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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 18H c by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 18H b by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 18H a by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 17A Solution by
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A Givens rotation is the identity except in rows and columns , where it has the blockFor and , choosewhen . ThenIf both entries vanish, any angle works.
Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 16D Solution by
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Let point downslope and point normally away from the plane, with . Write the parallel velocity as and take to be the magnitude of the air's upslope stress. The steady equations arewith boundary conditionsThe free-surface condition makes , and integration gives
Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 15C ii by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 15C i by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 15C Solution by
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Differentiate under the integral and use :The omitted boundary term vanishes if the current is localized sufficiently rapidly. A steady current obeys charge conservation , hence
For much larger than the source size,Localization and imply . They also implyby integrating . Thus the first nonzero moment is antisymmetric and can be written using the magnetic dipole momentConsequently the Coulomb-gauge vector potential of a localized steady current has far fieldThe dimensions are
Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 14A iv by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 14A ii by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 14A i by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 13B Solution by
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Continuity at is automatic in the proposed expression. Integrating the differential equation through gives the derivative jumpThusIn terms of the Wronskianone hasThe boundary conditions hold because and .
The Abel identity gives . If , the Wronskian and hence are constant. The two branches of the displayed formula are then interchanged by , provingThis is the symmetry of the Neumann Green function for a second-order ordinary differential equation in the self-adjoint case.
Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 12F c by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 12F b by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 11E iv by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 11E iii by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 11E ii by
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Past exam of the mathematics course of the University of Cambridge 2024 ib Paper 1 11E i by
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Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





