I violently hate calculus and physics

The BBQ Pit
41

Well I got the 5 books today and I finally know what a derivitive is now, having done them for the last 2 weeks but never knowing ‘what’ they were.

However, can’t a tangent line have any angle to the function? Lets say I pick a point on the graph and I mark it, how do I know what angle the tangent line goes in? Is it parallel to the graph, perpindicular, 70 degrees, 15 degrees, as close to superimposing on the graph as possible or what?

The intro calculus books help, and I understand that when you have something like y=x^3 that the derivative of 3x^2 means that for every movement of x, the y value moves 3x^2 and that derivatives are used to find the slopes of tangent lines and get the slopes of non-linear functions. However I don’t think I can visualize how it works when you get to an advanced function. What about a function (assuming its a function and passes the vertical line test) like (x^2+1/4x)^1/3 (aka the cubed root). I’m not 100% sure how to find the derivative of that (maybe doing F of G after getting the derivatives of x^2+1/4x, i’d have to look it up). What does the derivative mean then? Is the derivative going to reflect all the abnormal movements the function will make when you get into advanced functions like that?

Do you need a function (with only one value of y for every value of x) to have a derivative or will derivatives work on graphs that fail the vertical line test?

I did pretty well in algebra so that is not a problem.

42

Well, no. The angle between a line and a curve is defined to be the angle between the line and the tangent line to the curve at the point of intersection. The angle between a line and itself is always 0.

Were you asking about the angle between the tangent line and the origin? That’s the inverse tangent of the slope, which is the derivative, so again, that’s fixed.

The derivative means the same thing for all functions in this context.

No, but in that case, the value of the derivative may depend on the y-coordinate as well.

43

Here’s my story about organic chemistry: When I went to college, I thought I would probably be a physics major but since the school I went to was supposed to be particularly good in chemistry which I also moderately liked, I left open the possibility that I’d major in that.

Well, the first week there, I went and talked to a chem professor and he told me to take the physics first. Then, as it turned out, I was living on a hall with several pre-meds. The second semester of that year, they were all walking around with their notecards for organic chemistry, trying to memorize the various chemical names and so forth. I saw them doing this and thought, “You know, I don’t think I really want to take chemistry.” And, you know what, I never did!..Got a PhD in physics and haven’t taken chemistry since high school…And, I don’t really regret it!

44

The idea is, you pick another point a teensy tiny distance away from the first point on the same curve. There’s only one line you can draw between those two points. That line is almost the tangent line. If you then let the second point approach the first one (this is where limits come in!), that limit is the tangent line.

If a graph has a sharp point (like the x[sup]2/3[/sup] function or the absolute value function, both at (0, 0)), there is not a unique tangent line at that point, and we say the function is “not differentiable” at that point. But if the curve is nice and smooth, there is a specific, uniquely determined tangent line at any point.

The derivative of something to a power is
power(something)[sup]power-1[/sup](derivative of the something).
This comes from putting the rule for differentiating x^n together with the Chain Rule.

When you get to the section on Implicit Differentiation, you’ll see how to do this for any graph described by any equation, even if the x’s and y’s are all mixed up together.

45

A good way to understand derivatives is to actually graph them.
Try graphing a function, then graphing its derivative, and then the second derivative, in different colors all on top of each other. You might have a computer program to do this.
Then just study the graphs for a while. You should see things like the fact that when the graph of the derivative is above zero, the original function is increasing. And that when the second derivative is negative, the original function is concave down. Just look for all the relationships between the three graphs that you can and you will start understanding.
It will work no matter how complicated the function is, so long as the function is differentiable.

I’ve actually just recently changed my major to math. I’m taking calc III and differential equations right now, and they are both fun classes, at least to me.

The only thing I would warn you about is that DE will be difficult for you if you aren’t good at integrating. You should know the basic strategies, like substitution, trigonomic substitution, integration by parts, and partial fractions. But if you do know them, you should be able to do it no problem.

46

I was the same…theoretical math was refined and elegant and a thing of beauty. I hated mucking it up with applications.

47

See, I’m just the opposite. I’m fine as long as I can use it but the instant they get to something that I can’t use IMMEDIATELY my attention wanes. Who knew the second half of Trig that 25 years later I’d be turning into a half-assed audio engineer and would need that shit? So it’s catch-up time. :frowning:

48

WOO HOO. I am all but guaranteed to pass calculus I.

