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Saturday, November 27, 2010

MST209 - Overview Blocks Units

I'll be doing MST209 next year. It is the most logical choice after MST121, MS221 and M208 the courses I have done sofar. The course looks quite interesting if you ask me. I already studied some topics based on the OpenLearn version of MST209 supported by corresponding MIT 18.02 / 18.03 video lectures. Although I don't study mathematics because of the stuff offered in MST209 I accept that MST209 is part of the mathematical language shared by all scientists ( and engineers ). Besides that MST209 is packed with examples I can play with in Mathematica, do some Mathematica programming as well.

Since I don't have the course materials yet ( haven't even registered yet ) I made a simple planning in a spreadsheet. Blocks / Units as rows, weeks as columns. The TMA cut-offs are estimated based on M208 data of this year. My study 'capacity' in net study hours is roughly as follows on a weekly basis.

Mon Tue Wed Thu Fri Sat Sun Total
2 6 2 2 - 6 6 = 24

Total 24hrs or 90P / year. ( Read: Work + Study and do nothing else. )

I scheduled the MST209 data in the schedule and it fits very well. I usually work two weeks on a TMA. Because I use LaTeX, do a lot of quality-checks, and start asap on a TMA, which means I might need to study stuff while working on the TMA. Anyway this means that I have two weeks to study a block, 5 Units or roughly 20 sections, do exercises, etc. You all know the drill.

Working on a degree is basically an excuse for spending time on math. In most circles it is considered anything between nerdy, nutty and plain vanilla crazy. ( Ignorance is NOT bliss. ) I am just explaining that my plan objective is not completing the project at the earliest possible date.

I have the following options.
- Blank MST209
- MST209 + M381 Number theory and logic ( As in my original overall plan )
- MST209 + M337 Complex analysis
- MST209 + MST326 Mathematical methods and fluid mechanics

My next step is, based on my study and OU experiences sofar, trying to 'fit in' another 30 point course ( any course for that matter ). If ( and only if ! ) that works I have to choose which module I will do next to MST209.

What's in MST209 :

Unit 1 Getting Started
This unit focuses mainly on mathematical techniques, but also covers some examples involving skills in the application of mathematics.

Unit 2 First-order Differential Equations
This unit considers in detail how a differential equation arises in a mathematical model with basic definitions and terminology associated with differential equations and their solutions.

Unit 3 Second-order Differential Equations
This unit considers second-order differential equations, that is, differential equations that involve a second (but no higher) derivative.

Unit 4 Vector Algebra
We often need to represent physical quantities such as mass, force, velocity, acceleration, time, etc., mathematically. Most of the physical quantities that we need can be classified into two types: scalars and vectors. This unit defines a vector and discusses ways of representing vectors in two and three (or more) dimensions. Also considered are ways of operating on and combining vectors - that is, they provide the fundamentals of vector algebra.

Unit 5 Statics
This unit and unit 6 lay the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. This unit considers how and why they move. This unit assumes a good working knowledge of vectors.

Unit 6 Dynamics
Continuing on from Unit 5 this unit considers how and why objects move and outlines the procedure for solving dynamics problems. There is a video sequence associated with section 2 of this unit and is available on the DVD (order code MST209/DVDR01).

Unit 7 Oscillations
All around you there are mechanical systems that vibrate or oscillate. Each day you probable experience oscillations in a wide variety of forms: the buzzing of an alarm clock, the vibrations of an electric hair-drier or razor, the sideways movements of a train or boat, and so on. This unit describes a simple experiment involving an oscillating system, introduces Hooke's law as a model for the force exerted by a spring, and goes on to consider how this law applies in various situations where no movement takes place. It also shows how to use Newton's second law to model the oscillations of the simplest oscillating system, which consists of a single particle attached to a single horizontal spring.

Unit 8 Energy and Consolidation
This unit consolidates the mechanics covered in the previous units and introduces the topic of energy in mechanical systems.

Unit 9 Matrices and Determinants
This unit examines some of the properties and applications of matrices. It introduces the matrix method of solving large systems of linear equations, called the Gaussian elimination method, and explains the conditions required for this method to work.

Unit 10 Eigenvalues and Eigenvectors
This unit introduces eigenvectors showing simplified problems. It considers the eigenvectors and eigenvalues associated with various linear transformations of the plane and outlines situations where eigenvectors and eigenvalues are useful.

