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Want to understand partial differential equations (linear and non-linear) more deeply. I am not a mathematician and I am more interessted in a more practical source that is teaching this topic from a very intuitive approach. I would also be very interessted in video lectures.

shai horowitz
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MrYouMath
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    http://math.stackexchange.com/questions/2827/good-1st-pde-book-for-self-study http://math.stackexchange.com/questions/194152/good-reference-texts-for-introduction-to-partial-differential-equation?lq=1 http://math.stackexchange.com/questions/948480/textbook-for-partial-differential-equations-with-a-viewpoint-towards-geometry?rq=1 , http://math.stackexchange.com/questions/757511/what-are-good-resources-for-learning-numerical-methods-for-partial-differential?rq=1 http://math.stackexchange.com/questions/785312/request-for-advice-about-studying-for-a-degree-in-partial-differential-equations?rq=1 – Winther May 19 '16 at 17:09

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I would recommend "An Introduction to Linear Analysis" which can be downloaded for free here: https://archive.org/details/AnIntroductionToLinearAnalysis. This was actually the book we used when I took a class on PDE's. It introduces all of the linear algebra needed for the classical theory on PDE's and in my opinion explains everything quite clearly. You can also look at the MIT opencourseware for this topic: http://ocw.mit.edu/courses/mathematics/18-152-introduction-to-partial-differential-equations-fall-2011/ This course does not have video lectures put the notes and practice assignments are there which would be a good source for practice. Hope this helps!