# Mathematics 1B

## Regarding the Mathematics 1B Exam, January 2008

### Examination Syllabus

The examination syllabus for the course is the following sections of Edwards and Penney, Calculus, 7th edition, Prentice Hall:

Appendix C, A-13 to A-17
Section 3.1
Section 3.7
Section 5.3
Section 11.1
Section 11.2
Section 11.3 until the middle of page 839
Section 11.4
Section 11.5 until the bottom of page 856
Section 12.1
Section 12.2
Section 12.4

Furthermore, the mathematical aspects of the article
O'Brien J.F. and Hodgins J.K., Dynamic Simulation of Splashing fluids, Computer Animations '95, pages 198-205, 1995,
and the mathematical aspects of an animation program.

### The role of the article and the animation program

In groups you are to prepare a talk covering the mathematical aspects of the article, with special emphasis on section 3, and the mathematical aspects of the animation program. The talk is to be planned in such a way that the mathematical methods are clearly visible and in such a way that each member of the group presents a fair share of these mathematical methods.

The preparation of the manuscript for the talk is a part of the Mathematics 1B course, and you are strongly recommended to have at least a draft version of the manuscript ready at the end of the course in December.

At the exam in January, which is individual, each student must give a talk of 7-8 minutes on her/his part of the manuscript. Each person in the group is responsible for the entire manuscript and must be able to answer questions also within the parts which are presented by other group members.

### Exam topics, January 2008

1. Areas and sums.
2. The dot product; definition, properties, applications.
3. The cross product; definition, properties, applications.
4. Lines in space.
5. Planes in space.
6. Curves and motion in space.
7. Functions of two variables.
8. Partial derivatives.

### Preparation of the exam topics

You are expected to have prepared talks on all eight topics and you are welcome to bring along manuscripts to the exam. You will, however, not get any credit for just reading from the manuscript or copying the manuscript to the blackboard!

You are not expected to cover every aspect of each exam topic. You are to choose some important areas for presentation so that you during the presentation of 6-8 minutes explain something important about the exam topic. Do not focus too much on being fast in order to explain as mush as possible. The most important thing is that you explain things, definitions, results or maybe examples, in such a way that the audience can feel that you yourselves understand what you are saying.

### The organization of the exam

The exam is individual. You will receive a time schedule from the secretary. The examination of each student will last for 20 minutes.

The student is expected to start by giving a talk presenting her/his part of the article and the animation program lasting for 7-8 minutes. Then censor and examiner may ask questions. After that the student draws one of the 8 exam questions and gives a prepared talk on this question lasting 7-8 minutes. Again, the censor and the examiner may ask questions. The student then leaves the room, and after some time you will receive the result: passed or failed.

The official document regarding the exam, written in Danish: The exam in Mathematics 1B.

Latest update 12. October 2007 by Iver Ottosen