Math 251 - Multivariable Calculus. Section H1. Fall 2008.
Contact Information
Instructor: Corey HoelscherOffice: Hill Center, room 515.
Office Phone: 732-445-2390 ext. 5935.
Office hours: Mondays 4:20-4:50, Tuesdays 2:20-3:20, Wednesdays 4:20-4:50
e-mail:

Peer Mentor: Matt Edwards
e-mail: mjedward@eden
Announcements
Stay tuned here for important announcements about the course.
- The final exam will take place Tuesday December 16, 8:00-11:00am in the usual classroom, SEC 202. It will cover roughly 3/4 new material and 1/4 review. The new material consists of everything we have done since the last exam, specifically sections 15.5, 16.1, 16.2, 16.3, 16.4, 16.5, 17.1, 17.2 and 17.3, and the old material is everything that was covered on the previous exams.
- I will be giving a review session on Sunday 3:00-5:00pm in Scott Hall room 219, on College Ave, where I will go over problems from the practice exam.
- The final exam review questions are available here. Once you have finished the problems you can check most of your answers here.
- The final exam equation sheet is available here. You will be given an identical copy of this note sheet on the final exam.
- I will have extra office hours Monday 3:20-4:50.
- The in-class demonstrations I did are available here. The best ones are Rogness' and Nykamp's applets, though some of the MIT demos are good as well.
- Solutions to the first and second midterm exams are available on Sakai under Resources.
- A discounted version of Maple is available here if you want to buy it.
- The Introduction to Maple is still available.
- Quiz, homework and exam grades will be posted on Sakai.
General Information
Class will meet Mondays and Wednesdays 5:00 PM - 6:20 PM in the Science and Engineering Resource Center, room 202, for lecture, and Tuesdays 5:00 PM - 6:20 PM in room 211, in the same building, for workshop.The topics for the course will include: Vector Geometry, Vector-Valued Functions, Functions of Several Variables, Partial Derivatives, Multiple Integrals, Line and Surface Integrals, Stokes' Theorem, and much more. The main Math 251 website has more general information about this course.
The text for the course is Jon Rogawski: "Calculus Early Transcendentals." The required textbook may be supplemented by an optional "Student's solution manual."
Homework
Doing homework problems is the best way to make sure you understand the material and to reinforce what you have learned. Every week there will be a homework assignment on the material covered in class. The assignments will be posted in the course calendar below and it is your responsibility to check this calendar for the assignments and due dates. The homeworks will be graded for completion and the quiz questions will generally be taken directly from the homework. Doing homework problems is the only way to really learn math. It is easy to sit through a lecture or read a book and think you understand everything. But when you sit down to solve problems you realize there are lots of holes in your knowledge. This is why the homework is an essential part of the course.Each homework assignment will also have assigned reading from the book. These readings are very important for several reasons. First, we will not always have time to cover everything from the book in class and you will have to read the skipped parts of the book in order to be able to do the homework and be prepared for the quizzes and exams. Second, it is an important skill to be able to read and follow written mathematics and this is one of the goals of the course.
Workshops
Every Tuesday we will have a Workshop designed to improve your problem solving skills and deepen your understanding of the course material. During these workshops, you will be given a series of difficult problems to work on in groups. The professor and the peer mentor for the course will move around the room to answer questions, give hints on the problems and keep you on the right track. At the end of the workshop each day the professor will select one of the problems which will then have to be written up by each student individually and handed in at the following workshop. Your write-ups must be clear, well organized, well written and logically correct, as they will be graded on this criteria.
Maple Projects
Although a deep understanding of the mathematics behind real-world problems is essential, many problems require computations which are far too difficult to do with a pencil and paper. So learning how to use computers to help solve problems is a key part of a good math education in our modern world. To that end, there will be four Maple projects due throughout the semester for this course. These are short projects designed to familiarize you with the computer mathematics program Maple. The due dates of these projects are posted on the course calendar below.
