Linear Algebra I (Science)
Summer 2006 Instructor: Alice McLeod
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.
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.
Step 1: Read the following:
a) Anton, Howard and Chris Rorres. Elementary Linear Algebra. 9th 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. 3rd 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 27th, and one hour on July 4th). However, team work outside of class time will likely also be necessary.
Complete report due: Thursday, July 6th, 2006.
A quiz on solving electrical circuits will be given in class on Thursday, July 6th.
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!