Calculus III book with focus on problems.

[moe darklight]

We're currently using Stewart's in my class, and I'm not at all happy with it. I actually liked Stewart's for single variable, but the multivariable volume feels like it rushes over all the concepts and provides very little insight, and the problems are WAY too easy. They are useless for practice; they require no thought: you've done one, you've done them all.

Anyone know of any good Multivariable Calc book with plenty good examples? -- I'm not looking for anything where every problem is crazy-hard, just challenging enough to get a deeper understanding of the concepts in time for exams.

I need to seriously rase my marks this semester. Due to health problems I'm convinced I did very poorly on my first midterm (haven't gotten our marks back yet), so I have to get some serious marks going on the remaining tests or I'm screwed.

I also prefer a "drier" or succinct style of textbook, with more examples than long winded paragraphs that you have to read 10 times.

Are these any good?

• https://www.amazon.com/dp/0387909850/?tag=pfamazon01-20
• https://www.amazon.com/dp/0471608408/?tag=pfamazon01-20
• https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20
• https://www.amazon.com/dp/0071635343/?tag=pfamazon01-20

thanks

 

[naele]

The Schaum's outline is good, if only because it's mostly solved problems, but the calculus survey doesn't include Stoke's theorem. You can find that in the Schaum's Outline of Vector Analysis, which is pretty good too and has a chapter on tensor analysis.

Marsden's Vector Calculus is also pretty decent too, I think.

 

[moe darklight]

I just Got Calculus III by Marsden and Weinstein along with the study guide -- well, I downloaded them and then ordered them right away, because they're both fantastic! Like, possibly-the-best-calculus-textbook-I've-ever-seen fantastic not to mention at like 1/3 of the price of other textbooks -- I'm ordering I and II as soon as I got the money!

The textbook goes into so much more detail than Stewarts, and exactly when it matters and helps clear up the lesson: the chapters I read follow a rational progression as ideas are derived. We're on gradient vectors and min max right now, and instead of just throwing theorems and definitions at you like Stweart, the book actually leads up to the ideas in incremental steps that get to the heart of it.

The examples in the text are also more challenging than Stweart's, which feel kind of rushed "let's get this out of the way and move on to the next theorem" sort of thing. It's the perfect mix of rigor and accessibility for someone at my level.

The study guide is also just the greatest thing ever! -- it was written by a student of theirs who studied with the text, so wherever the text is lacking, the study guide is there to help you out! -- it includes answers to problems, review quizzes at the beginning of each chapter to help you brush up on old concepts that are relevant, hints and tricks from a student, and even quizzes at the end of each section, chapter tests, and even sample 3-hour midterms and exams with full answers provided!

They made sure to include problems in both books that are purposefully "tricky", in that they involve the most common mistakes students make.

Where the hell was this book all my life? -- And why can't all textbooks be written so thoughtfully with the student's needs in mind! -- I don't care about pretty color 3D graphs and online animations that are of no use.

 

[Pinu7]

Jerrold E. Marsden is one of those prolific scientific authors that is good at everything.

https://www.amazon.com/dp/0716724324/?tag=pfamazon01-20

His vector calculus book is long, however, it is full of insight and maths, so it certainly is not wordy. He also has several applications to physics. It's hard to recommend anything better.

The problems are enjoyably difficult.