MAT
371 - Advanced Calculus I
Fall 2007
Definitions
You will be responsible for producing precise definitions of each of
the following key terms from the text. In some cases you will be asked
to show that some mathematical object satisfies or does not satisfy a
particular definition. Also be sure to know the various synonyms and
abbreviations for each of these terms.
Chapter
0
Section 0.1: set equality,
subset, proper subset, set union, set intersection, complement
Section 0.2: Cartesian
product, relation, function, domain, image, one to one, inverse,
inverse image, injection, surjection, bijection, composition
Section 0.5: real numbers,
bounded from above (below), upper bound (lower bound), least upper
bound, greatest lower bound
Chapter
1
Section 1.1: sequence,
convergence (of a sequence), neighborhood, bounded from above (below),
bounded
Section 1.2: Cauchy sequence,
accumulation point
Section 1.4: subsequence,
increasing (decreasing) sequence, monotone sequence
Chapter
2
Section 2.1: limit of a
function at a point
Section 2.4: increasing
(decreasing) function, monotone function
Other: limit of a function at
infinity (negative infinity), infinite limit of a function at a point
Chapter
3
Section 3.1: continuity of a
function at a point, continuity of a function on its domain
Section 3.3: uniform
continuity, closed, open, relatively open, compact, cover, open cover,
subcover, finite
subcover
Chapter
4
Section 4.1: differentiable at
a point, differentiable, derivative at a point, derivative
Section 4.3: relative maximum
(minimum)
Chapter
5
Section 5.1: partition, refinement, upper
sum, lower sum, upper integral, lower integral, Riemann integral,
Riemann-integrable
Section 5.3: Riemann sum, mesh