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- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- Difference between ≈, ≃, and ≅ - Mathematics Stack Exchange
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B
- Good book for self study of a First Course in Real Analysis
Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introducti
- Pole-zero cancelation method for PI controller design
I have found a literature where the authors use a method based on the idea when the zero of the PI controller cancels the pole of the system My question is whether this method is really worthy of following My doubts arise from the fact that in real situation the pole location is loaded with some uncertainty In other words I am not able to place the controller zero exactly at the system pole
- Prove that $1^3 + 2^3 + . . . + n^3 = (1+ 2 + . . . + n)^2$
HINT: You want that last expression to turn out to be (1 + 2 + … + k + (k + 1))2 (1 + 2 + … + k + (k + 1)) 2, so you want (k + 1)3 (k + 1) 3 to be equal to the difference
- Show that $ e^{A+B}=e^A e^B$ - e^ {A+B}=e^A e^B$ - Mathematics Stack . . .
As a remark, it is actually legitimate to assume that A and B are simultaneously diagonalisable (surprise, surprise!), so the proposition is trivial But obviously, the reason why we can make such an assumption is way beyond the scope of undergraduate (or even graduate) linear algebra courses
- Vector cross product identity for $(a\\times b)\\cdot(c \\times d)$
It might be helpful if you first introduce a new symbol to refer to one of the vector cross-products as a whole E g , let's define (a × b) =: x Using the cyclic property of the scalar triple product, we equate the scalar quadruple product to the dot-product of one of the vectors with the vector triple product of the other three: (a × b) ⋅ (c × d) = x ⋅ (c × d) = d ⋅ (x × c) = d
- Use of and and or in Union and intersection of sets.
De Morgan laws : the negation of "P and Q" is "not-P or not-Q" Thus, when you check for the complement of a set, you have to negate the condition defining it
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