I'm sorry, but this is absolutely wrong.
What you learn will have great relevance to your work - at least if you intend to be a decent engineer.
Some topics will be more immediately relevant, some topics will be less. However, there are two things you are not taking into account:
Students almost never actually know where they're going to end up. Some may think they do, but the reality is very different. Working engineers often move from project to project, and the skills required for each one often differs from the rest. Part of what engineers do is address problems that have not come up before, and having a good and varied mental toolbox is essential to being a good engineer. You never know what subset of knowledge you may need to draw upon tomorrow, and the day will come when you'll be using some of the information you think right now is irrelevant. Or you'll be stumped by a problem and watch someone else solve it with that same knowledge you're currently disparaging.
Even under the hypothetical circumstance that a particular piece of knowledge will never be directly used by a particular engineer, the act of learning it teaches you different aspects of problem solving, and gives you a core understanding that can indirectly be helpful in many scenarios. You may not need to directly write a particular set of equations, but that doesn't mean that understanding the math behind how they operate won't be useful and relevant. Engineers are not about rote facts - we do what we do by having a deep and advanced understanding of science and mathematics.
You're making judgements based on several incorrect assumptions. I can tell you that there are absolutely engineers out there who work with differential equations, just as there are engineers who routinely work with pretty much any subject matter you have taken or will take.
And having worked with engineers who clearly do not have the understanding they're supposed to, I can tell you that it is absolutely NOT bullshit that someone who earned an engineering degree dishonestly could end up designing something defective. It absolutely happens.
One reason you don't see the effects of this too often is that most companies acknowledge the possibility of error and have multiple engineers check anything critical, so mistakes made by the incompetant engineer are usually caught. Another reason is that incompetance usually shows itself early and many of those people end up fired and having difficultly getting new jobs. Eventually, many of them give up and change fields.
You have a lot of responsibility in your hands. A doctor who makes a mistake can kill a man. An engineer who makes a mistake can kill thousands. If you can't respect that responsibility, find another field.