How to make sure that my lecture notes do not infringe on copyrights? I'm trying to change the numbers in problems I write for examples I use in my class as well as assignments. However the problems are still inspired by the textbook. Are the problems sufficiently different from the textbook problems to not have copyright issues? There is also an issue of theorems and definitions. Authors of the calculus textbook certainly did not come up with these things. Is it OK to just copy them down in my lecture notes?

By the way I do share my lecture notes on Piazza and the course I'm teaching is multivariable calculus.
In the case of using problems from a text book, you would not need to worry about copyrights as long as you cite it (whether you change the numbers or not). It would be good to include a references section with the bibliography information of the book included in it.

Edit:

Academic textbooks are generally meant to be reusable for educational purposes. Having stated the above, depending on the country and the copyrights explicitly mentioned in the textbook, you might have to obtain prior permission from the publisher or author. (Please refer the discussion in the comments for details)