Calculus 3 -- looking for ways to help me understand

[jlmccart03]

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig function answers such as what sin(pi/2) is etc. now that calc 3 is upon me and includes a much greater amount of these functions and use I am freaking out. AND on top of that I don't remember calc 1 stuff as all I remember were series from calc 2.

This is where I need some guidance. What should I do to retain this "old" information? I know I can just go back and read the concepts and do problems, but I'm bound to forget once again. More importantly how can I remember rudimentary concepts such as the unit circle, algebra-calc stuff, and other necessary concepts for calc 3.

My issue with much of this stuff is my inability to remember the stuff. When I do homework I just look up the concepts and simply replicate for my solutions but the test doesn't allow for such advantages obviously. So what is everyone's secret to remember and do well in calculus? Thanks to all replies!

Side note: I am busy with classes obviously so please allow for some time to respond and ask follow up questions to your posts. Thanks!

 

[Choppy]

My issue with much of this stuff is my inability to remember the stuff. When I do homework I just look up the concepts and simply replicate for my solutions but the test doesn't allow for such advantages obviously. So what is everyone's secret to remember and do well in calculus? Thanks to all replies!

I don't have any great secrets to reveal here. What worked for me was to just keep doing problems through homework and study until I didn't have to look the identities in most of the cases. Of course there's also something to be said for taking the time to review the fundamentals so that you understand the "why" behind them as well.

 

[jlmccart03]

I don't have any great secrets to reveal here. What worked for me was to just keep doing problems through homework and study until I didn't have to look the identities in most of the cases. Of course there's also something to be said for taking the time to review the fundamentals so that you understand the "why" behind them as well.

So the best way to keep these things in my head is just practice a lot. Do you have any recommendations for problems sets. By this I mean do you have any recommended sites or books filled with problems but I can check my answer to see if it's right. I guess I should just do a problem at least every hour in addition to my required work. Thanks!

 

[Mark44]

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig function answers such as what sin(pi/2) is etc. now that calc 3 is upon me and includes a much greater amount of these functions and use I am freaking out. AND on top of that I don't remember calc 1 stuff as all I remember were series from calc 2.

I see several things happening here.
1) In the courses leading up to the calculus courses you should have gotten a good understanding of the graphs of the basic trig functions as well as a good understanding of how the sine and cosine functions are defined in terms of the unit circle. For a very small set of angles you should know the exact values of the sine and cosine of these angles, such as sin(0), sin(pi/4), cos(pi/6), and a small number of others.
2) Your grade of C+ in the second course suggests to me that there were some significant gaps in your knowledge. As you probably know, these courses build on one another, so if there are concepts in the previous course that you didn't master, things will get worse in the following course.
3) If you find that you aren't remembering topics from calc 1 or from trig and/or algebra, you're just about guaranteed to do much worse than the C+ you got in calc 2. It might be helpful to revise your schedule by dropping the calc 3 class and spend the time you would have spent on calc 3 just reviewing all the topics you're weak on. If you do that, sign up for the calc 3 class, and your chances of doing well are much improved.

This is where I need some guidance. What should I do to retain this "old" information? I know I can just go back and read the concepts and do problems, but I'm bound to forget once again. More importantly how can I remember rudimentary concepts such as the unit circle, algebra-calc stuff, and other necessary concepts for calc 3.

Go back over these rudimentary concepts and work a lot of problems. The more problems you do, the more you'll remember about them. It's the same principle that athletes and musicians use -- practice, practice, practice.

My issue with much of this stuff is my inability to remember the stuff. When I do homework I just look up the concepts and simply replicate for my solutions but the test doesn't allow for such advantages obviously. So what is everyone's secret to remember and do well in calculus?

Don't treat your homework as "write-only." After you have done a problem, take another look at your work to see if you understand why you did what you did. Something that might be helpful is to find another student to work with. A good exercise for each to do is to explain the workings of a problem. There's an old saying, "the best way to learn something is to teach it to someone else."

 

[symbolipoint]

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig function answers such as what sin(pi/2) is etc. now that calc 3 is upon me and includes a much greater amount of these functions and use I am freaking out. AND on top of that I don't remember calc 1 stuff as all I remember were series from calc 2.

This is where I need some guidance. What should I do to retain this "old" information? I know I can just go back and read the concepts and do problems, but I'm bound to forget once again. More importantly how can I remember rudimentary concepts such as the unit circle, algebra-calc stuff, and other necessary concepts for calc 3.

My issue with much of this stuff is my inability to remember the stuff. When I do homework I just look up the concepts and simply replicate for my solutions but the test doesn't allow for such advantages obviously. So what is everyone's secret to remember and do well in calculus? Thanks to all replies!

