Book 3 Suggestions for Improving Equation Consistency

[Bowen951209]

Hello, I'm reading through chapter 3.6 in book 3 and noticed some inconsistencies in the equations. Here are two examples that I believe should be corrected:

First, the book states that $f$ is the inverse function of $P$ and and provides the equation:

$$ f(d) = P^{-1}(x) $$

I believe this should be corrected to:

$$ f(x) = P^{-1}(x) $$

The reason is that it is standard practice to express equations consistently with respect to the same variable. For example, if we define $g(x)=2x$ and $h(x)=2x$, it would not make sense to write $g(x) = 2x = h(d) = 2d$.

Second, regarding the equality involving $ICD$, the original text states:

$$ P^{-1}(r) = ICD(r) = \sqrt{4y} $$

Same problem. I think it should be changed to:

$$ P^{-1}(r) = ICD(r) = \sqrt{4r} $$

While I understand the intended meaning, the original notation may confuse readers.

[Bowen951209]

Also for ch3.7, $P^{-1}(x) = ICD(d)$ should be changed to $P^{-1}(d) = ICD(d)$

[Bowen951209]

I found another issue with the equation in Chapter 12.3:

$$ solid angle = \int_{0}^{2\pi} \int_{0}^{\theta_{max}} \sin(\theta) = 2 \pi \cdot (1-\cos(\theta_{max})) $$

The original equation is missing $d\theta$ and $d\phi$.
The correct form should be:

$$ solid angle = \int_{0}^{2\pi} \int_{0}^{\theta_{max}} \sin\theta d\theta d\phi = 2\pi \cdot (1 - \cos(\theta_{\max})) $$