One of the advantages of using Marsden's Calculus book is the fact that you can find it, under a certain license, 100% free online. After downloading a few of its chapters, I saw some quality on the material. But that was before I dove deep into it.
Yesterday I was reading the chapter on double integrals over general regions, section 17.2. The integrals are very involved, which is expected. But then I noticed a few things.
On exercise 10, the boundaries for the integral involve two functions whose intersection you cannot calculate analytically. Below you will find an image of the exercise and the graph in geogebra.
Without the correct boundaries, it's impossible to break the integral and calculate it piece by piece (which, by the way, would be Avery time consuming thing to do).
Also, on exercise 11, something similar happens, and even the answer on the back of the book shows an incorrect function (instead of plotting $y^{2/3}$, the author plots $y^{1/3}$
It seems like these exercises were not checked before publishing the book.
What is your opinion on Marsden's Calculus books? Should I keep using it or move to something else?
Even though I'm not familiar with this particular book, I think I do have something to say that will be helpful. Many math books have typographical errors in spite of having been proofread by dozens of intelligent people. Even if you have found a typo in this particular book, that doesn't mean it's a bad book.
Whenever you read any math book, you should always be on the lookout for typos. This is not just because a good book might still have some typos. It's because you should be trying to think deeply about what you read, and asking "Is it true? Does it make sense?"
Writing a good book on calculus is a long, time-consuming, difficult, and in some ways thankless jobs. It's quite remarkable that we live in an age when there are people who are not only willing to produce such a book, but also willing to make it available freely.