Side note: I am busy with classes obviously so please allow for some time to respond and ask follow up questions to your posts. Thanks!

• You MUST review the courses which you did already study for credit.
• Learn to draw pictures and figures from your memory, like the unit circle, and like right-triangles with the parts labeled (which will help you during integrations involving trigonometric substitutions).

 

[jlmccart03]

I see several things happening here.
1) In the courses leading up to the calculus courses you should have gotten a good understanding of the graphs of the basic trig functions as well as a good understanding of how the sine and cosine functions are defined in terms of the unit circle. For a very small set of angles you should know the exact values of the sine and cosine of these angles, such as sin(0), sin(pi/4), cos(pi/6), and a small number of others.
2) Your grade of C+ in the second course suggests to me that there were some significant gaps in your knowledge. As you probably know, these courses build on one another, so if there are concepts in the previous course that you didn't master, things will get worse in the following course.
3) If you find that you aren't remembering topics from calc 1 or from trig and/or algebra, you're just about guaranteed to do much worse than the C+ you got in calc 2. It might be helpful to revise your schedule by dropping the calc 3 class and spend the time you would have spent on calc 3 just reviewing all the topics you're weak on. If you do that, sign up for the calc 3 class, and your chances of doing well are much improved.
Go back over these rudimentary concepts and work a lot of problems. The more problems you do, the more you'll remember about them. It's the same principle that athletes and musicians use -- practice, practice, practice.

Don't treat your homework as "write-only." After you have done a problem, take another look at your work to see if you understand why you did what you did. Something that might be helpful is to find another student to work with. A good exercise for each to do is to explain the workings of a problem. There's an old saying, "the best way to learn something is to teach it to someone else."

Thank you very much for the reply! I can't drop calc 3 unfortunately as I would no longer be full-time and it would set me back a year in my degree. What I have been doing is going over these concepts since the summer time. I just simply have forgotten various things and was curious about ways of remembering things. I didn't do well in calc 2 because of the trig mostly. I understood the concepts, but as soon as trig substitution and radians were being used I lost all ability. A bad part to this lazy act was high school as that calc course we were allowed calculators on tests and quizzes. College is different, obviously, but I wlll plug through and keep working at it! I have already memorized various concepts such as derivatives and integrals so those parts are easy for me, but trig is definitley an issue as well as simplifying through algebra.

 

[jlmccart03]

• You MUST review the courses which you did already study for credit.
• Learn to draw pictures and figures from your memory, like the unit circle, and like right-triangles with the parts labeled (which will help you during integrations involving trigonometric substitutions).

Thanks for the advice! Is there any way to memorize these things without drawing them? For tests and such drawing these things might be time consuming and I was curious if there are any specific ways to remember these things in your head. I have read many different anecdotes and such, but never really found an effective memorizing way such as PEMDAS.

 

[symbolipoint]

Thank you very much for the reply! I can't drop calc 3 unfortunately as I would no longer be full-time and it would set me back a year in my degree. What I have been doing is going over these concepts since the summer time. I just simply have forgotten various things and was curious about ways of remembering things. I didn't do well in calc 2 because of the trig mostly. I understood the concepts, but as soon as trig substitution and radians were being used I lost all ability. A bad part to this lazy act was high school as that calc course we were allowed calculators on tests and quizzes. College is different, obviously, but I wlll plug through and keep working at it! I have already memorized various concepts such as derivatives and integrals so those parts are easy for me, but trig is definitley an issue as well as simplifying through algebra.

If you are suggesting that you are weak at your algebra, then this will continue to be bad for any progress in Calculus or Trigonometry. In case you are weak in Trigonometry, then like said before, you NEED to review this extensively; and this is why most colleges and universities offer the "Pre-Calculus" course (also called College Algebra And Trigonometry).

Repeat the necessary Math courses OFFICIALLY if you do not pass any at grade of C or better. Also understand that getting C or B or A in whatever Calculus n, does NOT mean that you know it well enough to enroll next in Calculus n+1. RESTUDY ON YOUR OWN...

 

[symbolipoint]

Thanks for the advice! Is there any way to memorize these things without drawing them? For tests and such drawing these things might be time consuming and I was curious if there are any specific ways to remember these things in your head. I have read many different anecdotes and such, but never really found an effective memorizing way such as PEMDAS.

You need to keep/maintain the knowledge of some things or ideas. You can try to keep all the useful pictures and other relations in your head, but you MUST understand them and MUST be able to draw them. If it is too difficult , then do not rely entirely on keeping everything only in your head as for only mental visualization. If you need some help from unit circle or relationships with right triangles during a test, THEN YOU DRAW THEM ON PAPER WHEN YOU NEED THEM!

