Studyguide for Math 2110Q
Room change: The midterm will take place in MSB 117.
Notecard: You will be allowed to bring one notecard (3x5) of your own, hand-written notes to
the exam.
Sect What you should be able to do
14.3. compute partial derivative (15-42, 61-68); estimate partial derivatives from tables (1-4);
estimate partial derivatives from graph or level set of function (5-8, 10)
14.4. find the equation of a tangent plane of a surface at a point (1-6); find linearization at a
point and use it (11-19, 21); applications (31-38)
14.5. use the chain rule to compute (partial) derivatives of compositions of functions (1-15); use
chain rule to compute implicit derivatives (27-34); application to real world examples (35-43)
14.6. find gradient vector and directional derivative in direction of a vector (7-19); find maximal
value of directional derivative at a point (21-26); real world applications (30-35); estimate
directional derivative at a point from level set (36, 38)
14.7. find local maxima and minima of functions (1-18); find absolute minima and maxima of
functions on a set (29-36); set up functions from word problems and find maxima/minima
of such functions (31-51);
15.1. estimate double integrals (in particular volumes) using Riemann sums (3,4); estimate aver-
age value (9-10)
15.2 compute double integral over rectangle using Fubini’s theorem (1-22); compute volumes of
solids (23-31); compute average value (35-36)
15.3 compute double intgrals over more general regions (1-18); find volumes of solids using double
integrals (19-28); simplify integrals by changing order of integration (39-50)
15.4 evaluate double integral using polar coordinates (7-14, 29-32); determine areas of regions
and volumes of solids by integration using polar coordinates (15-27, 33-34); decide whether
to use polar coordinates or usual coordinates (1-4)
15.6 evaluate triple integrals (3-18); find volume of solid (19-22); sketch shape of solid given a
triple integral (27-28)
15.7 convert cylindrical coordinates to rectangular coordinates and vice versa (1-4); describe
regions in cylindrical coordinates (1-13); use cylindrical coordinates to compute volumes
(15-16); use cylindrical coordinates to compute triple integrals (17-23a, 27-28)
15.8 convert spherical coordinates to rectangular coordinates and vice versa (1-4); describe sur-
faces and solids using spherical coordinates (5-16); compute triple integrals using spherical
coordinates (17-30, 35, 36, 39,40)
15.9 compute the Jacobian of a transformation (1–6); express images of regions of transformations
(7–10); use the change of variables formula to evaluate an integral (11-16).
16.1 sketch vector fields (1-10), match vector fields with their plots (11-18), find gradient vector
fields (21-26).
16.2 compute line integrals, with respsect to ds, dx and dy (1-16); explain and compute line
integrals of vector fields (17-22, 29a, 30a); applications: work (39-42)
16.3 decide whether a vector is conservative (3-10), use fundamental theorem (1, 2, 12-20)
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