Is practicing every problem necessary for self-studying Calculus?

[Daniel Y.]

So I'm studying Calculus: Seventh Edition by Larson on my own, and I'm having good fun learning the material, but I have a complaint: things are going too slowly! I spend some time on it each day (probably two+ hours), doing every exercise of every section. Usually there are about a hundred (for instance, 124 in the 'evaluating limits analytically' section of the limits chapter). Do you guys think that's too many problems? I realize that practice makes perfect, and I'm as happy as anyone to hone my skills, but it seems like I could be learning much more stuff in a shorter time-span if I only did half the problems (all the odd ones so I can cut down on time and check my answers when I'm done).

So would it be wise to continue doing all the problems, but take quite a bit more time, or would cutting out 1/4th of the problems or something not affect my proficiency much?

How do you guys self study?

 

[moose]

Only you can answer this... Do you think you understand everything halfway through the problems?

 

[tmc]

If you already understand the material, why are you doing the other 60 problems?

 

[rootX]

If you already understand the material, why are you doing the other 60 problems?

No one ever understands the material fully. I think math is just practice.

Even a professor can have hard time solving a problem from first year calculus book (e.g. my profs).

Does Larson have pretty good paper and pictures!? I love those big calculus books! Last summers, I was doing Larson/and other calculus (Stewart, .. ) books on my work breaks, ..etc :_) They are so addictive!

 

[LowlyPion]

So would it be wise to continue doing all the problems, but take quite a bit more time, or would cutting out 1/4th of the problems or something not affect my proficiency much?

Doesn't it pretty much depend on what you are planning to do with what you learn?

I'd compare it to eating. If you like to chew your food and thoroughly savor the texture and flavors of each bite, to linger over the associations that may be evoked, then who can argue with your taking longer at the table to finish a meal. Just as who can argue with the runner grabbing a snack and gulping a drink while spilling half in his haste.

Education is a journey after all and there are many paths. Determine where you're heading and eat in the way that's most appropriate for getting you there. You wouldn't want to not get there because you took so long eating. Neither would you want to miss critical sign posts along the way because you had spilled that part of the meal in your haste.

 

[Daniel Y.]

Does Larson have pretty good paper and pictures!? I love those big calculus books! Last summers, I was doing Larson/and other calculus (Stewart, .. ) books on my work breaks, ..etc :_) They are so addictive!

Yeah, lots of pretty pictures. The pictues helped a lot with Epsilon-Delta limits (I did not understand that at all the first few read throughs).

I can usually understand the material after 30-40 exercises, but perhaps that's just me *thinking* I understand the material, when I'm not proficient enough; and I would think aspiring physicists would need to be very proficient!

Bah! I worry too much.

 

[Bense]

I am using the 8th edition of your book, in the three calculus courses that I'm taking (calc1,2,3) all of them use that book. What I do is I work a handful of problems, but more importantly I write myself excellent notes, so that when I need to look back at the topic again, I don't have to decipher their language, I rewrite the instructions in a way that I will be able to understand them more easily. I date and label everything.

Whenever I run into one of those problems, I get my notes out and jog my memory while studying for the next step. In my program (ME) I'm sure I'll have plenty of practice with calculus, so I'm not sweating every single problem. Although I have noticed that some of the most difficult problems are the last examples at the end of each section.

 

[Fra]

How do you guys self study?

Without exception I always self stufy in mini-project form. I have a question, or a problem, that I want to answer. Then this leads me to dig into things. That is usually efficient since your motivation is at peak.

I remember the first time I learn the concept of intergrals and differentials, it was beacase I was reading a book on physical chemistry and noticed that all the gibbs energies are stated as standard forms, and standard concentrations. And I understood that this makes no sense, when it came to a real reaction where the concetrations change. At this poitn I new nothing about calculus. Then I was lead to study the concept of differentials and howto integrate them.

So for me to efficiently study something, I'd first acquire a solid thrust of motivation.

To follow an authors reasoning and make made up exercises can kill motivation. So maybe try to inject some miniproject that at least gives the topic some "life".

/Fredrik