Calculus 1 - Page 1
Forum section: electronics / general

author: Cujo
author_rank: Regular Contributor
timestamp: November 01, 2020, 07:09:59 am
content: I have highlighted the topics in the Calculus 1 class at my school. I just want to know if those topics are normally taught in Calculus 1?

author: ataradov
author_rank: Super Contributor
timestamp: November 01, 2020, 07:31:41 am
content: I'm not sure how different program names map to each other. In my university (in Russia) this stuff was in the first and second semester.Taylor series is specifically important to get in early, since it is used in a ton of theorem proofs later on. I'm not sure if it is necessary in all those cases, but mathematicians like to use that stuff.

author: boB
author_rank: Frequent Contributor
timestamp: November 01, 2020, 07:50:42 am
content: L'Hopital's rule was the 1st thing in Calculus 2 here I think.Pretty much all other highlighted was Calculus 1

author: Cerebus
author_rank: Super Contributor
timestamp: November 01, 2020, 10:23:28 am
content: Presumably we're talking about an undergraduate (university) level course here?The last two, differential equations, used to be thefirst thingyou'd hit in a university level course here in England, with most of the rest being stuff you'd expect people to have learned at secondary school (as long as A-level maths was a course entry requirement). You might get a break-neck speed revision over a couple of lectures of the rest. L'Hopital wasn't taught in my A-level course, Taylor was. Some A-level syllabi covered differential equations too, but that wasn't universal - mine didn't except in very rudimentary form.I've heard people saying that universities were finding that they had to teach a lot of maths to 1st year students that they used to take for granted. I thought it was just old men moaning that "the kids of today know half of what we did" and I'm genuinely surprised to see a university syllabus that covers what was in my A-level syllabus with just a few extras.

author: mathsquid
author_rank: Frequent Contributor
timestamp: November 01, 2020, 04:21:14 pm
content: I don't know about Australia, but at most universities in the US calc I, doesn't include any of the topics you highlighted (apart from really basic initial value problems), or the review stuff up through continuous functions.Calc I is pretty much limits, derivatives, applications of derivatives (mainly rates of change, optimization and related rates, but maybe linearization and newton's method), and then the basics of integration/antiderivatives up through u-substitution.Calc II is split into four parts: applications of integration (mostly areas and volumes), integration techniques, parametric and polar calculus, and sequences and series. Calc II texts usually have a chapter on ODEs, but I've never covered it in calc II.This is based on my experience at a few universities, but I know that it varies--particularly at engineering-heavy schools such as MIT, Carnegie Mellon, or Ga Tech.

author: TimFox
author_rank: Super Contributor
timestamp: November 01, 2020, 05:40:21 pm
content: In my youth (USA), we had trimesters (roughly 12 weeks each) at college, and some of your highlighted topics would be in the second trimester of the usual math course for math and science majors. How long a time period does your syllabus cover?

author: ferdieCX
author_rank: Regular Contributor
timestamp: November 01, 2020, 06:09:11 pm
content: Here in Uruguay all the topics in the list up to including Taylor Series, are studied at the Technical High School or the regular Highschool with majors in science.Some High School teachers also teach the basics of Integration (mine did it).The other topics are in the 1st and 2nd semester at the university or college level

author: JacobPilsen
author_rank: Regular Contributor
timestamp: November 01, 2020, 08:20:10 pm
content: Swim or drown.Nothing more, nothing less.

author: ataradov
author_rank: Super Contributor
timestamp: November 01, 2020, 08:25:18 pm
content: Quote from: Cerebus on November 01, 2020, 10:23:28 amThat is what happens in Russia too. There issue is that there is not really a standardized high school program that teaches necessary minimum.So they have to start with the common base knowledge everyone will have for sure. Basically the stuff you had to know to pass entry exams.This means that kids from math-oriented classes may be bored for a couple months. At the same time those kids are always warned to not relax, since things pick up quickly and it is easy to miss the part that was not covered in school.And it is not like review of material hurts anyone anyway.Also in many cases the way the same thing is taught in different places differs slightly. So it is useful to establish a common terminology and symbols used for the duration of the course.

author: rstofer
author_rank: Super Contributor
timestamp: November 02, 2020, 01:57:45 am
content: Around here there is a course called "Pre-Calc" that is two semesters (a full year), the contents of which are a prerequisite to enter Calc I (Differential Calculus). Some high school students will have the equivalent and start Calc I in their first semester of college. Others are going to be delayed by a full year. That's what happens when you don't pay attention in high school.There is no realistic way to pass Calc I without the contents of Pre-Calc.Of course there will be a group of over-achievers who finish at least Calc I in high school. I think finishing the college equivalent of Calc II (Integral Calculus) in high school is a stretch. Maybe...

