Overcoming Struggles with Calculus: Is Skipping Tough Problems OK?

[marcusip]

Hi.

Right now I'm working on Morris Kline's Calculus: An Intuitive and Physical Approach after having finished Saxon's Advanced Mathematics (precaclulus book).

I came in feeling strong and now honestly I just feel very frustrated. I can do something like 60-70% of the problems but there seems to always be a few problems that I have just no idea what to do. Differentaition (product rule, chain rule, quotient rule) i have down pretty well but mainly because that all just seems like an simple extension of algebra. I'm mainly struggling with the word problems/applications, which is unfortuante because the whole point of this book seems to be get the student to do applications. Some word problems I don't even understand what the question is asking me!

So I'm wondering. If I can get through 60-70% percent of the problems, should I really stick it out on the tough problems or should I just skip them? The book is called an intuitive approach but honestly it seems quite unintuitive at times.

The thing is my goal is to complete the following books after this one.

How to Prove it - Velleman
Calculus Vol 1- Apostol
Linear Algebra and Its Applications - Strang
Calculus Vol 2 - Apostol
Concrete Mathematics - Knuth

Since i have plans of going over Apostol's calc anyway, I wonder if it's okay to kinda skip through Kline's book and only get the major ideas, doing the simpler problems only.

Question: Is there a limit on how many questions I can ask a day? I'm studying math ~8hrs a day (for better or worse). For some reason I'm a little nervous to ask questions. Also this book is a physical approach. A lot of the questions are Caclulus mixed with Physics. What would be the appropriate homework section to ask for help?

 

[Student100]

Hi.

Right now I'm working on Morris Kline's Calculus: An Intuitive and Physical Approach after having finished Saxon's Advanced Mathematics (precaclulus book).

I came in feeling strong and now honestly I just feel very frustrated. I can do something like 60-70% of the problems but there seems to always be a few problems that I have just no idea what to do. Differentaition (product rule, chain rule, quotient rule) i have down pretty well but mainly because that all just seems like an simple extension of algebra. I'm mainly struggling with the word problems/applications, which is unfortuante because the whole point of this book seems to be get the student to do applications. Some word problems I don't even understand what the question is asking me!

So I'm wondering. If I can get through 60-70% percent of the problems, should I really stick it out on the tough problems or should I just skip them? The book is called an intuitive approach but honestly it seems quite unintuitive at times.

The thing is my goal is to complete the following books after this one.

How to Prove it - Velleman
Calculus Vol 1- Apostol
Linear Algebra and Its Applications - Strang
Calculus Vol 2 - Apostol
Concrete Mathematics - Knuth

Since i have plans of going over Apostol's calc anyway, I wonder if it's okay to kinda skip through Kline's book and only get the major ideas, doing the simpler problems only.

Question: Is there a limit on how many questions I can ask a day? I'm studying math ~8hrs a day (for better or worse). For some reason I'm a little nervous to ask questions. Also this book is a physical approach. A lot of the questions are Caclulus mixed with Physics. What would be the appropriate homework section to ask for help?

Are you going to be satisfied with only learning 60-70% of the material? I actually have both Klines book (dover 2nd edition) and both volumes of Apostol. The problem sets in Apostols text are much more of the "wordy type problems that require some deep thinking and connecting of concepts" rather than simple calculation problems like most of Klines problem sets (less physical, sure, but they're there though).

Calculating type problems (using chain rule/product rule, etc.) are there to teach you the mechanics of what you've covered. They're simple for that reason. The problems you're struggling on are probably the ones that actually teach you the math and how to connect it to something useful or show why it's true. You should be spending a considerable amount of time on these types of problems, and it's very satisfying when you do come to a solution on your own.

Do you have the same edition of Kline? Can you give me an example of problems that you can and can't solve from the same chapter?

For the last question, no. As long as you're showing effort you can post in the homework help as much as you'd like, just don't lean on it too heavily. Ask in whatever forum seems most appropriate to the problem.

 

[marcusip]

I do have the same edition of Kline. An example problem would be page 54 (chapter 3 section 3) number 23. Actually looking at my work now the number of solved problems is higher than 70% but I think I relied on the solutions manual for the tougher problems. I'm getting out of the habit starting now.

For the question above, for the most part I understand the question and what I'm supposed to be getting to.

On a problem like on page 59, # 7 I don't even understand what the question is asking me.

 

[CalcNerd]

On a problem like on page 59, # 7 I don't even understand what the question is asking me.

.
If you want a wider group of helpers, it is advisable to also post the question verbatim with any diagrams that may be included. Otherwise, you are limiting your question to only those with that particular edition and text (often, that is really the only practical difference between textbook editions, the renumbering of questions!)

