Note: More information, with possible changes, will be added as the exam dates near.

exam 1: wed feb 22 (in class)

• find/sketch domain, range, graphs for simple functions of 2 variables. you may also be asked about level curves.
• determine partial derivatives, gradients of functions of 2 or 3 variables, and use this to write down equations for the tangent plane of a graph z=f(x,y) at a point. you may need to use a tangent plane to do linear approximation to approximate the value of a 2-variable function at a point.
• compute directional derivatives of functions of 2 or 3 variables, be able to determine the direction of fastest increase or decrease of a function of 2 or 3 variables (e.g., convert the gradient to convert to a unit vector)
• find local/absolute minima/maxima, as well as saddle points, of functions of 2 variables. (think: critical points and second derivatives test) expect to have to deal with regions with boundary points, where you may need to:
• use lagrange multipliers to maximize/minimize a function of 2 or 3 variables subject to a constraint. unless explicitly stated that you need to use lagrange multipliers, you are also allowed to solve such problems by the "substitution/reduction" method (e.g., as in example 5 in sec 14.7, though it may not be possible/easy to do so).

exam 2: fri apr 7 (in class)

this exam will cover everything we did, in lecture and homework, on chapter 15. while not necessarily a comprehensive list of things you may be expected to do on the exam, here are the main points you should be comfortable with (though there may not be time to ask about all of them on the exam):

• compute double and triple integrals in cartesian (rectangular coordinates. this includes setting up, and possibly changing the order of, iterated integrals.
• compute areas of regions in the plane, and surface areas and volumes of regions in 3-space.
• be able to go back and forth between cartesian coordinates and polar coordinates or cylindrical and spherical coordinates, including translating integrals between these different coordinate systems.
• compute double integrals using general change of variables

• concept check: 1(abc), 2(a), 3, 6, 9, 10(ab)
• true-false: 1, 2, 3, 4, 5, 9
• exercises: 3, 5, 9, 10, 13, 15, 25, 37, 38, 55

final exam: fri may 12 (8-10am)

this exam will be cumulative, covering chapters 14, 15 and 16 of stewart. you should expect one page of true/false questions as well as 2-4 problems on each of the 3 chapters covered. (each of the 3 chapters will account for roughtly 1/3 of the exam.) a list of the main (but not necessarily all) topics covered on the final exam is:

• all the topics listed in the bullet points above for exams 1 and 2
• vector fields: be able to draw them, determine if they are conservative, and compute curl and div, and know basic facts about div and curl.
• line integrals: be able to compute the various kinds of line integrals (ds, dx, dy, dz and vector field line integrals), both directly as well as using the fundamental theorem, green's theorem and stokes' theorem
• surface area: be able to compute surface area in the plane with double integrals as in ch 15 as well as with green's theorem, and areas of more general surfaces such as graphs of functions or parametric surfaces as in sec 16.6
• surface integrals: be able to compute surface integrals of scalar and vector fields (flux), both by rewriting as double integrals as well as with the divergence theorem

sec 16.7: 5, 21, 25, 27
sec 16.8: 3, 7
sec 16.9: 5, 7

• concept check: 2a, 3abde, 4ab, 5-10, 11bc, 12abc, 13cd, 14-16
• true-false: 1-13
• exercises: 3, 4, 9, 11, 13, 17, 18, 25, 27, 29, 30, 33, 34