MATE 3063 Practice problems
You are responsible for the problems posted in the syllabus . You do not have to spend the
same amount of time on every problem, but you must identify groups of
problems corresponding to each topic, and you must spend enough time
on as many from each group, as you think is necessary for you to master
that skill. On quizzes and tests, you are graded for carefully
justifying the steps, not simply for getting the right
answer. Clusters of problems posted here will be identified by the
posting date; problems posted on, say, Wednesday, are fair game for an
unannounced quiz on the following Monday.
A link: set
notation .
(18/08) (Dates are coded by dd/mm): section 12.6, all exercises from
syllabus.
(19/08) Section 14.1. Finding domain and range.
(21/08) Graphs, level lines, level curves. From now on, unless
specified otherwise, all exercises in syllabus.
(23/08) Graphically solving inequalities for a function of a single
variable. We illustrated with 1-x^2 >= 0 (x^2 means x squared). We
have so far shown two graphical methods: finding the image f(A) of a
set A, if the graph of f is known, and ``solving'' graphically f(x) <=
m (or f(x) >= m).
(28/08) Finding range using level sets. Definition of limit.
(8/09) When limits do not exist. Continuity. Comment on the previous
note: these two methods are for functions of a single variable, the
graph of which is known. We have also shown how to find the region
f(x,y) <= m, using the level set f(x,y) = m in the xy plane.
(11/09) Partial derivatives. Sample
first partial exam , due 19/09 in class.
(18/09) Tangent planes to surfaces and linear approximation. Chain
rule.
(24/09) Directional derivative and gradient.
(30/09) Maxima and minima: definition, critical points. Hessian
sufficiency criterion.
(14/10) Multiple integral: definition and properties. Iterated
integral.
(15/10) Sample second partial exam
, due 23/10 in class.
(17/10) Integral over general domain.
(25/10) Polar coordinates.
(28/10) Triple integral.
(4/11) Triple integral in spherical coordinates. Passing mention was
made of integral in cylindrical coordinates; of that section, do
problems 9, 19, 23, 26, 28, 30.
(8/11) Change of variables in multiple integrals. Sample third partial exam , due 15/11 in
class.
(14/11) Suggested exercises from section 15.10: 3, 5, 7, 9, 13, 14,
17, 18, 25, 27, and one of 21 or 22.
(18/11) Vector fields. Gradient vector fields.
(27/11) Surfaces in parametric form. Surface integrals.
Last modified: Wed Nov 27 00:44:36 AST 2013