MATH348 - Advanced Engineering Mathematics 1
E. Kreyszig, Advanced Engineering Mathematics, 9th ed. Section N/A, pgs. N/A
Lecture: Overview and Outline Module: 01
Suggested Problem Set: {NULL}June 15, 2009
Quote of Lecture 1
Montgomery Burns: I’ll keep it short and sweet. Family, religion, friendship. These
are the three demons you must slay if you wish to succeed in business.
The Simpsons: The Old Man and the Lisa (1997)
The course Advanced Engineering Mathematics serves the following CSM disciplines,
•Engineering (Civil, Electrical, Environmental, Mechanical)
•Geophysics
•Rouge Physicists
•Students pursuing an ASI or minor in Mathematics
by introducing them to concepts from,
•Linear Algebra
•Partial Differential Equations
in order to connect their two-years of post secondary mathematics to the rich field of applied mathematical
modeling.
If mathematics is the study of the meaning and properties associated with the symbolic formalism then
applied mathematical modeling is the application of this knowledge to real-world phenomenon in an effort
to draw non-experimental conclusions. The ultimate goal is to make predictions about natural o ccurrences
in order to gain control over them.1Since this has been going on for most of human existence the body of
material is massive and deep. We will be mostly concerned with calculation, but if we remember to also
concern ourselves with the mathematical roots we will achieve a more comprehensive and thus connected
understanding enabling us to remember more concepts for a longer period of time.
It is my perspective that the key point of this material is to draw as many conclusions about the symbols,
which naturally arise as solutions to certain differential equations, as possible. This is by no means a small
task and there are many different and equally justifiable routes to this goal. However, this goal, I feel, is
best served by studying first the straight-forward concepts of linear algebra and connect these concepts to
the more complicated study of linear partial differential equations used to model ideal, flows, vibrations, and
potential fields. 2 3
My opinion is largely due to the fact that linear algebra can abstract a method, which you should already
be aware of, to any finite number of directions. That is, for certain two-dimensional linear problems say,
dY
dt ="a b
c d #Y,Y(0) = "x0
y0#,(1)
1For example, it is sometimes difficult to construct experiments involving complicated fluid flow but it is ‘easier’
to write down mathematical models for these flows and evaluate them under ‘experimental conditions’. A reason for
this might be to understand how to mix two fluids into one fluid while using the least amount of energy.
2I must note that it is highly useful to study the theory of linear algebra as it is the most applicable mathematical
tool in the sciences and well worth a stand alone course. Those interested should consider taking MATH332-Linear
Algebra.
3The concept of linearity is a powerful tool that allows one to say that an object with a certain property is equivalent
to the sum of of other objects having the same property. This is not generally true of nonlinear phenomenon.
