One last question. Since there are at least two approaches to EM (relativity first like you say or building up from electro and magnetostatics), what am I going to miss by going with relativity first? Surely the "pedagogical" approach has some merits other than not requiring sophisticated math?
Does it make more sense then to tackle fluid mechanics first? It was within that context that vector calculus was developed. Electrostatics weren't even known at the time and correct me if I'm wrong but knowledge of how fluids behave builds up intuition for electromagnetism as electricity can...
For what it’s worth, an AI software found Newton’s laws of motion by brute force. It was fed raw data coming from various physical experiments and used a recipe of simple rules from what I understand.
https://www.wired.com/2009/04/Newtonai/
I found a really nice set of lectures by Herb Gross on the subject of calculus, but I'm confused by his usage of if and only if and if ... then in his supplementary notes.
It seems to me that he describes identical situations on both pages, but in one case the author uses the wording "if and...
It still feels weird. On the previous page the author gives his definition of an infinite numerical sequence as a rule assigning every natural number to a definite term in the sequence, but 1 doesn't correspond with anything, at least for the given expression. But I see what you mean
The book is Calculus: Basic Concepts for High School
on the first page you are given the following sequence:
1, -1, 1/3, -1/3, 1/5, -1/5, 1/7, -1/7, ...
several pages later the rule is given:
in the second rule, for the first term in the sequence, the coefficient of one of the terms is 1/0...
I had to ask because topology and sets are relatively new. If I'm correct, people were doing rigorous mathematics long before these two branches were introduced (I can think of Fourier and Cauchy). The addition of new notions (propositional logic, sets, topology, etc.) to an already complex...
Do you think a first course in analysis should focus entirely on inequalities and leave set-theoretic topology for another occasion? Should this depend on whether or not the student had a first rigorous calculus course first? If I'm not mistaken, Victor Bryant (Yet Another Introduction to...
I wonder, did mathematicians back in the days (200 years ago) use propositional calculus? It seems like a brute force method. Or were they doing plain and simple direct proofs with no fancy contrapositives and truth tables?
I don’t think you can self study proving/analysis for the simple fact that there is no way to verify an answer unless someone with good knowledge of proofs checks your work. There are just too many ways to write a proof. That’s why most analysis books come with few or no solutions.
Which one of the 3 books by Marsden and what parts concern high school studies?
I had a look at Feynman's lecture notes and to me it seems he does assume previous knowledge from the reader. For example, in volume II he begins with: "Also we will want to use the two following equalities from the...
Exactly. I had a glance at the table of contents and it has less content. What I'm looking for is really a book or resource that teaches multivariable calculus within the context of mechanics/electromagnetism. A sort of marriage so to this speak between physics and math. I liked Morris Kline's...