## 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 , W.H.Freeman, 2015,
ISBN 978-1-319-04911-9.
It has been augmented with some Rutgers "local matter," which is also
available
here.
Calculus Early
Transcendentals |

Syllabus and Maple labs for 640:251 | |||
---|---|---|---|

Lecture | Topic(s) and text sections | Maple labs | |

1 | 12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions |
Lab 0 | |

2 | 12.3 Dot Product and the Angle Between Two
Vectors 12.4 The Cross Product |
||

3 | 12.5 Planes in Three-Space | ||

4 | 13.1 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 workshopsThe 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.