 

[Student100]

Hey,

For other people to see:

So number 23 asks "A subway train travels over a distance s in t seconds. It starts from rest (zero velocity) and ends at rest. In the first part of its journey it moves with a constant acceleration f and it in the second part with a constant deceleration (negative acceleration) r. Show that s = [fr/(f+r)]t^2/2

Number 7 asks "An object slides down an inclined plane OP' starting from rest at O. Show that the point Q reached in the time t1 required to fall straight down to P lies on a circle with OP as diameter."

I've attached the figure associated with the problem.

So number 23 you find solvable, correct?

To break down number 7, think about what you just covered. So the previous text talked about motion along an inclined plane, you need to use that to formulate an expression that shows the object slides along the inclined plane from O to Q in the same time an object would fall from O to P, and that the points O and Q lie on the same circle with a diameter of OP. How much do recall about coordinate geometry? Are you skipping a lot of these geometric problems?

 

[marcusip]

Hey,

For other people to see:

So number 23 asks "A subway train travels over a distance s in t seconds. It starts from rest (zero velocity) and ends at rest. In the first part of its journey it moves with a constant acceleration f and it in the second part with a constant deceleration (negative acceleration) r. Show that s = [fr/(f+r)]t^2/2

Number 7 asks "An object slides down an inclined plane OP' starting from rest at O. Show that the point Q reached in the time t1 required to fall straight down to P lies on a circle with OP as diameter."

View attachment 104766

I've attached the figure associated with the problem.

So number 23 you find solvable, correct?

To break down number 7, think about what you just covered. So the previous text talked about motion along an inclined plane, you need to use that to formulate an expression that shows the object slides along the inclined plane from O to Q in the same time an object would fall from O to P, and that the points O and Q lie on the same circle with a diameter of OP. How much do recall about coordinate geometry? Are you skipping a lot of these geometric problems?

Thank you for your thorough response. I feel as though I recall a decent amount of geometry. There haven't been very many geometric problems but 7-9 on that same page all built off of number 7 so yes I did skip all of those. Would you recommend picking up a geometry book? You have two of the same calculus books. I'm curious as to your pre calculus preparation.

I feel like I'm ready to do this mostly but there's just a few holes that I can patch up which would make this all much more smoother. But then I think that maybe this is just supposed to be tough and I'm setting false expectations for myself. I think a lot of my frustration comes from not knowing how hard this is supposed to be. I know there's no way to objectively quantify that but it's just an observation. Not sure if you know of Saxons books but they come with tests as well. I went through every single problem in the book and aced every test so honestly I thought I was prepared for this calculus journey.

Anyway I'm determined to get through this regardless of how. What do you recommend?

 

[marcusip]

Hey,

For other people to see:

So number 23 asks "A subway train travels over a distance s in t seconds. It starts from rest (zero velocity) and ends at rest. In the first part of its journey it moves with a constant acceleration f and it in the second part with a constant deceleration (negative acceleration) r. Show that s = [fr/(f+r)]t^2/2

Number 7 asks "An object slides down an inclined plane OP' starting from rest at O. Show that the point Q reached in the time t1 required to fall straight down to P lies on a circle with OP as diameter."

View attachment 104766

I've attached the figure associated with the problem.

So number 23 you find solvable, correct?

To break down number 7, think about what you just covered. So the previous text talked about motion along an inclined plane, you need to use that to formulate an expression that shows the object slides along the inclined plane from O to Q in the same time an object would fall from O to P, and that the points O and Q lie on the same circle with a diameter of OP. How much do recall about coordinate geometry? Are you skipping a lot of these geometric problems?

Thank you for your thorough response. I feel as though I recall a decent amount of geometry. There haven't been very many geometric problems but 7-9 on that same page all built off of number 7 so yes I did skip all of those. Would you recommend picking up a geometry book? You have two of the same calculus books. I'm curious as to your pre calculus preparation.

I feel like I'm ready to do this mostly but there's just a few holes that I can patch up which would make this all much more smoother. But then I think that maybe this is just supposed to be tough and I'm setting false expectations for myself. I think a lot of my frustration comes from not knowing how hard this is supposed to be. I know there's no way to objectively quantify that but it's just an observation. Not sure if you know of Saxons books but they come with tests as well. I went through every single problem in the book and aced every test so honestly I thought I was prepared for this calculus journey.

Anyway I'm determined to get through this regardless of how. What do you recommend?

 

[Student100]

Thank you for your thorough response. I feel as though I recall a decent amount of geometry. There haven't been very many geometric problems but 7-9 on that same page all built off of number 7 so yes I did skip all of those. Would you recommend picking up a geometry book? You have two of the same calculus books. I'm curious as to your pre calculus preparation.

