19 votes
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Co-curricular lessons between geometry and chemistry?

One angle you could look at is molecular geometry. Not really my subject area but a couple of examples: Organic molecules can have different chiralities. That means that while one is the mirror image ...
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  • 1,881
13 votes

Best way to memorize the conversion between m/s and km/h

Better don't learn such conversion factors, learn how to derive such on the fly. This helps also in the case you want to change inches per second into feet per hour, or cubic feet per hour into cubic ...
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  • 12k
12 votes

Physical applications of higher terms of Taylor series

Here's one that I just thought of, by modifying a problem in the ODEs section of my textbook. Question: In the presence of air resistance, does a thrown ball take longer to go up or to come down? We ...
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  • 6,238
11 votes

Physical applications of higher terms of Taylor series

First f all, check out this great paper. It has some interesting examples, especially in Appendix A. A typical example is relativistic mechanics: the usual first order approximation yields the ...
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10 votes

Physical applications of higher terms of Taylor series

Much of quantum mechanics is only known in a perturbative framework. Essentially, the basic objects of interest are series. Terms are calculated by Feynman diagrams of increasingly complex diagrams ...
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10 votes
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Scientific results on the usefulness of physical units in secondary education?

This is not exactly what you seek, but at least you can find educational research articles under the key phrase dimensional analysis. Below [1] says it's useful, [2] questions that usefulness. [1] ...
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9 votes
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How to explain that we live in a three-dimensional world?

As celeriko took the what I consider as what "ambient" space the object lies in approach (I.e., Whittney's embedding), I'll consider the degrees of freedom of movement. Consider the normal ...
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8 votes

How to explain that we live in a three-dimensional world?

Unfortunately, dimensionality is a very tough concept to truly understand, even for adults. I know that you are trying to find a clear and simple method, which what I have typed below is certainly not....
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  • 4,840
8 votes

Examples of real-life vector fields for vector calculus

Air speed/direction on a weather map) is a very intuitive one. There's also other fluid velocity (and flux) vector fields in various chemE, mechE, and nukeE applications. I personally think the air ...
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  • 284
7 votes

Best way to memorize the conversion between m/s and km/h

It might help to make vivid what this conversion means. 10 km/h is a reasonable running speed. A soccer field is 105 m long. In one second, can you run a few meters, or can you run a third of a soccer ...
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7 votes

Physical applications of higher terms of Taylor series

I don't know if this is the sort of thing you're thinking about -- it seems to me like a too-obvious example, but it seems to fit your question pretty well. Suppose you have a particle moving along ...
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7 votes

How to explain that we live in a three-dimensional world?

Flatland. W. Abbott, 1884 Here's the Project Gutenberg link to read or download in your preferred e-version: https://www.gutenberg.org/ebooks/97 As an advanced student in elem school, my engineer ...
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7 votes

Best way to memorize the conversion between m/s and km/h

To answer the question Is there any real life situation where you can intuitively see that the km/h number is higher? and seeing that you are based in Germany: The ICE goes up to 300 km/h, but ...
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  • 2,671
6 votes

What are the mathematical prerequisites to quantum mechanics?

As stated above QM can be taught and understood at a variety of mathematical levels. At a minimum the required concepts are: 1) Linear Algebra 2) Probability Theory 3) Calculus (basic derivatives ...
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  • 61
6 votes
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Elementary physics course for pure math student

While I did not attend any elementary physics courses by mathematicians for mathematicians, I did attend a curriculum of courses called "Mathematical Physics" held by mathematicians for mathematicians ...
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  • 1,791
6 votes

Co-curricular lessons between geometry and chemistry?

Pick your battles. Don't expect to have synergy in every place. But where you do have synergy, exploit that, call it a win, and move on. Concentrate on the partial fullness of the glass, not the ...
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  • 61
5 votes

How to explain that we live in a three-dimensional world?

All the above good answers aside, I think that this question misses the mark in so far as the real problem is to internalize a good notion of what 'dimension' means. In particular, someone that age ...
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  • 4,850
5 votes

What are the mathematical prerequisites to quantum mechanics?

As for almost any course, the best person to ask is whoever is teaching the following course. They are the only ones who really are in position to know what is needed. Yes, it will happen that they ...
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  • 12k
5 votes

Does education research support the idea that answer keys are bad?

In the paper Research on teaching and learning Mathematics at the Tertiary level, by Biza, Victor-Giraldo, Hochmuth, Khakbaz, Rasmussen, recently published by Springer (ICME 13 Topical Surveys) you ...
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5 votes

Activities for calc based physics

I am going to assume that you are teaching a calculus "helper" versus the entire physics class. Your initial statements don't match that. But then all your content described is math, not physics. ...
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  • 51
5 votes
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How can I visualize differential equations and Integration in real life?

You have asked two very different questions. I'll leave the differential equations for someone else. There is one particular application of integration which is my favorite last problem to do in Calc ...
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4 votes

Applications of Calculus 2 to Physics

What I try to emphasize is that any formula they're familiar with requires integral calculus once some of the quantities vary. Basic example: (distance)=(rate)*(time). How far do you go if your rate ...
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  • 6,350
4 votes

How to explain that we live in a three-dimensional world?

You'll want to keep it simple and visual. Use easy, real-world examples. I would say a dimension is similar to a "direction you can move in". On a string you can only move left and right. It has one ...
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  • 141
4 votes

Physical applications of higher terms of Taylor series

While this isn't a 'mainstream' topic, I feel like homotopy analysis methods are worth a glance here. The idea is to approximate some non-linear equation by a linear one, take a continuous connection ...
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4 votes

Designing a Good Question on Kinematics: Test and Develop

How many suvat equations do you use? I have taught, in two countries in multiple schools using multiple books, four equations of constant acceleration. That seems to be standard. Each equation leaves ...
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  • 2,496
4 votes

Co-curricular lessons between geometry and chemistry?

This is perhaps more molecular biology than it is chemistry. There are some accessible planar geometric questions suggested by the H-P (hydrophobic-hydrophilic) model of protein (amino acid) folding,...
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4 votes

A Question about Theodore Frankel's "The Geometry of Physics"

I've owned the revised first edition of Frankel's The Geometry of Physics: an Introduction at least since I was a graduate student. The texts I suggest in this answer are largely based on my personal ...
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