**Linear
Algebra I (Science)**

**Summer 2006 Instructor:
Alice McLeod**

*Introduction:*

Students
should be familiar with the role of Kirchoff’s and Ohm’s Laws in the analysis
of electrical circuits involving electromotive forces and resistors. From a
Linear Algebra perspective, the students will solve basic electrical circuit
problems using systems of linear equations.

*Competencies:*

This module is designed to specifically achieve
the following goals of the Exit Profile (at an advanced level):

(4B) Apply a systematic approach
to problem solving.

(6B) Reason logically.

(9B) Work as members of a team.

In addition to the goals listed above, the
module will also address the following exit profile goals:

(5) Use appropriate
data-processing technologies.

(7.1) Read a topic from a textbook and summarize the content.

(12) Put in context the emergence
and development of scientific concepts.

(14) Apply what has been learned
to new situations.

*Work Required:*

__Step 1__**:** Read the following:

a)
Anton,
Howard and Chris Rorres. __Elementary Linear Algebra.__ 9^{th} ed. abridged. Wiley
Publishing. pp. 302 – 306

b)
McMaster,
Robert. __Vector Geometry and Linear
Algebra.__ Revised May 2003. pp. 103-106, 126-129.

c)
Nicholson,
Keith. __Linear Algebra With Applications.__ 3^{rd} ed. PWS Publishing. pp. 29-30.

Photocopies
of relevant pages of (b) and (c) will be distributed to each group.

__Step 2__**:
**Get a copy
of the module problem sets (available from my website).

__Step 3__**:
**Students will
work in teams of three or four. Each student will meet in his or her group to
put together a complete team written report to include:

a)
A
short history of Karl Friedrich Gauss (1777-1855) and his contribution to
physics and mathematics. (Must be between
250 and 500 words, typed and double-spaced.
The report should be based on information from Boyer’s *A History of Mathematics*, Turnbull’s *The Great Mathematicians*, and/or Bell’s *Men of Mathematics*, all of which are on
two-hour reserve at the JAC library.)

b)
A
summary of electrical networks including Ohm’s Law, Kirchoff’s Current Law and
Kirchoff’s Voltage Law. Your summary should include specific examples similar
to those in (b) to illustrate how the laws are applied to circuit problems.

c)
Complete
solutions to *Problem Set I* (just
numbers 2, 4, 6, and 8) and to *Problem
Set II*. Do *Problem Set I* by hand and use Maple for *Problem Set II*. In each
case, set up the appropriate linear systems and solve for currents using
matrices where applicable. Interpret all negative signs which occur in your
solution for the currents.

*Timeline / Deadlines:*

You will have a little class time in which to work on the
project (one hour on June 27^{th}, and one hour on July 4^{th}). However, team work outside of class time will
likely also be necessary.

Complete
report due: Thursday, July 6^{th}, 2006.

A quiz on
solving electrical circuits will be given in class on Thursday, July 6^{th}.

*Evaluation:*

The mark
assigned for this module will represent 20% of each student’s class mark. A
mark below 12 on 20 constitutes a failure in this module.

·
Module
Quiz 5/20

·
Team
Report 15/20

·
Paper
on Gauss: 5 marks

·
Summary
of electrical networks: 2 marks

·
Solutions
to problem sets I and II: 4 marks each

Each
student will complete the group participation sheet for all members of the
group. This information will be taken into consideration during assessment of
each student’s final mark for the module.

**Graded modules will not be returned. So please
make copies before your submission!**