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3 questions. One question on limits of standard sequences. Other two on finding least $N$ such that $|a_n-L |lt 10^{-r},;;n geq N$ where $L$ is limit of $(a_n)$. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

The focus of this HE STEM guide is to provide mathematics support to students across all STEM disciplines to ease the transition from School/College in to University. This is a key factor influencing drop-out from STEM degrees and a targeted provision for mathematics support is a proven way to counter this. It includes cases studies from the Universities of Coventry, Portsmouth, York. Lincoln and Kent and articulates the experiences of the two Sigma Directors Professor Duncan Lawson, Coventry University and Professor Tony Croft, Loughborough University joint winners of the 2011 Times Higher Award for Outstanding Support for Students

Sigma notation is a method used to write out a long sum in a concise way. In this unit we look at ways of using sigma notation, and establish some useful rules. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Sigma notation is a method used to write out a long sum in a concise way. In this unit we look at ways of using sigma notation, and establish some useful rules. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x2, x3, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x2, x3, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

This video explains how algebraic fractions can be simplified by cancelling common factors. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

This video explains how algebraic fractions can be simplified by cancelling common factors. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

This leaflet explains how algebraic fractions can be simplified by cancelling common factors. (Engineering Maths First Aid Kit 2.7)

EXCEL has been used to provide simulation facilities in support of teaching control to engineers. This dictates a sampled data approach which fits in naturally with digital implementation of control. The technique also allows students to explore the affects of non-linearities in systems such as control signal saturation. It provides a â??hands-onâ?? dimension which students find valuable. The approach is capable of use with other dynamic systems and is not restricted to teaching control.

This leaflet explains how two equations in two unknowns can be solved by elimination. (Engineering Maths First Aid Kit 2.13)

Two questions on solving systems of simultaneous equations. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

This is a complete workbook introducing the solution of a pair of simultaneous linear equations. It contains plenty of examples and exercises.
It can be used as a free-standing resource or in conjunction with the mathtutor DVD.

This mathtutor animation shows how solutions to simultaneous linear equations may be found. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Knowledge of the trigonometric ratios sine, cosine and tangent is vital in many fields of engineering, maths and science. This unit explains how the sine, cosine and tangent of an arbitrarily sized angle can be found. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Knowledge of the trigonometric ratios sine, cosine and tangent is vital in many fields of engineering, maths and science. This unit explains how the sine, cosine and tangent of an arbitrarily sized angle can be found. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

All cubic equations have either one real root, or three real roots. In this video we explore why this is so. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

All cubic equations have either one real root, or three real roots. In this video we explore why this is so. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quick Reference leaflet on first order differential equations. This Quick Reference leaflet is contributed to the mathcentre Community Project by Katy Dobson and reviewed by Alan Slomson, University of Leeds.

A zip file containing LaTeX source and eps files for the quick reference leaflet 'Solving Differential Equations by Separating Variables' contributed to the mathcentre Community Project by Katy Dobson and reviewed by Alan Slomson, University of Leeds.

Quick Reference leaflet on solving differential equations. This Quick Reference leaflet is contributed to the mathcentre Community Project by Katy Dobson and reviewed by Alan Slomson, University of Leeds.

A zip file containing LaTeX source and eps files for the quick reference leaflet 'Solving Differential Equations with Integrating Factors' contributed to the mathcentre Community Project by Katy Dobson and reviewed by Alan Slomson, University of Leeds.

This leaflet shows how simple equations involving logarithms or exponentials can be solved. (Engineering Maths First Aid Kit 3.8)