author: Cujo
author_rank: Regular Contributor
timestamp: November 02, 2020, 03:30:01 am
content: Quote from: Cerebus on November 01, 2020, 10:23:28 amIt's a undergraduate Calculus 1 course.I've seen over the internet and other university's that the topics that I have highlighted are from Calculus 2 and/or a Differential Equations course(s). So I think that my university crammed those topics into a Calculus 1 for whatever reason.

author: Cerebus
author_rank: Super Contributor
timestamp: November 02, 2020, 01:52:00 pm
content: Quote from: rstofer on November 02, 2020, 01:57:45 amYet that was regarded as the norm here in Britain when I did my maths A-level back at the end of the 70s. I don't know about the whole of 'calculus II*', but we were expected to have at least a good grasp of Integral calculus and be able to symbolically integrate expressions of real variables of reasonable complexity and know how to do numerical integration. As I've said, the dividing line between 'school' and 'university' seemed to be drawn just before you started doing differential equations.To give you a flavour of what was expected, here's half a question from a maths A-level**paper from 1980 that'shereI've rendered half of one question here in mathjax to save folks from having to download and read that.Here's the first of two parts of question 7. This is the easy part, part (b) is harder but I am not taking the time to render that into mathjax, it's way too long - see the pdf if you're curious.7 (a) It is known that, for any integer \$k\$, \$\int^\pi_{-\pi} sin(k x) dx = 0, \text{and} \int^\pi_{-\pi} sin(k x) dx = \begin{cases}2\pi & if k = 0 \\0 & if k \neq 0\end{cases}\$Using the above results, show that if \$m, n\$ are positive integers,(i) \$\int^\pi_{-\pi} sin(m x) cos(n x) dx = 0\$(ii) \$\int^\pi_{-\pi} sin(m x) sin(n x) dx = \begin{cases}\pi & if m = n \\0 & if m \neq n\end{cases}\$(iii) \$\int^\pi_{-\pi} cos(m x) cos(n x) dx = \begin{cases}\pi & if m = n \\0 & if m \neq n\end{cases}\$* A bit of a foreign concept to a Brit, this uniform naming of undergraduate course units (and similar content between institutions) wasn't a 'thing' at British universities. At least, not in my day - I don't know about now.** A-levels are the school examinations that Brits take at age ~18, covering material that was studied from ages ~17-18.

author: westfw
author_rank: Super Contributor
timestamp: November 03, 2020, 03:32:32 am
content: In the US, it'd be sort-of one semester of Differentiation, one of Integration, and differential equations the next year.Except that differentiation and integration would be somewhat mixed. For example "AP Calculus" - a year-long class given in high school - would have "AB" versions that covered D&I, and a "BC" version that would be pretty much "more advanced D&I and maybe Taylor series."It was a great time in college, when the calc classes, the physics classes, the chemistry classes, and the engineering classes, were all doing more or less the same math...QuoteUm... math majors would probably be expected to have different (more theoretical) classes than engineering/science majors.I don't recall every being particularly exposed to proofs at all (which is a weakness that hurts every time I try to take an "advanced" online CS class :-( )

author: Rick Law
author_rank: Super Contributor
timestamp: November 03, 2020, 05:08:16 am
content: Quote from: Cujo on November 01, 2020, 07:09:59 amWhat is in Calc1 and Calc2 varies from school to school. It also varies depending on the student's major. I have some details below, but first some background on "two tracks".Some universities have two separate 100 level (ie: first year) tracks for calculus: a more in-depth one for engineering and science majors (seeking BS degree) and the other for the less math-utilizing majors such as Economy/Business (seeking BA degree). The university I attended has two separate 100 level tracks for Physics and Chemistry as well - an in-depth tracks for engineering/science major. So multiple tracks is not uncommon.In older days (less than a decade ago), even high schools have A and B class with A path going more in-depth.Below are two links to "AP Calculus" with a lot of details. AP is "Advanced Placement" for high school students to earn some college credits while in high school. Since the high school student likely don't know what university they may be attending in the future,AP is therefore designed to be able to satisfy as many universities as feasiblemeaing the AP credits are accepted and counted as qualified credits towards graduation at the receiving university. So, (at least for the USA) AP is probably a good gauge to compare against to decide if your university has more, or not enough.Note also thatAP Calculus also have two tracks, AB and BC, one more in-depth than the other. You may want to review the links below and see if your university covers enough. If not, you can always supplement it by taking additional courses. Math and Physics in my opinion are great ways to practice and learn analytical skills.Course at a Glance (4 pages)This is a good curriculum overview for you to compare against.https://apcentral.collegeboard.org/pdf/ap-calculus-ab-bc-course-a-glance-0.pdf?course=ap-calculus-abCourse details and examination details (248 pages deep dive):https://apcentral.collegeboard.org/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf

author: george.b
author_rank: Frequent Contributor
timestamp: November 03, 2020, 06:39:42 am
content: Here in Brazil, at least at my university, we have differential equations in Calculus II. All of the rest we see in Calculus I, Taylor series included.