Using Laplace to analyse circuits

[IanB]

Your system is MUCH different than ours.  The expectation on entry to a STEM program is pre-calculus in High School.  Some may have had differential calculus but not all.

Then the progression for the first two years (up to the AS degree):
Calc 1 - Differential
Calc 2 - Integral
Calc 3 - Linear Algebra and Numerical Analysis - a lot of matrix math.
Differential Equations - the end for the lower level stuff

Those courses are all 1 semester each and cover the entire lower level 2 year program.

Then we get into the things like Laplace Transforms, Fourier Analysis, Field Theory and so on, all as part of the
upper level (BS) program.  Every STEM major does the first 4 classes and then it splits.  Laplace and so on will be in the EE program and I have no idea what happens in the other majors.
 
So, in some ways it's a slow path - two years to get through differential equations.  BUT, the subjects are taught in depth - as though you intend to major in math.  Perhaps a little too much depth and not enough utility.

Yes, the UK system is a bit different. The main difference is that not all students continue to the equivalent of 11th and 12th grades (sixth form in the UK), and those students that do elect to study a limited range of subjects. Not all students elect to study mathematics, but those that do will be introduced [from 11th grade onward] to series, convergence, limits, differentiation, integration and real analysis. I think there may also be an introduction to complex numbers and linear algebra.

It is normally expected that students entering a STEM degree will have this foundation and can start studying more advanced material, although there have been some complaints that students today are not prepared as well as they were in previous generations.

For various reasons I got exposed to a richer range of subjects in my sixth form studies including group theory and modern algebra, statistics and confidence tests, differential equations and numerical methods.

[mtdoc]

Your system is MUCH different than ours.  The expectation on entry to a STEM program is pre-calculus in High School.  Some may have had differential calculus but not all.

Then the progression for the first two years (up to the AS degree):
Calc 1 - Differential
Calc 2 - Integral
Calc 3 - Linear Algebra and Numerical Analysis - a lot of matrix math.
Differential Equations - the end for the lower level stuff.

Not really true. First of all many universities are on the quarter system- not semesters-  so calculus is completed in one year. Secondly, most top universities expect entering STEM students to have completed calculus in high school (grade 12) i.e. before entering college. Also, AS degrees are only given out in junior colleges not in 4 year colleges and universities.

Every STEM major does the first 4 classes and then it splits.

Not always true. For example, the biological sciences often only require Calculus 1 and 2 (often done in high school as stated above). Sometimes true for other sciences as well.
 

[Simon]

Do I correctly remember that a constant current fed into a parallel resistor and capacitor would bring about a steady state across the resistor and capacitor in five time constants? Much in a similar way to a voltage applied to a resistor capacitor series circuit brings the capacitor to a full charge after five time cycles? I'm sure I read this somewhere but the Internet provides scant and argumentative information and I have read so much printed matter I can't find it anymore.

[rstofer]

I have never thought about the problem using a current source.  Were it not for the resistor, the charge would be linear but, of course, the resistor is taking increasing amounts of current as the capacitor takes charge.

So, AFAICT, the equation is still related to 1-e^-t/RC.  So, at 5 time constants, the capacitor is about 99% charged.

I have attached an LTspice file and a screen shot - the time constant is 1 ms so at 5 ms we're pretty close to fully charged.

[Andy Watson]

Do I correctly remember that a constant current fed into a parallel resistor and capacitor ...

Yes.
Think about the constant current source and resistor as its Thevenin equivalent - now put the capacitor back in series - you have the more usual RC circuit which will charge to 99% within 5 time constants.