The theory of radio waves and waveguides is explained in terms of equations in the form of vector calculus. Examples are Maxwell's equations.
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Depends on how difficult you find Physics and Calculus.
The sex of the engineer has no meaning. What matters is the training, desire, and aptitude. It does not matter if a girl chooses electrical engineering or electronics engineering - it is her choice - based on her will to excel in one field or the other.
You need to take up to 4 years of calculus, as well as many science classes in physics and chemistry. Classes in algebra and trigonometry may be prerequisites for calculus.
For engineering fields, mathematics. If you do not understand calculus by the end of your first year of college, then it is time to change majors. It would be help to have studied calculus in high school in your senior year. In my first year of AE, my first quarter was the entire year of pre-calculus in high school.
Many, many applications. Calc is the basis of all higher math, for one. It's used intensively by scientists, engineers, economists, and computer programmers to name a few. Calculus attempts to model the natural world, so any profession that attempts to model natural phenomena can and should use calculus.