Supplementary material for Calculus?

[QuantumCurt]

Hey everyone, I'm starting calculus in a few weeks, and I've been wanting to pick up some supplementary material. I'm using the Larson Calculus book, 9th edition- https://www.amazon.com/dp/0547167024/?tag=pfamazon01-20 - which I've read very mixed reviews about. Some people say it's a great first exposure to calculus, others say it's a horrible book. My experience with Larson books so far has been somewhat mixed. My school uses basically all Larson books. The Larson College Algebra book was quite good. Great explanations, and very challenging exercises. The Larson Trigonometry book was, in my opinion...horrible. Very little in the way of explaining the ideas behind "why" what we were doing worked the way that it did. Challenging exercises, but the chapters didn't really prepare you for the exercises that well.

What are some good supplementary materials to have? I've read a lot about the Spivak Calculus book, although I've gathered that it isn't really ideal for someone just being exposed to Calculus for the first time. Would it still be worth picking up?

I've read some great reviews on the Dover mathematics books. I was looking at this one- https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20 and it sounds like a good book. Sounds like it approaches calculus from a more intuitive perspective, with a focus on the theory, rather than the "how this is done" approach. Any thoughts?

Any other suggestions for me to check out? Any help would be much appreciated. :)

 

[micromass]

Don't pick up Spivak, it's going to be close to useless for you. You'll be intimidated more than anything. It's just not good as a first encounter. Do pick it up later on.

I really dislike Larson, Stewart and the other books. I think it should be a rule that if a book has 9 editions, then it's crap. I really recommend "A first course in calculus" by Lang. The Kline book is pretty good too.

Here's another book worth looking into: https://www.amazon.com/dp/0883857650/?tag=pfamazon01-20

 

[QuantumCurt]

Don't pick up Spivak, it's going to be close to useless for you. You'll be intimidated more than anything. It's just not good as a first encounter. Do pick it up later on.

Duly noted.

I really dislike Larson, Stewart and the other books. I think it should be a rule that if a book has 9 editions, then it's crap.

Unfortunately, the Larson book is the required text for all 3 calculus courses. The sequence at my school is Calc I, II, then differential equations, then Calc III. The Larson book is used for Calc I, II, and III. So, I'll be stuck with it. I've read a ton of bad reviews, and I haven't been that fond of most of the Larson books I've used in the past, hence my needing supplementary material.

The Larson books seem to leave out the theory in basically every topic. They don't tell you "why." They seem to basically just give an incredibly simple example, then assume that you can solve the vastly more complicated exercises in the back. I can typically puzzle them out, but I feel bad for the people in my classes that aren't very mathematically adept.

The Larson College Algebra book wasn't bad though, in all fairness.

I really recommend "A first course in calculus" by Lang. The Kline book is pretty good too.

Here's another book worth looking into: https://www.amazon.com/dp/0883857650/?tag=pfamazon01-20

The Lang book looks really good. Lots of great reviews, and it sounds like the intuitive/conceptual basis that I really want. I think I'm going to pick that up, along with the Kline book.

The Counterexamples book you linked looks interesting. Definitely an interesting idea for a supplementary material. The Larson books actually incorporate a similar idea into their exercises. Most of the sections have a few "error correction" type problems...those can be fun to figure out sometimes. I might have to pick that book up sometime down the line.

Will those two books basically be relevant through the whole Calculus sequence, or will I get to a point where the material I'm doing in class is beyond the scope of those books? They both go up to multivariable calc, so it sounds like they should be good for all three semesters.

Thanks for the suggestions!edit-I agree about the 9 editions = crap statement. The 10th edition of Larson's Calculus actually just came out. I got lucky though, this is the last sequence that will be using the 9th edition. Anyone start Calc I after this fall is going to use the 10th edition. That would have cost me substantially more.

I really don't understand why they update their math books every 3 years or so. I mean...really...has anything that fundamental changed in Algebra or Calculus in the last 5 years?...lol

 

[QuantumCurt]

I see there's another Lang book for Calculus of Several Variables- https://www.amazon.com/dp/0387964053/?tag=pfamazon01-20

Would it be a good idea to pick this up when I'm getting closer to Calc III? Still a ways down the road...but it looks like this book covers a lot more of the material that's in Calc III, where as the First Course in Calculus book just goes into multi-variable calc briefly at the end, and focuses mainly on the material from Calc I and II.

 

[verty]

My recommendation is to use this resource (MIT's course), if you need it, for things you are struggling with or want another explanation for. Also look at the non-Scholar versions if you want supplementary problems.

 

[QuantumCurt]

My recommendation is to use this resource (MIT's course), if you need it, for things you are struggling with or want another explanation for. Also look at the non-Scholar versions if you want supplementary problems.

That looks like a great resource! Thanks for the link! I just browsed around on that site a little bit, and it looks like that will be a great resource for many courses in the future as well.