Unit 11 Systems of Differential Equations
This unit focuses on systems of linear differential equations relating two more functions and their derivatives. It shows how various situations can be modelled by a system of linear differential equations, how such a system can be written in matrix form, and how eigenvalues and eigenvectors can be used to solve it when the equations are homogeneous with constant coefficients.

Unit 12 Functions of Several Variables
This unit extends the calculus of functions of one variable to functions of several variables. It also discusses the application of functions of several variables to mechanics.

Unit 13 Modelling with Non-linear Differential Equations
In this unit we study the mathematical models associated with two physical systems: the growth of two interacting populations, one a predator and the other its prey and the motion of a rigid pendulum.
This is demonstrated through the use of Lotka-Volterra equations, which apply to a pair of interacting populations. How these equations can be linearized near an equilibrium state and the graphical representation of the solutions are discussed.

Unit 14 Modelling Motion in Two and Three Dimensions
This unit turns the attention to motion and forces in more than one dimension. It draws on ideas about vectors, forces and component forces and fundamental ideas about mechanics of particles, in particular Newton's second law. There is also mention of kinetic energy and potential energy. The video sequences associated with this unit are available on the DVD (order code MST/209/DVDR01), however it is not essential for you to view these.

Unit 15 Modelling Heat Transfer
This unit makes use of ideas relating to energy and first-order differential equations. It begins by developing models that could be used to answer questions such as the following.

How much does it cost to heat up a tank full of hot water?
What thickness of insulation should be applied to a hot-water tank?
What thickness of insulation should I use in my loft, and what savings would I make over a year?
What should the gap be in double-glazing?

Is it better to insulate the roof, insulate the walls or double-glaze the windows of my house?
The common factor in answering all these questions is the need to consider the transfer of heat energy between different regions of space. This unit introduces the basic ideas of heat energy and temperature. It discusses conduction and convection as well as a third mode of heat energy transfer, radiation.

Unit 16 Interpretation of Mathematical Models
This unit introduces the ideas of mathematical modelling. It discusses the five key stages of the mathematical modelling process in detail and looks at dimensions and units of physical quantities to see how they can be used to predict and check the outcomes of the modelling process.

Unit 17 Damping, Forcing and Resonance
This unit refers back to the contents of several earlier units. In particular it builds upon and extends the model of simple harmonic motion and uses this approach in analysing one-dimensional motion. It also returns to the concept of a resistance force proportional to the velocity of a particle.

Unit 18 Normal Modes
This unit continues with the theme of mechanics, in particular, it builds on earlier units that dealt with oscillations. In order to solve the equations of motion derived for the mechanical systems studied, it uses the methods used for solving systems of differential equations. This unit also draws heavily on the discussions regarding eigenvalues and eigenvectors.

Unit 19 Systems of Particles
The main objective of this unit is to show how to obtain useful information on the complicated motion of an object or system, and demonstrates that the concept of centre of mass is crucial to this process.

Unit 20 Circular Motion
The theme of this unit is rotational motion. It concentrates mainly on analysing the circular motion of a particle. This can be used to model a wide range of situations, such as a child on a swing, the pendulum of a clock and a chair-o-plane roundabout at a fairground. This unit builds on many of the ideas from earlier units mainly: polar coordinates, vectors, torque and Newton's second law.

Unit 21 Fourier Series
This unit is concerned with the technique of expressing a periodic function as a sum of terms, where each term is a constant, a sine function or a cosine function. This unit assumes you have a background knowledge of the definition of the period (unit 7), forced oscillations and resonance (Unit 17, and integration by parts (Unit 1).

Unit 22 Partial Differential Equations
This unit builds on ideas previously introduced in unit 12 regarding The diffusion equation and the wave equation, in the context of modelling the vibrations of a taut string (such as guitar string).

Unit 23 Scalar and Vector Fields
The main focus of this unit is the differential calculus of scalar and vector fields, i.e. the study of how scalar and vector fields vary from one point to another. A brief introduction to the properties of orthogonal matrices and pictorial representations of scalar and vector fields is given along with an extended discussion of the gradient function of a scalar field. Cylindrical and spherical polar coordinate systems for specifying points in three dimensions is also introduced in this unit.

Unit 24 Vector Calculus
This unit discusses the divergence of a vector field, the curl of a vector field, the scalar line integral and linking line integrals curl and gradient. This unit also builds on the concepts of kinetic energy and potential energy.

