The following are recommended problems from the textbook.  

Introduction, three dimensional coordinate systems, vectors
(12.1, 12.2)
Section 12.1, problems 21, 33, 35, 41
Section 12.2, problems 4, 9, 15, 21, 25, 29, 35

Dot product, cross product, equations of lines and planes
(12.3, 12.4, 12.5)
Section 12.3, problems 7, 9, 17, 25, 41, 45, 49, 51, 55
Section 12.4, problems 3, 9, 15, 19, 27, 31
Section 12.5, problems 5, 9, 19, 33, 35, 37, 45, 51, 57, 65

Equations of lines and planes (cont.), cylinders, and
quadric surfaces, functions of several variables (12.5, 12.6, 14.1)
Section 12.5, problems 5, 9, 19, 33, 35, 37, 45, 51, 57, 65
Section 12.6, problems 1-19 (odd), 21-28 (all), 43, 45
Section 14.1, problems 7, 11, 15, 19, 25, 32, 33, 43, 47, 59, 61, 63, 67

Functions of several variables (cont.), Partial
derivatives, tangent planes and linear approximation (14.1-14.3)
Section 14.1, problems 7, 11, 15, 19, 25, 32, 33, 43, 47, 59, 61, 63, 67
Section 14.3, problems 3, 9, 25, 43, 49, 51, 75, 77, 93, 95, 99
Section 14.4, problems 3, 13, 21, 25, 35, 39

Tangent planes and linear approximations (cont.), chain
rule (14.4, 14.5)
Section 14.4, problems 3, 13, 21, 25, 35, 39
Section 14.5, problems 3, 7, 13, 21, 35, 39, 45, 49, 51

Chain rule (cont.), directional derivatives and gradient
(14.5, 14.6)
Section 14.5, problems 3, 7, 13, 21, 35, 39, 45, 49, 51
Section 14.6, problems 7, 17, 25, 27, 31, 33, 35, 41, 49, 53, 57, 63

Maximum and minimum values (14.7)
Section 14.7, problems 1, 7, 13, 15, 19, 29, 31, 39, 43, 45, 47

Lagrange multipliers, double integrals over rectangles
(14.8, 15.1)
Section 14.8, problems 1, 9, 15, 21, 29, 33, 35, 37, 43
Section 15.1, problems 1(a), 6, 13

Iterated integrals continued, double integrals over general
regions (15.2, 15.3)
Section 15.2, problems 9, 23, 25, 31, 35
Section 15.3, problems 5, 17, 19, 23, 27, 35, 47, 49, 53

Double integrals in polar coordinates, applications of
double integrals (10.3, 15.4, 15.5)
Section 10.3 (Polar Coordinates), problems 4, 6(i), 10, 16, 18, 22
Section 15.4, problems 5, 11, 13, 14, 21, 27, 31, 35
Section 15.5, problems 7, 11, 16

Applications of double integrals (cont.), triple integral
(15.5, 15.7)
Section 15.5, problems 7, 11, 16
Section 15.7, problems 13, 15, 21, 27, 31, 33, 35, 41

Triple integals (cont.), triple integrals in cylindrical
coordinates (15.7, 15.8)
Section 15.7, problems 13, 15, 21, 27, 31, 33, 35, 41
Section 15.8, problems 19, 21, 25, 29

Triple integrals in cylindrical and spherical coordinates
(15.8, 15.9)
Section 15.8, problems 19, 21, 25, 29
Section 15.9, problems 23, 25, 35, 39