MATE 3022 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 grasp that concept. 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.
(24/01) (Dates are coded by dd/mm): section 6.1. Topic: (i) the
definite integral as limit of Riemann sums. (ii) Properties of the
definite integral. Problems: all from syllabus.
(3/02) section 6.2. Topic: (iii) fundamental theorem of
calculus. Problems from syllabus.
(19/02) Section 6.3. Topics: (iv) area between curves. (v) Cumulative
change and average value; average rate of change as the average of the
derivative. Problems: 1--32 from syllabus. (vi) Substitution rule. All
problems from syllabus.
(25/02) (vii) Integration by parts. Problems 2--47 of syllabus.
(5/03) (viii) Practising integration (7.2). Problems 48--69 of
syllabus.
(12/03) (ix) Rational functions and partial fractions. (x)
Improper integrals. (Unless otherwise indicated, all problems from
syllabus).
(9/04) (xi) Functions of two or more independent variables. Problems
from syllabus. For problem 13, referring to the notation explained in
class:
Find f(A), image of A under f, in the following cases: (a) A is the
circle of centre the origin and radius 2. (b) A is the subset { (x,0)
: x < -1 } of the x-axis. In both cases, plot A.
Find the inverse image of B under f, if B is the interval z >=
1. Shade the inverse image in question in the xy plane.
(14/04) (xii) Limit, defined by a two-person game. Examples given in
class.
(21/04) (xiii) Continuity.
(25/04) (xiv) Partial derivative.
(29/04) (xv) Counting.
(5/05) (xvi) Axioms of probability. (xvii) Computing probabilities of
events.
(8/05) (xviii) Conditional probability, and the law of total
probability.
(14/05) (xix) Independence. (xx) Bayes formula. (xxi) Discrete random
variable. (xxii) Mean and variance of a random variable. (xxiii)
Binomial distribution: read up to "sampling with and without
replacement". Exercises up to #43.
Last modified: Mon May 13 23:45:30 AST 2013