How can I improve my understanding of Calculus 1 by tackling tougher problems?

[calcstudent1]

Hi All:

I am taking Calc 1 at a community college and we are using Calculus by James Stewart 7th edition. I am able to do homework problems that are assigned to us which are only a small subset of problems from end of the chapter exercises. However, we are not doing any of the remaining problems and that's where I am having problem since they appear to be tougher problems.

Am I supposed to do these to get a good grasp of the concept? Is that how some of ivy league students prepare? I am just worried that our instructor might be making it little too easy since Calc 1 is taken by various majors but I want to be an engineering major. I cannot blame my instructor because that's how syllabus is prepared keeping in mind diverse majors.

In the 7th edition, every sub chapter has about 70 problems.

Thanks for any pointers!

 

[Highway]

there is a lot of information out there for a class like calc1. Try getting a Schaum's Guide for the topic and work through the problems they have in there -- all have worked out solutions to check yourself against. These are good for other basic courses (chem/physics/calc2,3) as well as your core engineering classes.

If you are struggling with concepts, try Bob Miller's "Calc for the Clueless" -- it really breaks the theorems down with clear examples that should enable you to do homework level problems. He has these books for Calc 1-3.

 

[calcstudent1]

I do understand the overall concept. My problem is the problems in the exercises where I get stuck up. Do I need to be able to solve those to be well prepared for advanced classes like Calc 2 and Calc 3.

 

[Highway]

it doesn't hurt

 

[DivisionByZro]

It is likely that they don't require you to be able to work out the tougher problems, but bear in mind that some of them may be tricky even for your instructors (Maybe). It really is up to you; you should be sufficiently prepared if you do well with the problems given, but it's always good to go beyond what is taught in the classroom. If you can, do all/most/some of the other problems. If you get stuck, these forums are great for helping you out.

Also, "Ive League students" is a very broad term. If you're speaking of "honors" calculus classes, then the problems are often quite more challenging than what is found in Stewart's text.

 

[calcstudent1]

It is likely that they don't require you to be able to work out the tougher problems, but bear in mind that some of them may be tricky even for your instructors (Maybe). It really is up to you; you should be sufficiently prepared if you do well with the problems given, but it's always good to go beyond what is taught in the classroom. If you can, do all/most/some of the other problems. If you get stuck, these forums are great for helping you out.

Also, "Ive League students" is a very broad term. If you're speaking of "honors" calculus classes, then the problems are often quite more challenging than what is found in Stewart's text.

Thank you. By ivy league I mean, MIT, harvard, princeton etc. So, honors calculus problems are much tougher than the problems in the exercises of Stewart?

 

[1mmorta1]

Sometimes the tougher problems in Calc 1 are only more difficult because they require more background knowledge- a better working understanding of algebra or trigonometry. Some courses don't cover those questions because they aren't required for a course on how to do Calculus.

Try taking the problems to a fellow student(like a math major) or the teacher and having them show how to solve it. If you notice extra steps, like factoring, or trigonometric identities, then THAT is why your class isn't touching them.