Quizzes
Quizzes are a good way for you to make sure you can solve important types of problems and they give you a bit more practice with the material. There will be a quiz each week in class that will cover the material from the previous homework. The quiz will usually consist of a few problems directly from the homework. The best way to study for the quizzes is to do the homework. If you know how to do all the problems on the homework then you will have no problem with the quiz. The two lowest quizzes will be dropped at the end of the semester and there will be no make-up quizzes for any reason.
Exams
There are two in-class midterm exams and one cumulative final exam. The midterms are tentatively scheduled for 10/8/08 and 11/5/08. Let me know now if you have any problems making these dates as make-up exams will only be given under extreme circumstances. The final exam will be on Tuesday, December 16, 8:00 AM to 11:00 AM. No notecards or calculators will be allowed on any exam or quiz.
Grading
The grading will be roughly computed according to the following table.| Component | Weight |
| Quizzes | 10% |
| Homework/Workshops/Maple | 10% |
| Midterm 1 | 23% |
| Midterm 2 | 23% |
| Final exam | 34% |
| Total | 100% |
Tentative syllabus
| Lecture | Sections | Topics | Notes |
|---|---|---|---|
| Tue 9/2 |
Workshop 0 | ||
| Wed 9/3 |
12.1, 12.2 | Vectors in the Plane; Vectors in Three Dimensions | |
| Mon 9/8 |
12.3, 12.4 | Dot Product and the Angle Between Two Vectors; The Cross Product | HW 1 due |
| Tue 9/9 |
Workshop - Computer lab: ARC - PC 116 | Quiz 1 | |
| Wed 9/10 |
12.5 | Planes in Three-Space | Maple 1 due (help, data) |
| Mon 9/15 |
13.1, 13.2 | Vector-Valued Functions; Calculus of Vector-Valued Functions | HW 2 due |
| Tue 9/16 |
Workshop 1 | Quiz 2 | |
| Wed 9/17 |
13.3, 13.4, 13.5 | Arc Length and Speed; Curvature; Motion in Three-Space | |
| Mon 9/22 |
14.1, 14.2 | Functions of Two or More Variables; Limits and Continuity in Several Variables | HW 3 due |
| Tue 9/23 |
Workshop 2 | Quiz 3 | |
| Wed 9/24 |
14.3, 14.4 | Partial Derivatives; Differentiability, Linear Approximation and Tangent Planes | |
| Mon 9/29 |
14.5 | The Gradient and Directional Derivatives | HW 4 due |
| Tue 9/30 |
Workshop 3 | Quiz 4 | |
| Wed 10/1 |
14.6 | The Chain Rule | Maple 2 due (help, data) |
| Mon 10/6 |
14.7 | Optimization in Several Variables | HW 5 due |
| Tue 10/7 |
Workshop 4 -- Exam 1 Review | ||
| Wed 10/8 |
Midterm exam 1 | ||
| Mon 10/13 |
14.8 | Lagrange Multipliers: Optimizing with a Constraint | |
| Tue 10/14 |
Workshop 5 | Quiz 5 | |
| Wed 10/15 |
15.1 | Integration in Several Variables | Maple 3 due (help, data) |
| Mon 10/20 |
15.2 | Double Integrals over More General Regions | HW 6 due |
| Tue 10/21 |
Workshop 6 | Quiz 6 | |
| Wed 10/22 |
15.3 | Triple Integrals | |
| Mon 10/27 |
12.7 | Cylindrical and Spherical Coordinates | HW 7 due |
| Tue 10/28 |
Workshop 7 | Quiz 7 | |
| Wed 10/29 |
15.4 | Integration in Polar, Cylindrical, and Spherical Coordinates | |
| Mon 11/3 |
15.5 | Change of Variables | HW 8 due |
| Tue 11/4 |
Workshop 8 -- Exam 2 Review | ||
| Wed 11/5 |
Midterm exam #2 | ||
| Mon 11/10 |
16.1 | Vector Fields | |
| Tue 11/11 |
Workshop 9 | Quiz 8 | |
| Wed 11/12 |
16.2 | Line Integrals | Maple 4 due (help, data) |
| Mon 11/17 |
16.3 | Conservative Vector Fields | HW 9 due |
| Tue 11/18 |
Workshop 10 | Quiz 9 | |
| Wed 11/19 |
16.4 | Parameterized Surfaces and Surface Integrals | |
| Mon 11/24 |
16.5 | Surface Integrals of Vector Fields | HW 10 due |
| Tue 11/25 |
No class. Thursday schedule. | ||
| Wed 11/26 |
No class. Friday schedule. | Happy Thanksgiving | |
| Mon 12/1 |
17.1 | Green's Theorem | |
| Tue 12/2 |
Workshop 11 | Quiz 10 | |
| Wed 12/3 |
17.2 | Stokes' Theorem | HW 11 due |
| Mon 12/8 |
17.3 | Divergence Theorem | |
| Tue 12/9 |
Workshop 12 | Quiz 11 | |
| Wed 12/10 |
Review for final | HW 12 due |
Homework assignments
Read the following description of how to present your work.
