Should I take Calculus IV as a 4 week summer course?

[treebeard]

Hi.

I have taken Cal 1-2 and am now wrapping up Cal 3 this Spring semester. My university offers a Cal 4 course during a 4 week summer term.

This past summer, I took Calculus 1 during the summer, after a couple years break from mathematics (I'm a natural resources graduate student), and got a B. Following this, during the next 4 week term, I enrolled in Calculus 2 and dropped it midway - my reasoning being that I had not had any trigonometry since high school (I had forgotten nearly every trig relationship).

That said, I brushed up on my trig and got an A when I re-enrolled in Cal 2 in the Fall. I expect to get a B at the lowest in Cal 3.

With all of this background presented, my question is: do you think that the material and concepts in Calculus 4 can truly be appreciated/learned during a summer term course at the university level? I will follow this course with Numerical Analysis 1 and 2 and end after Math Stats 1 and 2.

I greatly appreciate any thoughts/comments. I really want to understand this stuff, and I know a full semester is the best option but as I'm pressed for time, I'd like to move on and get it over with.


treebeard

 

[micromass]

Can you please tell us the contents of "Calculus IV", since I don't think this is standard?

 

[Dishsoap]

I had to also look this up. From what I understand, Calc I (differentiation and integration) is divided up into Calc I and II, calc III is the standard calc 2, and calc IV is the standard calc III (vectors, curl, divergence, etc.)

 

[Vanadium 50]

Unless you are at the same university, I think we should let treebeard describe what it is where he is taking it.

 

[treebeard]

Hi all,

My apologies for not including the course descriptions in my original post.

Calculus I. Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions; applications of the derivative. Honors section available.

Calculus II. Three hours lecture. Antidifferentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available.

Calculus III. Three hours lecture. Further methods of integration; polar coordinates; vectors; infinite series. Honors section available.

Calculus IV . Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available.

These are direct copy/paste from the course descriptions at my university. In regards to the three hour lecture, they are worth 3 credit hours each.

I would be happy to answer any other questions in regard to content within Calculus I-III, as I have taken/taking those.

 

[LincolnLamar]

Hi all,


Calculus I. Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions; applications of the derivative. Honors section available.

Calculus II. Three hours lecture. Antidifferentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available.

Calculus III. Three hours lecture. Further methods of integration; polar coordinates; vectors; infinite series. Honors section available.

Calculus IV . Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available.

This sounds almost identical to the Calculus sequence at my college, and I would definitely advise taking this over the summer. This course is really, more or less an introduction to DE and Linear algebra with multiple variables added in. You will be bored to death if you take this class over an entire semester. If you are comfortable with differentiation and integration, this class will be simple. If you have taken or are planning to take DE and Linear; this class will complement those more so than calculus.

 

[AlephZero]

I don't think it will be a step change in difficulty (either up or down) from the courses you have done already. So if you were happy with those, there's no obvious reason not to take it in summer IMO.

 

[treebeard]

This sounds almost identical to the Calculus sequence at my college, and I would definitely advise taking this over the summer. This course is really, more or less an introduction to DE and Linear algebra with multiple variables added in. You will be bored to death if you take this class over an entire semester. If you are comfortable with differentiation and integration, this class will be simple. If you have taken or are planning to take DE and Linear; this class will complement those more so than calculus.

I am taking Introduction to Linear Algebra this semester in addition to Calculus III and have enjoyed the content - it's interesting how varied the treatment of notation can be in different textbooks but I've grasped it pretty well. No differential equation experience yet, so far as classes are concerned, but I am planning on taking DE the Summer term following Calculus IV. Based on the nature of the homework regiment in Summer terms, I'll probably have to split them up but it otherwise sounds like it would be great to take DE and Calculus IV together.

 

[treebeard]

I don't think it will be a step change in difficulty (either up or down) from the courses you have done already. So if you were happy with those, there's no obvious reason not to take it in summer IMO.

Aside from the initial shock I experienced during Calculus I and II (II was where it really affected my grade) of not having read Trigonometry in close to 6 years, I don't find Calculus difficult. I think it will be fine to take Calculus IV this Summer.

 

[Dishsoap]

As a summer course, yes it shouldn't be an issue. As a four-week summer course... well, yikes.

 

[LincolnLamar]

I took Calculus I and II over last summer. It was broken up into two 4 week semesters. Calculus I, I did not have a problem with, but Calc II was a bear. I would not advise taking Calc II over a 4 week span. I took Calc III and linear in the fall, and now finishing up with Calc IV and DE this semester. I will say that this semester has by far been easier than the rest, but that depends on how well you grasped the concepts of your math classes so far.

 

[EricVT]

I took a few easier courses during the 4-week summer semester (sociology, philosophy, etc.) and found the time requirement for lecture each day to be pretty grueling. The material wasn't dense but it became a real chore to sit through those multi-hour lectures five days per week...not to mention the reading required each night.

I say go for it as long as your time management skills are good and you are confident that you can intensely focus on one subject for a month straight.

 

[Vanadium 50]

I've done this, and it is rather intense. Essentially, this is a full-time job. Also, missing one day is like missing a week - it's very hard to catch up once you get even a little bit behind.

 

[treebeard]

For what it is worth, it turned out to be very enjoyable but very much a full-day job. I ended with a B in the course but in some respects an A would have been easily obtainable at the regular semester pace.
I'm doing the same thing now with differential equations so here's to hoping that it will turn out as well as Cal IV!

 

[symbolipoint]

For what it is worth, it turned out to be very enjoyable but very much a full-day job. I ended with a B in the course but in some respects an A would have been easily obtainable at the regular semester pace.
I'm doing the same thing now with differential equations so here's to hoping that it will turn out as well as Cal IV!

How much of it do you KNOW now, after just that four-week course has ended?

 

[treebeard]

Welp, probably not 'quite' as much as is taught during the full semester but we had a thorough treatment of multivariate techniques; the thing that we slacked on primarily was applications in physics and engineering. For example, we covered Newton's Law of Conservation of Energy with respect to gradient vector fields but we weren't expected to barf it on paper during the exam. We primarily focused on learning the principles behind the methods and what approach to use given a scenario. My professor opted for knowledge of technique rather than stressing hard functions to integrate with the knowledge that we have CASs for that. For my purposes, it was a great class taught by a great teacher, but I expect that with more time (full three months), it would be a valuable class to take during the full semester. Definitely recommendable on a case-by-case basis, according to the individuals career/academic goals I suspect. Of course, most full-time students would have three or four courses in a semester; taking this in the summer as a four-week course allowed me to exclusively study my calculus textbook only, without needing to read for other classes as well. I'm fortunate to be on an assistantship so I treated it as my job and literally spent 8 hrs or more a day studying outside of the two hour class block. Needless to say, some students in the class were taking an additional class and the roster attendance dropped by half midway through. We had two students on separate occasions interrupt the professor during lecture to ask how to withdraw from the course. I don't go to Harvard or anywhere like that but I feel that it was a great discussion of the material despite the brief schedule.

 

[symbolipoint]

treebeard, maybe you are one of the stronger, maybe talented, mathematics students. I spent a couple of summers restudying material (Calculuses) that I had previously studied because I needed to learn the topics better. That effort was nothing like some 4, or 6, or 8 week course. I distributed the study time over two and a half months, studying on my own about 2 hours every day. Tough task but productive. I could not have done those efforts in any fewer weeks.