Course description
This course develops a wide
range of mathematical techniques,
and shows how they can be applied
to real-world problems. The
techniques include those of
differential equations, linear
algebra and vector calculus,
and one of the main applications
is classical (Newtonian) mechanics.
The latter is of fundamental
importance in physics and engineering.
Other applications treated in
the course include population
models and the theory of heat
transfer. All the techniques
are used in subsequent applied
maths and physics courses.
What do
I need?
This is a Level 2 course, and
you need a good knowledge of
the subject area, obtained either
from MST121 and MS221 with the
OU, or from equivalent work
at another university. You also
need the study skills associated
with distance learning.
The mathematical prerequisites
include a good basic working
knowledge of algebra, geometry,
trigonometry and calculus. In
algebra you must be able to
solve linear and quadratic equations
with one unknown, multiply and
add polynomials, factorize quadratic
polynomials, work with complex
numbers, and manipulate logs
and exponentials. In geometry
you must know Pythagoras's Theorem
and how to express the equations
of straight lines and circles
in Cartesian coordinates. In
trigonometry you must know the
definition and basic properties
of the three trigonometric functions
sine, cosine and tangent, and
the definitions of the corresponding
inverse functions. In calculus
you must be able to differentiate
and integrate. You will also
be expected to use a computer
using a Windows operating system.
Am
I ready?
We suggest that you try the
Diagnostic
Quiz and give yourself plenty
of time to work through the
questions. There is no
time limit on this exercise,
but you should try to do as
much as you can without reference
to any other materials. Only
when you have completed working
through all the questions should
you access the solutions.
Preparing
for the course MST209
Bridging Material
This is designed for students
who have done MST121 (or equivalent),
but not MS221. As long as you
are familiar with the calculus
in MST121 (or its equivalent),
then this bridging material
should take two or three weeks
to study. The topics revised,
in order of importance to MST209,
are as follows.
- Techniques for differentiating
products, quotients and composite
functions
- Integration methods, including
integration by parts and by
substitution
- Complex numbers
- Techniques for approximating
functions using Taylor polynomials
MST209 expects you to be proficient
at differentiation "by hand".
The integration methods are
needed less often, as most of
the integrals can be done by
using the table of standard
integrals given in the course
Handbook. Complex numbers and
Taylor polynomials are used
only a little, but you are still
expected to understand the ideas.
| You can often use Mathcad, the computer algebra
package, to help with integration (as well as with the differentiation of complicated functions). |
|
|
The MST209 Bridging Material
is available here: 
(To save the file, right click
the icon and choose "Save Target
as" or "Save Link Target as"
option.)
Unit 1 of MST209
This unit reviews a number
of topics used in MST209. It
does not introduce the topics
from scratch; rather, it provides
a reminder of them, and an opportunity
to refresh your memory and practise
techniques. Topics covered include
- sequences and limits
- standard functions such
as linear, quadratic, exponential
and logarithm functions, and
algebraic manipulations involving
these
- trigonometric functions
and identities involving these
- complex numbers
- differentiation
- integration
- use of the computer to manipulate
algebraic expressions, draw
graphs and solve equations
This unit includes the topics
in the Bridging Material (except
Taylor polynomials), but the
Bridging Material covers them
more thoroughly.
Later units of MST209 expect
you to be proficient in the
ideas and methods covered in
Unit 1, particularly the use
of the various standard functions,
including the trigonometric
functions, and manipulation
of expressions involving them,
differentiation, and integration
using the table of standard
integrals given in the course
Handbook. The other topics in
Unit 1 are used at times further
on in the course, but are less
crucial.
Computing Booklet
This covers installing and using all of the course software, both the multimedia presentations and Mathcad (the computer algebra
package). It contains activities designed to give you the basic skills in working with this software.
|
-
-
