Would you please explain a little about the grammar of "shall"?
For example, in a book that I'm reading, there's this sentence:
In the following, we shall consider the propagation of an electromagnetic wave in a linear medium (free of saturation and hysteresis), free of sources.
Why has "shall" been used here? What's the meaning of it? What's the usage of it?
When used to indicate Future Tense, shall gives the statement the tone of inevitability and/or natural progression, in contrast to will which usually expresses the desire, the readiness to act by the subject.
In your example, the consideration ("of the propagation of ...") is the inevitable, although not necessarily immediate, outcome of moving forward with the text of the book.
The eager lover could ask of the object of his affection:
Darling, shall I see you tonight?
, which inquires about the future that doesn't rely on his own decision, thus expressing the dependency on fate or circumstances.
If the same lover asks
Darling, will I see you tonight?
, the answer could simply be, "I don't know, will you?", suggesting that the question itself contains the doubt or allusion to dependency on the inquirer's knowledge and/or desire to meet.
"Within 90 days after appointment, the special representative shall notify the heirs and legatees of the following information ..."
"A notary who accepts such instructions shall notify the heirs thereof and shall procure the registration..."