Unit 25 Multiple Integrals
This unit generalises the idea of an integral still further to deal with two and three dimensions by introducing two new kinds of integrals, called area integrals and volume integrals. How area integrals can be evaluated as combinations of two ordinary integrals, is shown and applications of area integrals, including the evaluation of centres of mass of planar (i.e. two-dimensional) objects are described. How volume integrals can be expressed as combinations of three ordinary integrals and how area integrals can be used to compute the area of a curved surface are also demonstrated.

Unit 26 Numerical methods of Differential Equations
This unit introduces the study of numerical methods for differential equations. It covers the Taylor's theorem with exercises, recaps Euler's method for solving initial-value problems involving first-order differential equations and goes on to explain that more efficient methods exist. Three new methods known as Runge-Kutta methods, are derived and a way of determining how small the step size h would need to be in order to achieve a given accuracy for a given initial-value problem is established.

Unit 27 Rotating Bodies and Angular Momentum
This unit deals with the motion of extended bodies, and in particular with their rotational motion. Rotating bodies, Angular momentum, Rigid-body rotation about a fixed axis and rotation about a moving axis are all covered in this unit.

Unit 28 Planetary Orbits
This unit shows how Newton's laws of motion and Newton's law of universal gravitation can be used to predict the orbits of planets around the Sun. In particular, it shows that Kepler's laws of planetary motion can be derived using Newtonian mechanics.


  1. Hi Nilo
    Looks like you've got MST209 sussed. In your position I would be tempted to do M381 as an antidote to the pure maths and leave MST326 till the year after. There are rumours that M381 is going to be merged as part of a 60 point level 3 course which will replace Topology, Number theory and logic and group theory. The module is rumoured to contain stuff on metric spaces, Fields and Rings and Number theory. So no group theory or geometric topology or Logic. This will probably happen in a couple of years. So M381 in its current form might only appear once again in 2013. The only disadvantage as far as I can see is that in 2012 MST326 is moving to an October start. This does seem to be quite a period of change for the open university which makes long term planning difficult.

    As a final point (as if you haven't got enough on your plate already) Some diligent students from Cambridge University got together to produce lecture notes for the 1st year maths courses. For MST209 you would need differential equations, Vector calculus and Dynamics. The notes are concise you can access them here.

    The relevant notes are in part 1A

    The example sheets for the undegraduate courses can be got here.

    This also includes their second year mathematical methods course which goes way beyond MST209 and even MST326 as far as I can tell. Also the first year differential equations course includes an introduction to solutions of differential equations with variable coefficients by series. Something which is briefly touched on in MST326.

    Anyway plenty of stuff to get your teeth into
    Duncan (from MS221) and I have done a couple of the rotational motion problems examples which you can get from here.

    Best wishes Chris

  2. Chris,

    Thanks for the link to the Archimedeans!

    I noticed that they distinguish between Pure, Applicable and Applied mathematics. Hadn't seem that one before.

    Will reply more in my posts.

    kind regards,

    Have visited
    more than once over the weekend, but no posts?

  3. Sorry I've had quite a bad cold so not able to think coherently about mathematics. Will probably publish a review of the OU philosophy course I did last year. Then a review of the statistics courses and then the music courses.
    Am currently working through a few units of the Complex Analysis course and trying to complete Brannan's book by the end of Christmas. Glad I worked through the basics of continuity before tackling the complex analysis as although you could probably get away with not knowing real analysis the explanations are a bit more concise so it helps to have done something like M208 or at least familiarise yourself with the analysis part of it before embarking on M337. One intriguing thing is that the Argument of a complex number Arg(z) ie. Arctan (y/x) where z = x + iy is not continuous at a point a if a is a real number less than 0.

    This is because Arg(z) is defined so that it lies between -pi and + pi, To avoid ambiguities. Mind blowing stuff !!

    Best wishes Chris

    is not continous

  4. Ps I think the difference between Applied maths and Applicable maths is that Applied maths essentially concerns itself with problems from physics or science and engineering. Whereas Applicable maths is concerned with statistics, discrete maths and applications to financial modelling. Given the current financial crisis I think Applied mathematics is a lot more stable than Applicable mathematics :)

  5. Economics as a 'science' is a real mess with their models that are always wrong. Economics 'professors' are like the Emperors with new clothes. They are a disgrace to society considering the mess they made of things.

  6. Quite just goes to show that just because you can express a concept mathematically doesn't mean that the concept is correct.


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