Syllabus & textbook homework for Math 251

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 3rd edition of Rogawski's Calculus Early Transcendentals, W.H.Freeman, 2015, ISBN 978-1-319-04911-9. It has been augmented with some Rutgers "local matter," which is also available here.


Syllabus and Maple labs for 640:251
LectureTopic(s) and text sections Maple labs
112.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
Lab 0
212.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
312.5 Planes in Three-Space
413.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
Lab 1
5 13.3 Arc Length and Speed
13.4 Curvature
6 14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
7 14.3 Partial Derivatives
14.4 Differentiability, Linear Approximation and Tangent Planes
8 14.5 The Gradient and Directional Derivatives Lab 2
9 14.6 The Chain Rule
10 14.7 Optimization in Several Variables
11 14.8 Lagrange Multipliers: Optimizing with a Constraint
12 Exam 1 (timing approximate!)
13 15.1 Integration in Several Variables Lab 3
14 15.2 Double Integrals over More General Regions
15 15.3 Triple Integrals
16 12.7 Cylindrical and Spherical Coordinates
17 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates Lab 4
18 15.6 Change of Variables
19 16.1 Vector Fields
20 16.2 Line Integrals
21 16.3 Conservative Vector Fields
22 Exam 2 (timing approximate!)
23 16.4 Parameterized Surfaces and Surface Integrals Lab 5
24 16.5 Surface Integrals of Vector Fields
25 17.1 Green's Theorem
26 17.2 Stokes' Theorem
27 17.3 Divergence Theorem
28 Catch up & review; possible discussion of some applications of vector analysis.
Maple labs and workshops
The course has five 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.

Quadratic surfaces
The syllabus omits section 12.6, A Survey of Quadratic Surfaces. The ideas concerning quadratic surfaces are actually addressed in the third Maple lab, and certainly some knowledge of quadratic surfaces is useful when considering the graphs of functions of several variables and studying critical points. Although this section is formally omitted, appropriate examples and terminology should be introduced early in the course.


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