As a teacher, you can’t cover everything that is covered in the textbook. There simply isn’t enough time. You are leaning on the idea that the students will continue to learn as they do their homework later. You also hope the students read the textbook. Is it reasonable to expect the lecturer to be error-free? I know when I was an undergraduate I thought, “This is their JOB! Why can’t they present the material without making mistakes?” But in the end, the professor can always make a mistake. It happens when we teach Calculus and it happens when we teaches a graduate course in the subject of our choosing. Mistakes are human. This last semester I received mid-semester feedback from my students. They told me that the mistakes in the slides are frustrating. I can totally get on board with their complaint. I tried to explain it like this.
I am “Calculus 2: the movie”.
When you watch a movie version of the book, they sometimes get things wrong. Katniss isn’t wearing the right color backpack. Harry Potter never had a conversation with Snape in the classroom that day. Skeeter Phalen had a whole personal life in the book that was never discussed in the movie! But the movie was designed to be easily digestible. It’s restricted to take a certain amount of time. You spent 2 hours or so with a movie while you spend many more with the book. I hope that my calculus students spend time with their books. That’s the rigor. I’m the movie. I’m here to teach you something. I owe it to my students to have as few mistakes as possible. But ultimately, I have to stand up in front of them and present new material and I hope I don’t mess up too badly. I promise, I am trying to teach it to them as clearly as possible.
So in the end: I hope they read the book. But I also hope my students watch the movie. To my students I say: Try not to criticize either too much for its faults where the other may have strength. Both are designed to help you learn in different ways.