If I hadn't written it,

即使书不是我写的
I would prescribe it,

我也会指定它
but that is a little awkward moment.

但现在会有一点尴尬
You don't want to sell your own book.

你不想推销自己的书
On the other hand,

另一方面
you don't have to withhold information that may be useful to the class.

你又不能刻意保留对这门课有用的信息
I think that book will give you all the basic principles you need

我想那本书会给你所需的所有基本知识
in calculus of one variable, more variables,

包括一元和多元微积分
elementary complex numbers,

简单的复数运算
maybe solving some problems with vectors and so on,

可以解决一些与矢量有关的问题
which you're going to get into.

而这正是你们将要学的
Whether you are going into physics or not is irrelevant.

这和你是否学物理专业并不相关