INTEGRAL
RRR
E
f dV over general regions E:
-Know the basic idea behind the construction of the triple integral
in terms of a limit of triple Riemann sums.
-Know how, when possible, to express and calculate the triple integral as an iterated integral either in Cartesian coordinates, cylindrical
coordinates, or spherical coordinates. Know how, when possible, to
switch the order of integration in an iterated intetgral in Cartesian
cooridnates (using either dV = dxdydz or dV = dydxdz, etc). Recall
that choosing such an order of integration corresponds to viewing E as
either a type 1, type 2, or type 3 region in the space.
-You should be able to sketch a solid region E given a description of
the functions bounding it (provided it is not too complicated). Given
an iterated integral, you should know how to sketch the corresponding
region of integration E (provided it is not too complicated).
-Given a mass density function ρ on E, know how to compute the
total mass and the coordinates of the center of mass. You will be given
the formulas for these in the exam, if they are needed.