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Self-learning Calculus. Where does Lang's First Course in Calculus stay when compared to Apostol/Spivak/Courant
7 votes

I have a similar background most of my math has also been self studied. In fact I also started by reading Serge Lang's Basic Mathematics. This gives a great foundation and gives you a lot of nitty ...

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Rewriting expression to use at most one trigonometric function
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2 votes

It can be written like this as Donald Splutterwit mentioned, $$82\sin(v + \frac{\pi}{4} )$$ Factor out $41\sqrt{2}$, $$41\sqrt{2}(\cos(v) + \sin(v))$$ Then apply this formula (the key step your ...

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I have a number that represents 40%. How do I get the whole?
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1 votes

This can be done with basic algebra. Remember 40% $= \frac{40}{100}$ We are saying what number times 40% gives us $8000$, $$8000=x\frac{40}{100}$$ $$800000=40x$$ $$20000=x$$

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When are the eigenvalues of a matrix containing all squared elements irrational/rational?
0 votes

In conclusion for anyone who comes across this later, there are many cases where eigenvalues are rational for $2x2$ matrices containing only distinct squared integers.The case were the eigenvalues are ...

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