5
votes
What topics should be included in a course matching these specifications?
My first idea would be to aim to include applications at different levels (ones they might be able to calculate, ones they can get maths software to do, high-level maths research) and also across ...
- 5,762
4
votes
Accepted
What would be a good pacing for teaching this calculus 2 course?
In the US, most of both of your variants is covered in 3rd semester calc. A bit of a drive by of the different topics given the number of them and the differences if them. Still manageable with ...
- 152
4
votes
Is it necessary to teach the definition of a limit for engineering majors?
It is probably not the place of mathematics educators to decide what mathematics courses engineering majors should take. But a good reference point is ABET accreditation. Over 600 universities in the ...
- 10.3k
4
votes
Is it necessary to teach the definition of a limit for engineering majors?
Well it doesn't really feel right to get degrees in engineering and gain years of engineering experience without even knowing what a limit actually is. And even though many engineers will do just fine ...
- 41
4
votes
Should school syllabus include chapters partially?
Yes they do so in many places, I think the point is that the students are forced to finish a certain curriculum (depends on the country ofcourse), for example when students finish the $9^{th}$ grade ...
4
votes
Should school syllabus include chapters partially?
My sense is that often authors are encouraged (required?) by publishers to make books very 'complete'. This means the book has all the topics that any instructor would be likely to want for a subject. ...
- 647
4
votes
What topics should be included in a course matching these specifications?
Key points for goal #1:
Professor Krugman's intuitive summary of how a derivative is the limit of a sequence of differentials. Start with the graph of a function you want to differentiate. Find the ...
- 3,148
3
votes
What topics should be included in a course matching these specifications?
Have you checked out the Discovering the Art of Mathematics project? Their 11 books, one of which is Calculus, are free for educational use, and they provide lots of supportive community. If we taught ...
- 20.1k
3
votes
What topics should be included in a course matching these specifications?
For a look at the intellectual development of calculus (not a textbook nor a skeleton for a course, but something to peek at for the instructor), I'd recommend Dunham's "The Calculus Gallery" (2005). ...
- 12.3k
3
votes
What topics should be included in a course matching these specifications?
One really long answer to your question that I am fond of is the book Calculus in Context. Selected topics from the first four chapters might make for a nice one-semester course, though perhaps it ...
- 2,601
3
votes
What topics should be included in a course matching these specifications?
This will also say little in comparison to the breadth of your question.
I would include some of the history of how the notion of limit of a function,
$\lim_{x \to a} f(x)$, emerged over time.
I was ...
- 29.5k
3
votes
Should school syllabus include chapters partially?
I tend to see this in upper level college courses a lot. My impression is that the schools are trying to appear to have a solid course by using an iconic textbook (not often the best pedagogically). ...
- 159
2
votes
Should school syllabus include chapters partially?
Also, realize that many authors write "complete" (self-contained) texts, and by their own recommendations, may suggest various ways an instructor may want to approach the subject.
For example, an ...
- 2,075
2
votes
Is it necessary to teach the definition of a limit for engineering majors?
The concepts behind limits are actually very important to engineering (in the form of error/precision analysis), but are rarely phrased that way.
Given a function $f$, we can imagine an engineering ...
- 3,927
1
vote
Difference between the Cambridge IGCSE 0580 and 0607 mathematics courses
This answer assumes that both 0607 and 0580
are being considered
at the extended level
0607 is definitely a more challenging curriculum, primarily this is because it expects students to be extremely ...
- 257
1
vote
Is it necessary to teach the definition of a limit for engineering majors?
No, it's definitely not "necessary".
I'm not an engineering major, but roomed with one, did a general engineering minor, and worked in/around mechanical, nuclear, mining and chemical ...
- 27
1
vote
What topics should be included in a course matching these specifications?
Kinematics is easiest conceptual example of derivative and something everyone has visceral physical experience with (acceleration, speed, position). Optimization (particularly business or ...
- 89
1
vote
What topics should be included in a course matching these specifications?
Do hand-waving-in-the-air lectures building up to the calculus of variations. Then get them to build two slopes - one with a straight path and one with a cycloid path that they can actually roll two ...
- 111
Only top scored, non community-wiki answers of a minimum length are eligible