# What would it take to learn Calculus at a practical level?

#### djsfantasi

Joined Apr 11, 2010
7,631
OMG, where I went to school there was nothing so dreaded as an open book exam. It meant you had to know things at a much higher level.
Hmmm I always liked open book exams. Never thought that they required a deeper understanding. They seemed to fit my way of thinking. I never had to search for information to answer the question. Merely to support what I knew or confirm an equation or graph was the same as I saw it in my head. Basically, prevented me from making a stupid mistake.

#### bullzai

Joined Jan 19, 2015
42
For my memorization issue, and non-course related, this http://www.wolframalpha.com/input/?i=integral(sinx) works.

BTW: I got kicked out of EE after two years because of the memorization issue, then I went to a 2-year school and graduated with a 4.0 GPA using some tricks like being a "ghost" in classes and being thrown out of class with "If you have better things to do, don't bother coming to class" I did get a 4-year generic engineering degree as well. I happened to graduate from that school while on a leave of absence.

Basically because I had to be able to do the course work without the book to pass the exam. Doing the course work with the book in front of me was much easier except for Dynamics. The Thermodynamics professor had 1/2 the exams closed book and the second half open book.
It's nice to know that I'm not the only one who has trouble with the system. hehe As far as taking a closed-book test, I wonder how much sense that makes since, in "the real world," people use technical reference materials all the time. Shouldn't a test measure understanding as opposed to raw memory? Maybe there should be 2-stage tests? One for theory and the other for application?

#### bullzai

Joined Jan 19, 2015
42
From going over some examples, I can tell that I need to brush up on some basic "non-the-Calculus" maths. heh This is actually good because it gives me a reason to do so. For example, I didn't understand how this changed from one form to the other, having a negative exponent. In contrast, working with a positive exponent made sense to me.

I wonder if I could to to the public library and get some free help. heh Or work through a pre-calculus book on my own.

#### Papabravo

Joined Feb 24, 2006
15,779
If I write:

$$(x\;+\;dx)^{-2}=\frac{1}{(x\;+\;dx)^{2}}$$

does that help?

#### bullzai

Joined Jan 19, 2015
42
If I write:

$$(x\;+\;dx)^{-2}=\frac{1}{(x\;+\;dx)^{2}}$$

does that help?
That is less strenuous for my brain, yes. haha

#### #12

Joined Nov 30, 2010
18,217
Never thought that they required a deeper understanding.
I think the only open book exam I ever took was for a State License. There were about 30 books required for the education and it quickly got to, "You don't have to know everything, you have to know where to find it." So I don't know the ground water temperature in western Montana and I don't know the value of \$1,000 at 4% interest in 16 years, but I know which book to look in. If that's all an open book test is about, then it doesn't require a deeper understanding. It just requires remembering which book it's in.

As a matter of opinion, if there's only one book in the course, and I have to look it up, I haven't learned the material properly.

#### bullzai

Joined Jan 19, 2015
42
Anyway, I don't care about testing. It's all about learning to understand and implement. If, while implementing something information needs to be looked up, that should only increase my knowledge. Depending on how I choose to work with the information. The formal education system and testing is something else.

#### wayneh

Joined Sep 9, 2010
17,152
Hmmm I always liked open book exams. Never thought that they required a deeper understanding.
Thinking back, it depended on the topic and what you might need the text for. I was referring to the scenario where the test no longer contains any of the simple questions - the ones where the text might have helped – and now only contains questions where the book is of little use.

If there are tables and graphs you are expected to need as quick reference materials, that's fine. But I can remember taking an organic chemistry test that asked us to synthesize cholesterol form acetone (a task similar to building a TV from discrete components). The book wasn't so helpful.

#### djsfantasi

Joined Apr 11, 2010
7,631
I guess my experience was due to the subject matter. I was an Applied Mathematics major. There were hundreds or thousands of theorems.

An exam would consist of multiple mathematical profs. A proof required knowing these theorems. At least their resultant effect. So, while I had not memorized them, I at least knew the set of facts they encompassed, thus allowing me to build to the proof. If you didn't know where to look, the book was useless.

#### KeepItSimpleStupid

Joined Mar 4, 2014
4,667
The formal education system and testing is something else.
That I beat with 3 simple things:

1) made my own flash cards when reading the material and used them any chance I got. the rule when making the cards, "What i thnk should be on the test".
2) The goal of "A piece of paper by hook or crook" . Now that didn't mean cheating.
3) Class is a job. Spit out what teach, a.k.a. the boss wants.
Rule 1: The boss is always right.
Rule 2: If the boss is wrong, see rule 1.
I did challenge teach and won with my answer. He said I was not supposed to know that yet.
Just like the answer to "Are the days consecutive in October". One could answer yes or no and back up either answer. In one October long ago, there are 10 days that are missing. Are there 365. days in a year? Nope, but the answer is usually yes. Note the decimal point.
4) Worked on a medical issue.
5) Have a good meal before the exam.

\

#### Papabravo

Joined Feb 24, 2006
15,779
....
One could answer yes or no and back up either answer. In one October long ago, there are 10 days that are missing....
The skip was from Oct 4th, 1582 to October 15th 1582, a difference of 11, and we have Pope Gregory to thank.

When the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of 10 days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected).

The English did not observe the correction until 1752, nearly 170 year later, when they removed the days in September.

https://en.wikipedia.org/wiki/Gregorian_calendar

#### wayneh

Joined Sep 9, 2010
17,152
5) Have a good meal before the exam.
I didn't always have that option living in the dorm but I did even better: I never once studied for a final exam. Instead I spent time sleeping and relaxing, even camping out of town once. It drove my dorm mates crazy to see me playing my guitar and generally goofing off all during finals week, but I kicked ass on finals. Hourlies not so much, but what little I learned during the semester, I remembered. Seems most students did not. I always wished I could remember stuff without learning it but never had that good fortune. Still, I think I won in the end.

#### Papabravo

Joined Feb 24, 2006
15,779
That is less strenuous for my brain, yes. haha

$$(x\;+\;dx)=x\left(1\;+\;\frac{dx}{x}\right)$$

relatively straightforward algebra -- eh?

#### bullzai

Joined Jan 19, 2015
42

$$(x\;+\;dx)=x\left(1\;+\;\frac{dx}{x}\right)$$

relatively straightforward algebra -- eh?
I /think/ that makes sense.
= x(1) + x(dx/x)
= x + 1(dx/1)
= x + dx

#### djsfantasi

Joined Apr 11, 2010
7,631
So now all you are missing is the exponents. Ignore the value of -2 for just a moment... and use a variable n in its place...

$$x^{n}y^{n}$$

Can this be written another way?

$$(xy)^n$$

With that equality, your factoring can be done with any exponent, even negative ones. Just let x be x and y be (1+dx).

#### bullzai

Joined Jan 19, 2015
42
So now all you are missing is the exponents. Ignore the value of -2 for just a moment... and use a variable n in its place...

$$x^{n}y^{n}$$

Can this be written another way?

$$(xy)^n$$