LabSpace

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. There is a strong analogy with the technique of expressing a (non-periodic) ...

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. There is a strong analogy with the technique of expressing a (non-periodic) function as a Taylor series, which is a sum of terms that are powers of the independent variable(s); in both cases, working with just the first few terms generally gives a useful approximation. This unit assumes the following background knowledge: the definition of the period; forced oscillations and resonance; integration by parts.

This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some ...

This unit is intended to further develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in solving systems of differential equations, this unit assumes that you have some understanding of eigenvalues and eigenvectors.

This unit shows how various situations can be modelled by a system of linear differential equations. The prerequisite requirements to gain full advantage from this unit are a basic understanding of differential equations, a familiarity with the ...

This unit shows how various situations can be modelled by a system of linear differential equations. The prerequisite requirements to gain full advantage from this unit are a basic understanding of differential equations, a familiarity with the properties of matrices and determinants and some understanding of eigenvalues and eigenvectors.

This unit lays the foundation of Newtonian mechanics and in particular the procedure for solving dynamics problems. The preresquisite skills needed for this unit are the ability to solve first and second-order differential equations, a knowledge ...

This unit lays the foundation of Newtonian mechanics and in particular the procedure for solving dynamics problems. The preresquisite skills needed for this unit are the ability to solve first and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a force

This unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes ...

This unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes that you have a good working knowledge of vectors.

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic ...

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and ...

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these ...

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have ...

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian ...

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognise mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a ...

This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognise mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics. In order to complete this unit you will need to have obtained a Texas Instruments TI-83 calculator and the book Tapping into Mathematics With the TI-83 Graphics Calculator (ISBN 0201175479).

This unit is the first in the MSXR209 series of five units that introduce the idea of modelling with mathematics. This unit centres on a mathematical model of how pollution levels in the Great Lakes of North America vary over a period of time. It ...

This unit is the first in the MSXR209 series of five units that introduce the idea of modelling with mathematics. This unit centres on a mathematical model of how pollution levels in the Great Lakes of North America vary over a period of time. It demonstrates that, by keeping the model as simple as possible extremely complex systems can be understood and predicted.

This unit is the second in the MSXR209 series of five units on mathematical modelling. In this unit you are asked to relate the stages of the mathematical modelling process to a previously formulated mathematical model. This example, that of skid ...

This unit is the second in the MSXR209 series of five units on mathematical modelling. In this unit you are asked to relate the stages of the mathematical modelling process to a previously formulated mathematical model. This example, that of skid mark produced by vehicle tyres, is typical of accounts of modelling that you may see in books, or produced in the workplace. The aim of this unit is to help you to draw out and to clarify mathematical modelling ideas by considering the example. It assumes that you have studied Modelling pollution in the Great Lakes (MSXR209_1).

This unit is the third in the MSXR209 series of five units on mathematical modellng. It provides an overview of the processes involved in developing models, starting by explaining how to specify the purpose of the model. It then moves on to look ...

This unit is the third in the MSXR209 series of five units on mathematical modellng. It provides an overview of the processes involved in developing models, starting by explaining how to specify the purpose of the model. It then moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models. This unit assumes that you have previously studied Modelling pollution in the Great Lakes (MSXR209_1) and Analysing skid marks (MSXR209_2).

This unit is the fourth in the MSXR209 series of five units on mathematical modelling. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent ...

This unit is the fourth in the MSXR209 series of five units on mathematical modelling. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent revision of the model by changing one of the assumptions. The problem that will be examined is one based on heat transfer. This unit assumes you have studied Modelling pollution in the Great Lakes (MSXR209_1), Analysing skid marks (MSXR209_2) and Developing modelling skills (MSXR209_3).

This is the fifth and final unit in the MSXR209 series on mathematical modelling. In this unit we revisit the model developed in the first unit of this series on pollution in the Great Lakes of North America. Here we evaluate and revise the ...

This is the fifth and final unit in the MSXR209 series on mathematical modelling. In this unit we revisit the model developed in the first unit of this series on pollution in the Great Lakes of North America. Here we evaluate and revise the original model by comparing its predictions against data from the lakes before finally reflecting on the techniques used. This unit assumes you have studied Modelling pollution in the Great Lakes (MSXR209_1), Analysing skid marks (MSXR209_2), Developing modelling skills (MSXR209_3) and Modelling heat transfer (MSXR209_4).

This unit is intended to develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in calculus, this unit assumes that you have some understanding of how to solve second-order linear ...

This unit is intended to develop your understanding of Newtonian mechanics in relation to oscillating systems. In addition to a basic grounding in calculus, this unit assumes that you have some understanding of how to solve second-order linear constant-coefficient differential equations; how to take the dot product of two vectors; of solving statics problems; and of applying Newton's second law to mechanical problems.