Math 251 - Multivariable Calculus. Section H1. Fall 2008.

Contact Information
Instructor: Corey Hoelscher
Office: 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.
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