HW 1:
Reading:Sections 12.1 through 12.2
This article on Presenting Your Work
Problems:
12.1: 5, 9, 11, 15, 21, 40, 47
12.2: 11, 13, 19, 25, 27, 31, 51
HW 2:
Reading:Read sections 12.3 through 12.5 and skim through 12.6
Problems:
12.3: 1, 13, 21, 29, 31, 52, 57, 63
12.4: 1, 5, 13, 20, 25, 26, 43, 44
12.5: 1, 9, 11, 15, 25, 31, 53
12.6: 27, 28, 29
HW 3:
Reading:Sections 13.1 through 13.5
Problems:
13.1: 5, 13, 15, 18
13.2: 4, 14, 30, 31, 33, 41, 49
13.3: 3, 9, 13, 14
13.4: 1, 7, 17, 21
13.5: 3, 6, 32
HW 4:
Reading:Sections 14.1 through 14.4
Problems:
14.1: 7, 20, 23, 27, 36, 40
14.2: 5, 15, 27, 35
14.3: 3, 19, 21, 39, 47, 50, 53
14.4: 3, 4, 7, 15, 27, 33
HW 5:
Reading:Sections 14.5 and 14.6
Problems:
14.5: 7, 13, 27, 31, 33, 37, 39, 43
14.6: 1, 5, 7, 17, 20, 23, 27, 30
HW 6:
Reading:Sections 14.7, 14.8 and 15.1
Problems:
14.7: 1, 3, 7, 17, 19, 24, 25, 27, 29
14.8: 2, 7, 11, 13, 15
15.1: 10, 15, 23, 25, 33, 37, 44
HW 7:
Reading:Sections 15.2 and 15.3
Problems:
15.2: 3, 5, 11, 25, 32, 37, 43, 45, 49, 59
15.3: 3, 5, 11, 15, 17, 25, 33
HW 8:
Reading:Sections 12.7 and 15.4
Problems:
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
HW 9:
Reading:Sections 15.5, 16.1 and 16.2
Problems:
15.5: 1, 5, 14, 15, 21, 29, 33, 37
16.1: 1, 3, 10, 17, 23, 27
16.2: 3, 9, 13, 21, 27, 35, 39, 40
HW 10:
Reading:Sections 16.3 and 16.4
Problems:
16.3: 1, 5, 9, 13, 17, 19, 21
16.4: 1, 5, 8, 11, 19, 21, 37
HW 11:
Reading:Sections 16.5 and 17.1
Problems:
16.5: 1, 6, 9, 12, 15, 17, 23
17.1: 1, 3, 6, 9, 12, 23, 27
HW 12:
Reading:Sections 17.2 and 17.3
Problems:
17.2: 1, 5, 9, 11, 19, 23
17.3: 1, 5, 7, 11, 14, 15, 18
Be sure to check all your answers in the back of the book.
Last modified: September 1, 2008