Moving on from Single Variable to Multivariable Calculus: Marsden or Stewart?

[physicsnoob93]

Hello everyone.

I needed some guidance with calculus. I am currently a (sophomore? Sorry, I'm not following the US system) and I used stewart's book to learn single variable calculus, but I didn't do the exercises from the book, and I did the exercises at the AP level. I took my AP Calculus BC today. Although I'm hoping for a 5, I think I have the concepts but it's not entirely concrete yet.

My question is: I want to move on and learn multivariable calculus starting the end of May, probably continuing Stewart's or using Marsden. Do you think it's ok for me to do this without having a very rigorous base in single variable calculus?

And also, I know there have been many threads on this, but still, Marsden or Stewart? They both look very similar to me.

Thanks.

Edit: Oh, and to add. I am not doing all this preparation for pure math (Plan to do EE&CS). I am doing this for physics, because I enjoy physics.

 

[dx]

If you're not completely comfortable with single variable calculus, it would be better to study that more thoroughly before you start multivariable calculus. It's better to have a solid foundation rather than patchy knowledge of many things.

 

[physicsnoob93]

Any way to do that quick? Because each chapter in stewart has a hundred exercises. And i don't want to go through all of that for like 11 chapters. :

Is there anything that will help me get around this?

Thanks

 

[cristo]

Any way to do that quick? Because each chapter in stewart has a hundred exercises. And i don't want to go through all of that for like 11 chapters. :

There's no "quick" way of learning mathematics. The only way to learn, is to do.

 

[dx]

Also, there's no need to do every single exercise that is given in your book. Do as many as you need to to learn the material and feel comfortable.

 

[diazona]

Any way to do that quick? Because each chapter in stewart has a hundred exercises. And i don't want to go through all of that for like 11 chapters. :

Is there anything that will help me get around this?

Thanks

You don't need to do all 100 for every chapter, though - a typical college math course might assign 5-10 every week (well, it depends on what kind of problems they are).

 

[qntty]

You should also solve some problems in the the "problems plus" sections which have more challenging problems.

 

[physicsnoob93]

Will it be effective to skip the "Section" problems and jump right into the problems at the end of the chapter summary + problems plus? That would save loads of time.

Appreciate the input.

 

[snipez90]

Just want you to remind you that you essentially need to pass the AP Calc exam (get about 60% of the test right) to get a 5. Hence, you should judge your own level of comfort with the concepts partly based on the exam. If you think you could have done or did complete most of the problems on the exam, you should be in good shape to tackle a book such as stewart's MV calc. But if there were many concepts that you skimped over, then go through stewart's single var text again. Judge for yourself where your weaknesses are and remedy them if necessary.

But if you already know you need to work through Stewart single var, you should still judge for yourself which exercises are necessary. Most of the exercises are a lot like the examples in the chapter, so don't do the ones where it is immediately clear how to proceed with a solution. Don't solely focus on the problems plus section, because there are genuinely difficult problems there, not all of which will be particularly relevant for your purposes. Most importantly, don't rush ahead. Why so hurried?

 

[physicsnoob93]

To snipez, yeah I know the Calculus BC material throughout and I expect a 5. It's just that I don't think calculus BC is enough to continue to multivariate calculus. I think something deeper is required to understand it better. Obviously, the things covered in stewarts book are probably a level higher than the BC material. And yeah I'm doing this not because I want to hurry. It's just that school isn't very challenging. We're still doing sequences and binomial theorem fgs. Also, I want to learn E and M to a higher level with vector analysis.