# Mathematics 234

## Multiple Integration and Vector Calculus

### (Spring Quarter 2007, Northwestern University)

This is the homepage for Math 234, Spring Quarter 2007 (NU). The course will take place MWF 1:00-1:50 pm in Lunt 105.

### News :

The course is now finished ! Thank you for your participation. The final exam will be next Wedenesday (6/6/07) from 7 to 9 pm in Lunt 105.
There will exceptionnal office hours next Monday (6/4/07) from 1:30 pm to 3 pm. Work before that day, rest on Tueday ! Good luck.

A Klein bottle looks like this : Klein Bottle.

### Syllabus :

The homework will help you to understand the course. The quizzes will be based on them.

Chapter 11 : Multiple Integrals
(one section each day) [Homework Assignment]

11.1 Double Integrals [9,11,13,17,19,26,31,33,43,47,49,51]
11.2 Area, Volume and Center of Mass [Example 2.2, 7, 15, 26, 28]
11.3 Double Integrals in Polar Coordinates [Example 3.3, Example 3.5, 9, 12, 16, 26, 30]
11.4 Surface Area [2, 3, 9, 17]
11.5 Triple Integrals [Example 5.1, Example 5.3, Example 5.5, 22, 37]
11.6 Cylindrical Coordinates [Example 6.5, 13, 17, 25, 33, 37]
11.7 Spherical Coordinates [Example 7.3, 25, 31, 33, 37, 39, 53, 57]
11.8 Change of Variables in Multiple Integrals [1, 5, 11, 13, 17, 27, 29]
Review : 4/13/07

Mid-Term Exam I : 4/16/07

Chapter 11 : Vector Calculus (roughly one day and a half by section) [Homework Assignment]

12.1 Vector fields [3, 5, 9, 11, 13, 17, 27, 29, 35, 39, 47, 51]
12.2 Curl and Divergence [1, 5, 9 {The answer is <-x sin y, ...>}, 13, 19, 27, 31, 33, 35, 41, 45, 49]
12.3 Line Integrals [1, 7, 11, 17, Example 3.7, Example 3.9, 25, 27, 29, 37, 39, 41, 55 {Do you really need to compute an integral here ?}, 57]
12.4 Independance on Path and Conservative Vector Fields [1, 3, 7, 13, 15, 17, 19, 21, 27, 31, 33, 35, 37, 41, 43, 47]
12.5 Green's Theorem [1, 3, 7, 11, 15, 25, 33, 35]
Review : 5/9/07
Mid-Term Exam II : 5/14/07
12.6 Surface Integrals [Example 6.3 (b), Example 6.5, 3, 5, 7, 9, 11, 17, 19, 21, 25, 27, 29, 33, Example 6.7, 37, 39, 41]
12.7
The Divergence Theorem [Example 7.2, 1, 5, 7, 9, 17, 19, 25]
12.8
Stokes's Theorem [Example 8.2, Example 8.3, 1, 3, 5, 7, 11, 17, 21]
12.9
Applications of Vector Calculus [No homework]

Last lecture : 5/25/07

Reading Week (Review) : 5/30/07 and 6/1/07

Final Exam : 6/6/07  7:00-9:00 pm  Lunt 105

#### Teacher:Bruno Vallette

Office: Lunt 306
Office Hours
: Mondays, Wednesdays, 2:30-3:30 pm or by appointment

#### Teaching Assistants:

Qian Ding:
Office: Lunt B20
Office hours : 11am-12:50pm Thursday

Randy Qian:

Office: Lunt B12
Office hours: 4-5pm Tuesday, 5-6pm Thursday

#### Text Books:

Calculus: Concepts and Connections, Chapters 11-12, by R. Smith and R. Minton, McGraw Hill.

#### Quiz Sessions:

There will be 6 quizzes but only the 5 best will be taken into account.
1:00-1:50 pm Thursdays, Lunt 105 (Qian Ding), Lunt 103 (Randy Qian)

Final Exam 200 points, Mid-term Exams 100 points each, Quizzes 20 points each.

#### Exams:

To be excused from an exam, except for sudden illness, you must make arrangement at least 24 hours before the exam is scheduled. Anyone missing an exam without previously arranging to do so will receive 0 point. I do not give make-up exams.

### 100 Integrals :

You should be able to do to following 100 Integrals. Since the aim of this course is to learn multiple integrals, we will be using all the time methods of one dimensional integrals.