Calculus instructor's editions and solutions manuals?

February 4, 2023 12:44 PM

Help me find an older calculus textbook with solutions to all the problems.

I want to relearn calculus 35 years after getting a physics degree. My preferred method is to work though traditional textbooks. I'm currently halfway through a precalculus text, solving every problem. I'd like to do the same for calculus. I'd like to be able to check my work on the problems so I'm guessing that a solutions manual is what I'd need. Does a "solution's manual" contain only solutions to problems and nothing else? What is in an instructor's manual?

I am very familiar with Schaum's Outlines. I want the fuller explanation of material that's in a traditional textbook.

posted by neuron to Science & Nature (10 answers total)

Ken Stroud's Engineering Mathematics books are the ones that really stood out to me when I did my physics degree, also 35 years ago. They're still being printed, and get good very reviews. Lots of worked examples and questions to try (with answers). Look for K.A. Stroud and Dexter J. Booth (I assume Booth took over updating the book after Stroud died).
posted by pipeski at 2:02 PM on February 4, 2023 [1 favorite]

Do you want to see everything worked out or do you just want the answers? Every textbook I had in high school had the answers at the back so you could check your work. I understand from people who went to high school in the US that this is not common there. If you want a textbook with answers, just find a Canadian Calculus textbook. I don't imagine the instructors manual includes worked out solutions, since hopefully the instructor knows how to work out the solutions.
posted by If only I had a penguin... at 2:27 PM on February 4, 2023

All my math textbooks (from an American high school and then university in the 90's) had all the answers to odd questions so it's not unheard of and may still be the case.
posted by Tandem Affinity at 3:25 PM on February 4, 2023

I tend to trust a particular YouTuber's recommendations of books for self study in mathematics.

They seem to specialize in that, and in the linked video they discuss three "super-thick" calculus books suitable for self study.

And the comment section for that video features a very lively discussion of the virtues and shortcomings of those three books as well as others.

My only reservation is that I think you might be too sophisticated to enjoy a long ground campaign through calculus. If you can get access without buying it, you might get something out of glancing through the first volume of the rare first edition of Tom Apostol's elementary calculus text. I think he goes overboard with the 'from first principles' approach in the 2nd edition, although I think the typography and layout of the two volume set makes for one of the most beautiful math textbooks ever.
posted by jamjam at 3:36 PM on February 4, 2023 [1 favorite]

I should note that Wolfram Alpha can do provide answers to most first-year-calculus type problems (much to the chagrin of my colleagues in the math department.) So if you can't find a textbook with answers included, you could always just fire the problems into Wolfram Alpha to check your results.
posted by Johnny Assay at 3:46 PM on February 4, 2023

Although it was 35 years ago, your physics background makes me think that Spivak's Calculus + the solutions book is what you might want. It's really an analysis textbook, and approaches the calculus from the ground up, proving all important theorems (or leaving their proofs as an exercise for you) along the way. It's definitely a difficult text, but about as thorough as they come.
posted by dis_integration at 3:46 PM on February 4, 2023 [2 favorites]

I believe an instructor’s manual is a copy of the textbook with commentary on how to teach the concepts in the margins, while a solutions manual contains not just the solutions but the steps to reach them. I’m not a teacher, though. I have found both types of books on Thriftbooks. There also are good free online lectures for calculus; check MIT and Harvard if you’re interested.
posted by Comet Bug at 4:28 PM on February 4, 2023

I'll second Spivak, it's a very challenging way to learn calculus the first time (ie by not only teaching methods but also basically constructing the whole apparatus), but it should be more comfortable for someone in your position.

It will leave you with a far stronger and deeper understanding than any mass-market book pitched at high school or college students in a calc 101 class.
posted by SaltySalticid at 2:47 AM on February 5, 2023

I'm a physicist who had a bad undergraduate mathematics preparation and I have since gone back and taught myself math from textbooks.

Stewart's Calculus book is really excellent and will take you from Calc I (differential) through "Calc IV" (vector calculus). You can find older editions, e.g., on Bookfinder, for $5. You can also find various solution manuals there.
posted by pjenks at 6:34 AM on February 5, 2023 [2 favorites]

Response by poster: Lots of good suggestions here. Thank you so much.
posted by neuron at 8:56 AM on February 5, 2023