The class grade is divided into 6 things. 4 exams, the final, and homework/class participation worth 14, 14, 15, 14, 25 & 18% of the grade respectively. I have gotten an 84 and 83 on exams I & II and at my current rate will have a 88-ish on the homework/class participation. So I have completed 1/2 the class points with an 86ish average.

We got our midterm grades today and I got a B+. That means in order to fail I have to get lower than a 63% on both the next 2 tests and the final, which is extremely unlikely as the professor curves the classes so only 10% of the class gets a D or lower (I am usually in the median, about 50% do better and 50% do worse).

Yay me. Now I can take analytical chemistry in spring (Calculus I is a pre-requisite of analytical chemistry).

I worry too much about my grades. I usually spend the first half of the semester terrified I will fail only to end up with an A or B.

49

My hatred for calculus is well known. I took roughly 5 million credit hours of calculus in Grade 11 and first year cegep. I passed, but barely, and complete failure to cope was the primary reason I abandoned my idea of being an engineer or architect and went into linguistics instead.

It just makes me so angry the time I was made to spend on it in high school, when I could have been learning something useful, such as home repairs, first aid, cooking, things that everyone needs to know. Calculus, by contrast, was a 100% waste of time: I literally remember none of it, and I’ve never been in a position to regret not remembering any of it.

50

True. My philosophy is let the people who love calculus do the problems about lighthouses and determining rates of change. The rest of us learning it will only alienate us from higher math. What really sucks is all the people who have to give up on degrees they love due to math and physics. At my college you need 3 semesters of calculus and 2 semesters of physics to get a degree from the college of science. There are probably tons of people who would’ve been competent biologists, immunologists, chemists, and whatnot who didn’t get the chance since they couldn’t handle calculus and physics.

51

Why would you need physics to do biochemistry? Or chemistry, for that matter? I mean, beyond Physics for English Majors or something like that, where you learn enough not to make a fool of yourself in the real world. (I think everyone should know the Laws of Motion and Thermodynamics, at the very least.) Beyond that, what’s the point?

Do future physicians need to take more than one semester of physics? (Hm. Word roots go odd ways sometimes.) I’d rather have them focusing on the human body, thankyouverymuch. (Not to the point they skip class, of course.)

52

They are just part of the ‘universal requirements’ to get a degree. Arts and humanities classes, foreign language and things like that are all required.

There is ‘some’ physics and calculus in a biochemistry since biochemistry requires analytical chemistry and physical chemistry, which have some basis in physics and calculus.

But overall I do not support the current system. 70% of what you learn in college does not relate to your degree, and about 70% of what does relate to your degree wont get used on the job.

I think physicians need 2 semesters of calculus based physics. There are at least 2 types of physics in college, algebra based and calculus based. You need either 2 semesters of calculus based or 3 semesters of algebra based physics for a science degree and I think its the same for a physician application. What I found funny was pre-med students need physics and calculus but they don’t need to take anatomy and physiology, or any nutrition classes.

53

HAHAHHA

Final course grade 80.59%, B-. I was afraid of failing and I get a B-. Its like I said in this post “I worry too much about my grades. I usually spend the first half of the semester terrified I will fail only to end up with an A or B.”

So this semester I got an A, B, B- & B-. So not too bad considering 3 were science and math courses.

54

Grats that reminds me of the 93.01% I got in a class. .02% lower and I would have earned an A-! I should get extra points for efficeny.

55

So, do you still violently hate calculus and physics?

56

Astroboy , your study technique reminds me a lot of Arnold Rimmer’s…

I loved it when he discovered why you should use indelible ink when writing crib notes…

57

The class actually got alot better about a week or two after I made the original thread in this post because we went onto derivitives, integrals, limits and things which are alot easier to understand. So I still dislike/d the class but not as much.

58

I did this, too, from as early as I can remember. I found out years and years later that it was one sign (not the only one) of Generalized Anxiety Disorder. Just something to consider…

59

Thanks. I’m 90% sure I have GAD and I have been sure of it for a couple of years now. I have a prescription for Buspar but it gave me insomnia and made me gain weight so I quit taking it.

60

I received an 89.9% in a course that was rounded up to an “A” after I pled my case with the professor based on the fact that I had perfect attendence. He checked, I did, so I got an A.

But I will never forget the course I received an 89.96% in, where the professor was unwilling to move it to an A, saying “hey, there has to be a cut line. That’s what Real Life is, live and learn.” I did learn, motherfucker, and “Real Life” is not a binary state device.