All reading assignments, problem sets, and so forth will be posted on this page. Please check here at least every Tuesday to collect the readings and problem sets. Also, you'll find other handouts, class "news" updates, and Maple instructions.
News:
The midterm synthesis assignment is now ready! Please note the conditions: you must do this assignment consulting only your brain, your class notes, and our textbook. Do not use any outside sources. There is a hand-drawn picture for Q1, obviously missing from the computer file; I've placed a paper copy in your mailboxes.
Readings and Assignments:
Handouts:
Course syllabus
Suggested project topics
Diet preparation example
Diet preparation example (Mathematica)
Row echelon form example
Row echelon form example (Mathematica)
Maple Tips:
Below is a set of Maple commands to allow you to perform many of the operations
required for this course. If you have a graphing calculator, you might be able
to do most of the tasks required, but I might not be able to help you learn
how to use it.
Maple is a command-line environment. You must type a command and hit
The LinearAlgebra and linalg Packages
Many of the commands we will need for this course are in a special library
of functions called LinearAlgebra, which is not
automatically loaded at startup. It is a good practice to load it every time
you begin using Maple. Type
with(LinearAlgebra);
(You'll see a list of commands that have been loaded. Eventually you'll grow
tired of seeing this list; to suppress it, enter the command with a COLON
rather than a semicolon.) A similar package,
linalg, may be useful on occasion.
Getting Help on any Command
Maple has extensive help features, not all of which are easy to use. You can
browse the help menus; exploring them is the best way to figure out how they
work. To get help on a particular command (say,
simplify), just enter the following:
?simplify
A rather extensive window describing the simplify
command will be loaded.
Don't forget that there is a worksheet containing a general introduction to
Maple on my
multivariable calculus page.
Use the PALETTES!
Maple has various palettes that make entering various objects, especially
vectors and matrices, much easier. Go to the View menu and select the Palettes
flyout menu to access them.
Loading Homework Data Files
The CD that came with our textbook contains a variety of Maple worksheets
with all the matrices for the textbook homework problems already loaded. More
info later on how to use this great time-saving feature...
Performing Row Operations
All row operations can be performed using the
RowOperation command. While performing these operations, don't forget
that % refers to the results of the previously-
executed command. When performing a sequence of row operations, this can be
extremely handy!
To switch (say) rows 1 and 2 in matrix A, type
RowOperation(A,[1,2]);
To multiply (say) row 1 by 7, type
RowOperation(A,1,7);
To add to row 2 the result of 7 times row 1, type
RowOperation(A,[2,1],7);
Solving Linear Systems
The LinearAlgebra package contains all the commands you need to solve
any kind of linear system.
To perform Gaussian elimination on a matrix A, type
GaussianElimination(A);
To solve the reduced system by back substitution, type
BackwardSubstitute(A);
To reduce the matrix directly to reduced echelon form, type
ReducedRowEchelonForm(A);
To solve the entire linear system, enter into A the matrix containing all
but the numbers on the right-hand side of the equal sign. Then enter these
numbers as a column vector; let's call it b. Finally, type
LinearSolve(A,b,free='s');
If there are any free variables in the solution, they will appear as s_1,1,
s_1,2, etc.
Arithmetic with Matrices
Be warned; this is not as simple as it sounds. You must use the
evalm command to do arithmetic with matrices.
You can add matrices together, multiply them by a constant, and even raise them
to powers just as you might expect:
evalm(4*A);
evalm(A+B);
evalm(A^3);
To multiply matrices together, however, you must use a special way
of writing the multiplication sign:
evalm(A &* B);
Transposing a Matrix
The Transpose command is in the
LinearAlgebra package, so be sure to load it
first. Then type as follows (don't forget the capital T!):
Transpose(A);
Inverting a Matrix
The MatrixInverse command is in the
LinearAlgebra package . Then type the following
(again, watch lower versus upper case):
MatrixInverse(A);
Performing an LU-Decomposition
This is a little more complicated, because the Maple LU routine actually does
a lot more than what we need here. To decompose the matrix A, type
LUDecomposition(A,output=['L','U']);
This will display the L and U matrices, but will not give them names for you
to work with later. If you want to give the matrices names (say, Larry and
Uma), type
(Larry,Uma):=LUDecomposition(A,output=['L','U']);
You can then confirm the decomposition, if you wish, by multiplying Larry and
Uma together:
evalm(Larry &* Uma);
Last modified: April 10, 2002 / Glen Van Brummelen
Office: Dickinson 213. Phone numbers: (w) 440-4467; (h)
440-8142.