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Integration as summationAn integral is defined as an infinite sum. This leaflet explains how this is done. This notion is important when we want to apply integration in many fields. (Engineering Maths First Aid Kit 8.12)
Integration as the reverse of differentiationIntegration is introduced here as the reverse of differentiation. (Engineering Maths First Aid Kit 8.6)
Integration as the reverse of differentiationThis unit explain integration as the reverse of differentiation. (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.
Integration as the reverse of differentiationThis unit explain integration as the reverse of differentiation. (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.
Integration by partsThis leaflet explains integration by parts. This is a technique for integrating a product of two functions (two functions multiplied together). (Engineering Maths First Aid Kit 8.10)
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples. (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.
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples. (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.
Integration by Parts - Numbas4 questions on integrating by parts. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Integration by substitutionSome integrals can be evaluated by making an appropriate substitution to change the variable. This leaflet explains how this can be done. (Engineering Maths First Aid Kit 8.11)
Integration by substitutionThere are occasions when it is possible to perform an apparently difficult piece of integration by first making a
substitution. This has the effect of changing the variable and the integrand. When dealing with definite integrals,
the limits of integration can also change.
In this unit we will meet several examples of integrals where it is appropriate to make a substitution. (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.
Integration by substitutionThere are occasions when it is possible to perform an apparently difficult piece of integration by first making a
substitution. This has the effect of changing the variable and the integrand. When dealing with definite integrals,
the limits of integration can also change.
In this unit we will meet several examples of integrals where it is appropriate to make a substitution. (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.
Integration for Economics and Business Studies Overview of the rules of integration and their applications in Economics and Business Studies. This leaflet has been contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Anthony Cronin (University College Dublin).
Integration for Economics and Business Studies (SOURCE)Latex source, image files and metadata for the Fact & Formulae leaflet "Integration for Economics and Business Studies " contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Anthony Cronin (University College Dublin).
Integration that leads to log functionsThis unit is concerned with integrals which lead to logarithms.
Whenever the integrand is fraction with denominator f(x) and numerator f'(x)
the result of integrating is the natural logarithm of f(x). This unit illustrates this
behaviour with several examples. (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.
Integration that leads to log functionsThis unit is concerned with integrals which lead to logarithms.
Whenever the integrand is fraction with denominator f(x) and numerator f'(x)
the result of integrating is the natural logarithm of f(x). This unit illustrates this
behaviour with several examples. (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.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have a table of derivatives, we can read it backwards as a table of anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of Differentiation. (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.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have a table of derivatives, we can read it backwards as a table of anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of Differentiation. (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.
Integration using trig identities or a trig substitutionThis unit explains how trig identities and trig substitutions can help when finding integrals. (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.
Integration using trig identities or a trig substitutionThis unit explains how trig identities and trig substitutions can help when finding integrals. (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.
Integration: Laplace TransformsReviews the techniques of integration needed to find and manipulate Laplace Transforms. This Quick Reference leaflet is contributed to the mathcentre Community Project by Leslie Fletcher and reviewed by Martin Randles, Liverpool John Moores University.
Integration: Laplace Transforms SOURCEA zip file containing LaTeX source and eps files for the quick reference leaflet 'Integration: Laplace Transforms' contributed to the mathcentre Community Project by Leslie Fletcher, Liverpool John Moores University
Interactive Economics Facts and FormulaeThis document summarises some main mathematical ideas that you will probably
see in the first year of any economics degree course. The hot links allow you to
select questions, each randomised and with full feedback so you can ‘get your hands
dirty’ and reinforce your understanding. You are encouraged to make good use of
these links and to retain this document as a handy summary for revision. You/your
teacher is free to edit it as required. You will find questions on additional topics in
economics, as well as most of the underlying mathematical techniques, in the maths e.g. database.
Interactive starting points for problem solving in undergraduate mathematicsAn innovative and sustainable online bank of starting points for problem- solving, presented in an interactive, visual and engaging way that will nurture mathematical thinking, logical processes and modelling. The starting points will permit a range of teaching approaches - individual, small group and whole class. They will be fully functional on a range of digital technologies including handhelds. These resources were created by the project Problem Solving in Undergraduate Mathematics (PSUM) and are available via Nrich. This website is not made available under a Creative Commons licence but is freely available to UK universities for non-commerical educational use.
Introduction to differentiation 8.1This leaflet provides a rough and ready introduction to differentiation and gives some common terminology and notation. (Engineering Maths First Aid Kit 8.1) There is an accompanying podcast.
Introduction to differentiation 8.1 - PodcastPodcast to accompany the Quick Reference Engineering Maths First Aid Kit leaflet 'Introduction to differentiation 8.1' submitted under Creative Commons Licence BY-NC-SA to the mathcentre Community Project by Ciaran Mac an Bhaird, National University of Ireland Maynooth and reviewed by Ann O'Shea, National University of Ireland Maynooth.
Introduction to differentiation 8.1 - PodcastPodcast to accompany the Quick Reference Engineering Maths First Aid Kit leaflet 'Introduction to differentiation 8.1' submitted under Creative Commons Licence BY-NC-SA to the mathcentre Community Project by Ciaran Mac an Bhaird, National University of Ireland Maynooth and reviewed by Ann O'Shea, National University of Ireland Maynooth.
