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The Road to Reality Study Notes: Difference between revisions
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* $$e^{i\theta} = cos \theta + i sin \theta$$ | * $$e^{i\theta} = cos \theta + i sin \theta$$ | ||
* (Worth looking into [https://en.wikipedia.org/wiki/Taylor_series Taylor Series], which is related.) | * (Worth looking into [https://en.wikipedia.org/wiki/Taylor_series Taylor Series], which is related.) | ||
== Chapter 6 Real-number calculus == | |||
=== 6.1 What makes an honest function? === | |||
* Differentiable, Analytic | |||
=== 6.2 Slopes of functions === | |||
* Derivative is the slope of the tangent line | |||
* Finding the slope of the tangent line for every point | |||
=== 6.3 Higher derivatives; $$C^\infty$$-smooth functions === | |||
* Second derivatives | |||
* Euler would require you to have functions that are $$C^\infty$$-smooth | |||
* Not everything that is $$C^\infty$$-smooth is ok for Euler | |||
== Other Resources == | == Other Resources == | ||