I’m self-studying physics and mathematics out of interest and I am looking for some non-rigorous (text)books on mathematics. Perhaps one book covering all areas relevant to physics or separate books in the areas of non-linear dynamics, differential equations, differential geometry, group theory, etc. I am explicitly looking for non-rigorous, intuitive approaches to these fields. I feel overly rigorous books make the material needlessly difficult (to me often impossible) and slow to read. I am looking for things in the style of student’s guides, such as Dan Fleisch’s “A Student’s guide to vectors and tensors” but then more expanded: https://www.goodreads.com/book/show/11925464-a-student-s-guide-to-vectors-and-tensors?ac=1&from_search=true

Also, a mathematics book that shows the bigger picture on mathematics would be of interest. Something more or less popularising.

Thanks!

I’m self-studying physics and mathematics out of interest and I am looking for some non-rigorous (text)books on mathematics. Perhaps one book covering all areas relevant to physics or separate books in the areas of non-linear dynamics, differential equations, differential geometry, group theory, etc. I am explicitly looking for non-rigorous, intuitive approaches to these fields. I feel overly rigorous books make the material needlessly difficult (to me often impossible) and slow to read. I am looking for things in the style of student’s guides, such as Dan Fleisch’s “A Student’s guide to vectors and tensors” but then more expanded: https://www.goodreads.com/book/show/11925464-a-student-s-guide-to-vectors-and-tensors?ac=1&from_search=true

Also, a mathematics book that shows the bigger picture on mathematics would be of interest. Something more or less popularising.