Notes on topics of interest to First Year students
Sometimes when marking assignments I have a burning
desire to implant certain information in the minds of
the students who produced those assignments. The following notes
are the result. Except for Constant Coefficient Linear DEs,
each is no more than 2 A4 pages.
Over time this list will almost certainly grow.
The .pdf files can be viewed by any Macintosh in
the MacLab.
- Induction
[induction.dvi |
induction.ps |
induction.pdf ]
- Also see Patrick Hew's presentation of a
template for induction.
- Setting out a proof
[mvt.dvi |
mvt.ps |
mvt.pdf ]
- Describes general principles for good setting out
of proofs ... then applies those guidelines to
a problem that involves the application of the
Mean Value Theorem.
- More on proofs
[mat.dvi |
mat.ps |
mat.pdf ]
- Gives another example using the general principles
discussed in Setting out a proof. In
particular, the example is a matrix problem and
gives an idea of how one arrives at a correct
solution after coming up with an incomplete
initial draft.
- Some hints on finding derivatives
[diff.dvi |
diff.ps |
diff.pdf ]
- Shows why using the quotient rule is often not
a good idea, and gives an example to show why
it is often a good idea to rearrange the expression
that is to be differentiated.
- Finding solutions to systems of linear equations
[syslin.dvi |
syslin.ps |
syslin.pdf ]
- Describes an embellishment of the matrix reduction method
that is truly foolproof!
- Linear Independence
[linind.dvi |
linind.ps |
linind.pdf ]
- Defines a term ``linear independence equation''
in order to make the definition more palatable,
and gives an application to a proof-type
problem.
- Row rank = column rank
[ rowcolrank.pdf ]
- Shows by way of an example why row rank and column rank are
equal.
- Rank-nullity Theorem Applications
[ ranknulleg.pdf ]
- A page of examples.
- Constant Coefficient Linear DEs
[ccldes.dvi |
ccldes.ps |
ccldes.pdf ]
- These notes run to 12 pages ... but we do solve
11 d.e.s on the way. The presentation is somewhat
different to what you will have experienced in
lectures. We describe what a linear operator is
and explain in a uniform way how to solve
any constant coefficient d.e. up to second order
that does not require variation of parameters.
For other notes see
Patrick Hew's tutoring notes.
