## Syllabus & textbook homework for Math 251

 This is a very rapid plan of study. A great deal of energy and determination will be needed to keep up with it. Modifications may be necessary. Periodic assignments (Maple labs, workshops, etc.) may be due at times, and additional problems may be suggested. The text is the first edition of Rogawski's Calculus Early Transcendentals, W.H.Freeman, 2008, ISBN-10: 0-7167-7267-1. It has been augmented with some Rutgers "local matter," which is also available here.

Syllabus and suggested textbook homework problems for 640:251
LectureTopic(s) and text sectionsSuggested problems
112.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.1: 5, 9, 11, 15, 21, 40, 47
12.2: 11, 13, 19, 25, 27, 31, 51
212.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.3: 1, 13, 21, 29, 31, 52, 57, 63
12.4: 1, 5, 13, 20, 25, 26, 43, 44
312.5 Planes in Three-Space 12.5: 1, 9, 11, 15, 25, 31, 53
413.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.1: 5, 13, 15, 18
13.2: 4, 14, 30, 31, 33, 41, 49
513.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in Three-Space
13.3: 3, 9, 13, 14
13.4: 1, 7, 17, 21
13.5: 3, 6, 32
614.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.1: 7, 20, 23, 27, 36, 40
14.2: 5, 15, 27, 35
714.3 Partial Derivatives
14.4 Differentiability, Linear Approximation and Tangent Planes
14.3: 3, 19, 21, 39, 47, 50, 53
14.4: 3, 4, 7, 15, 27, 33
814.5 The Gradient and Directional Derivatives 14.5: 7, 13, 27, 31, 33, 37, 39, 43
914.6 The Chain Rule 14.6: 1, 5, 7, 17, 20, 23, 27, 30
1014.7 Optimization in Several Variables 14.7: 1, 3, 7, 17, 19, 24, 25, 27, 29
1114.8 Lagrange Multipliers: Optimizing with a Constraint 14.8: 2, 7, 11, 13, 15
12Exam 1 (timing approximate!)
1315.1 Integration in Several Variables 15.1: 10, 15, 23, 25, 33, 37, 44
1415.2 Double Integrals over More General Regions 15.2: 3, 5, 11, 25, 32, 37, 43, 45, 49, 59
1515.3 Triple Integrals 15.3: 3, 5, 11, 15, 17, 25, 33
16 12.7 Cylindrical and Spherical Coordinates
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
12.7: 1, 5, 23, 31, 41, 43, 48, 53
15.4: 1, 5, 9, 19, 23, 27, 31, 37, 39, 42, 47, 51, 59
17
1815.5 Change of Variables 15.5: 1, 5, 14, 15, 21, 29, 33, 37
1916.1 Vector Fields 16.1: 1, 3, 10, 17, 23, 27
2016.2 Line Integrals 16.2: 3, 9, 13, 21, 27, 35, 39, 40
2116.3 Conservative Vector Fields 16.3: 1, 5, 9, 13, 17, 19, 21
22Exam 2 (timing approximate!)
2316.4 Parameterized Surfaces and Surface Integrals 16.4: 1, 5, 8, 11, 19, 21, 37
2416.5 Surface Integrals of Vector Fields 16.5: 1, 6, 9, 12, 15, 17, 23
2517.1 Green's Theorem 17.1: 1, 3, 6, 9, 12, 23, 27
2617.2 Stokes' Theorem 17.2: 1, 5, 9, 11, 19, 23
2717.3 Divergence Theorem 17.3: 1, 5, 7, 11, 14, 15, 18
28Catch up & review; possible discussion of some applications of vector analysis.

Maple labs and workshops
The course has four suggested Maple labs during the standard semester, in addition to a Maple lab 0 which is introductory and should be discussed in the first week or two.
Instructors may also wish to assign some workshop problems so that students can continue to improve their skills in technical writing.