 

[Mark44]

I can't drop calc 3 unfortunately as I would no longer be full-time and it would set me back a year in my degree.

I don't know how not being full-time would affect things, but getting your degree a year later might be a reasonable price to pay to catch up and be successful in the later courses. Based on the grades you reported for calculus 1 and 2, a grade of D or F might be the result in your current class. This too could throw off your time table.

What I have been doing is going over these concepts since the summer time. I just simply have forgotten various things and was curious about ways of remembering things. I didn't do well in calc 2 because of the trig mostly. I understood the concepts, but as soon as trig substitution and radians were being used I lost all ability. A bad part to this lazy act was high school as that calc course we were allowed calculators on tests and quizzes. College is different, obviously, but I wlll plug through and keep working at it! I have already memorized various concepts such as derivatives and integrals so those parts are easy for me, but trig is definitley an issue as well as simplifying through algebra.

The gaps in certain areas in algebra and what seems to be many areas in trig are not going to go away. If you want to be successful in calculus and subsequent courses, you are going to have to fill in those missing areas.

Thanks for the advice! Is there any way to memorize these things without drawing them? For tests and such drawing these things might be time consuming and I was curious if there are any specific ways to remember these things in your head.

Your question is a little like askiing if there is a way to swim by just using one arm. Sure, it can be done, but it's much more efficient if you use both arms (and your legs). To do well in mathematics you need both your analytic ability and visual ability. There's the old saying, "A picture is worth a thousand words." You didn't say what is covered in you calc 3 course, but I suspect it covers vectors, vector functions, and multiple integrals, all of which are much harder to understand if you don't have a good grasp of the geometry. Being able to make a drawing goes a long way in understanding these concepts.

 

[jlmccart03]

I don't know how not being full-time would affect things, but getting your degree a year later might be a reasonable price to pay to catch up and be successful in the later courses. Based on the grades you reported for calculus 1 and 2, a grade of D or F might be the result in your current class. This too could throw off your time table.

The gaps in certain areas in algebra and what seems to be many areas in trig are not going to go away. If you want to be successful in calculus and subsequent courses, you are going to have to fill in those missing areas.
Your question is a little like askiing if there is a way to swim by just using one arm. Sure, it can be done, but it's much more efficient if you use both arms (and your legs). To do well in mathematics you need both your analytic ability and visual ability. There's the old saying, "A picture is worth a thousand words." You didn't say what is covered in you calc 3 course, but I suspect it covers vectors, vector functions, and multiple integrals, all of which are much harder to understand if you don't have a good grasp of the geometry. Being able to make a drawing goes a long way in understanding these concepts.

Not being a full time student affects my aid, and since it is four weeks into the semester and my stupid self didn't think of asking this earlier I really am in a catch 22. Therefore! Fear not, I will do my best to re-learn the basics as the course goes on. I know this is bad, but this is the best I can do right now. However, even though I passed with a C+ in Calc 2 it was everything series. The integrals (minus the trig stuff) and various aspects of derivatives and such I passed with flying colors. I think I said I passed Calc 1 with a B, but that was a mistake it was a B+. The only other issue with calc 2 was the volume and area stuff with 3-d objects. I for one cannot seem to grasp the ability to draw these 3-d things, which is what got me scared these past few weeks in calc 3. I am going to bed as it is late here, but I hope this kinda shows you my level in calculus. I understand derivatives and integrals, but I flaundered with series and volumes. Thanks for the reply!

 

[symbolipoint]

Not being a full time student affects my aid, and since it is four weeks into the semester and my stupid self didn't think of asking this earlier I really am in a catch 22. Therefore! Fear not, I will do my best to re-learn the basics as the course goes on. I know this is bad, but this is the best I can do right now. However, even though I passed with a C+ in Calc 2 it was everything series. The integrals (minus the trig stuff) and various aspects of derivatives and such I passed with flying colors. I think I said I passed Calc 1 with a B, but that was a mistake it was a B+. The only other issue with calc 2 was the volume and area stuff with 3-d objects. I for one cannot seem to grasp the ability to draw these 3-d things, which is what got me scared these past few weeks in calc 3. I am going to bed as it is late here, but I hope this kinda shows you my level in calculus. I understand derivatives and integrals, but I flaundered with series and volumes. Thanks for the reply!

Drawing things is important. If you find difficulty to draw, get help. One needs to be able to essentially draw a cirlce, a square, a rectangle, and as you go, three-dimensional figures using three dimensions represented ON the two-dimensional surface of a paper, and points in three-d. One usually cannot hold this stuff in the head, but must draw for real. Instruction on these things are or should be given in your classes.