# Cloud-AI augmented core contents

[This cloud computing framework comprehensively explores fundamental partial differential equations (the Wave, Heat, and Transport Equations) ](https://viadean.notion.site/A-Guide-to-Finite-Difference-Finite-Element-and-Finite-Volume-Methods-for-PDEs-plus-AI-Reasoning-1ef1ae7b9a3280c8beabe0bd588e077b?source=copy_link)and their numerical methods, delves into functional analysis and variational methods for PDEs, and examines the linear algebraic challenges inherent in numerical PDE solutions.

{% embed url="<https://youtu.be/rpiKJdVpzfs>" %}
This cloud computing framework comprehensively explores fundamental partial differential equations (the Wave, Heat, and Transport Equations) and their numerical methods, delves into functional analysis and variational methods for PDEs, and examines the linear algebraic challenges inherent in numerical PDE solutions.
{% endembed %}

{% content-ref url="cloud-ai-augmented-core-contents/delving-into-the-world-of-partial-differential-equations" %}
[delving-into-the-world-of-partial-differential-equations](https://via-dean.gitbook.io/all/interdisciplinary-perspective/multifaceted-viewpoint/a-guide-to-finite-difference-finite-element-and-finite-volume-methods-for-pdes-plus-ai-reasoning/cloud-ai-augmented-core-contents/delving-into-the-world-of-partial-differential-equations)
{% endcontent-ref %}

{% content-ref url="cloud-ai-augmented-core-contents/navigating-the-landscape-of-numerical-methods-for-pdes" %}
[navigating-the-landscape-of-numerical-methods-for-pdes](https://via-dean.gitbook.io/all/interdisciplinary-perspective/multifaceted-viewpoint/a-guide-to-finite-difference-finite-element-and-finite-volume-methods-for-pdes-plus-ai-reasoning/cloud-ai-augmented-core-contents/navigating-the-landscape-of-numerical-methods-for-pdes)
{% endcontent-ref %}

{% content-ref url="cloud-ai-augmented-core-contents/functional-analysis-and-variational-methods-for-pdes" %}
[functional-analysis-and-variational-methods-for-pdes](https://via-dean.gitbook.io/all/interdisciplinary-perspective/multifaceted-viewpoint/a-guide-to-finite-difference-finite-element-and-finite-volume-methods-for-pdes-plus-ai-reasoning/cloud-ai-augmented-core-contents/functional-analysis-and-variational-methods-for-pdes)
{% endcontent-ref %}

{% content-ref url="cloud-ai-augmented-core-contents/the-algebraic-backbone-of-numerical-pdes-linear-algebra-and-its-challenges" %}
[the-algebraic-backbone-of-numerical-pdes-linear-algebra-and-its-challenges](https://via-dean.gitbook.io/all/interdisciplinary-perspective/multifaceted-viewpoint/a-guide-to-finite-difference-finite-element-and-finite-volume-methods-for-pdes-plus-ai-reasoning/cloud-ai-augmented-core-contents/the-algebraic-backbone-of-numerical-pdes-linear-algebra-and-its-challenges)
{% endcontent-ref %}