I feel like I'm ready to do this mostly but there's just a few holes that I can patch up which would make this all much more smoother. But then I think that maybe this is just supposed to be tough and I'm setting false expectations for myself. I think a lot of my frustration comes from not knowing how hard this is supposed to be. I know there's no way to objectively quantify that but it's just an observation. Not sure if you know of Saxons books but they come with tests as well. I went through every single problem in the book and aced every test so honestly I thought I was prepared for this calculus journey.

Anyway I'm determined to get through this regardless of how. What do you recommend?

When I started CC years ago I had been out of school for about 10 years, I started with a college algebra course, then trig. When I got to calculus I realized my memory on geometry wasn't as good as it should have been, and picked up a few books on the subject. That's why I was wondering if it was the geometry that was getting you here as well.

What exactly about number 7 confuses you? I'm just trying to understand where the hole is, it's a pretty simple problem.

As far as books I own, I have about 8 or 9 books on elementary calculus, mostly from buying old books cheap online in bulk to donate to my old high school library that was pretty spartan otherwise. I haven't even read them all, in the example of Klines book I've gone through it a bit, but not overly in detail. They mostly just sit on my shelf, as I don't have the time or the desire to go through all of them - there's really no point. In my courses I used Anton's book for the first three courses in calculus, and then self studied Apostol. I just want to make it as clear as possible that there is no reason to own that many books for self study, most of my library is leftovers that didn't get donated if I had already sent too many. Having Klines book then moving to Apostol will be fine for an introductory calculus background.

When you get to a problem you don't understand right away, how do you approach it? Do you experiment, or do you just give up and look at the SM or move to the next problem?

 

[marcusip]

When I started CC years ago I had been out of school for about 10 years, I started with a college algebra course, then trig. When I got to calculus I realized my memory on geometry wasn't as good as it should have been, and picked up a few books on the subject. That's why I was wondering if it was the geometry that was getting you here as well.

What exactly about number 7 confuses you? I'm just trying to understand where the hole is, it's a pretty simple problem.

As far as books I own, I have about 8 or 9 books on elementary calculus, mostly from buying old books cheap online in bulk to donate to my old high school library that was pretty spartan otherwise. I haven't even read them all, in the example of Klines book I've gone through it a bit, but not overly in detail. They mostly just sit on my shelf, as I don't have the time or the desire to go through all of them - there's really no point. In my courses I used Anton's book for the first three courses in calculus, and then self studied Apostol. I just want to make it as clear as possible that there is no reason to own that many books for self study, most of my library is leftovers that didn't get donated if I had already sent too many. Having Klines book then moving to Apostol will be fine for an introductory calculus background.

When you get to a problem you don't understand right away, how do you approach it? Do you experiment, or do you just give up and look at the SM or move to the next problem?

Number 7 confuses me because I just don't know what to do. I get that a = 32 and then v = 32t, s = 16t^2 so that the freefall one would give a time of sqrt(OP)/4. And I know I can plug that time into the one that's falling along an angle of sin A by using the s = formula again.

so OQ = 16sinA(sqrt(OP)/4)^2
OQ = 16sinA(OP/16)
OQ = OPSinA

So SinA = OQ/OP.

But showing how they're on the same circle? Relating the sinA to the circle? I don't know what to do.

To answer what I do when I get to problems I don't understand, I'll experiment until I feel like I hit a wall then I'll look at the SM. I think I just hit that wall pretty quickly and get to the point where I think "I've never solved a problem like this before. I've never SEEN a problem like this solved before. I don't know what to do." I think I'm used to learning things by example and not used to figuring out a way to solve a new problem.

 

[bacte2013]

If you are interested in other books, I recommend Hairer/Wanner's Analysis by Its History. The book addresses both calculus and analysis by its historical progression, and contains both interesting information and proofs. You might be interested in it.

 

[Student100]

Number 7 confuses me because I just don't know what to do. I get that a = 32 and then v = 32t, s = 16t^2 so that the freefall one would give a time of sqrt(OP)/4. And I know I can plug that time into the one that's falling along an angle of sin A by using the s = formula again.

so OQ = 16sinA(sqrt(OP)/4)^2
OQ = 16sinA(OP/16)
OQ = OPSinA

So SinA = OQ/OP.

But showing how they're on the same circle? Relating the sinA to the circle? I don't know what to do.

You've nearly solved the problem, the next step would be to relate the angles.

Say X on OP' is on the circle, show that X = Q and you're done.

To answer what I do when I get to problems I don't understand, I'll experiment until I feel like I hit a wall then I'll look at the SM. I think I just hit that wall pretty quickly and get to the point where I think "I've never solved a problem like this before. I've never SEEN a problem like this solved before. I don't know what to do." I think I'm used to learning things by example and not used to figuring out a way to solve a new problem.

It's okay to need examples right now as you build up your "tool box" so to speak of methods of problem solving. As you progress try to rely on them less and less.

The above makes me think it might be a good idea for you to review both geometry and trig, and that might help you solve additional problems.