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I am after recommendations of books that teach in a specific way. Basically I have come out of a 3 year physics degree with just doing the work but not really understanding the material (the mathematics) that well.

I want to re-learn a bunch of topics in a way so I will actually understand them. The kind of books I am after are like the Students guide to vectors and tensors. It literally breaks the topics down and holds your hand every step of the way. This is the only way I can learn. I have learned more about vectors in 10 pages of this book than my entire undergrad maths course.

I also need a lot of applications of things being taught. I can't just read something as it is and understand the point unless I see it applied to a problem. Basically most books start with a proof or the definition and that stuff just blows over me. I am more after the physical Meaning of what these functions / operations / do.

That being said, does anyone have any books they've come across that teach in such a way? I am mainly after topics such as matrices and their uses to real problems. Formulating problems into matrix algebra and solving them. And books on ODE and PDE.

Thanks