17
votes
How can I build a protractor without a protractor?
As Will Orrick says in the comments under user20315's answer, it is possible, with straightedge and compass, to construct a regular 120-gon, and therefore it is possible to mark off every 3 degrees on ...
- 17.3k
13
votes
How can I build a protractor without a protractor?
Step 1: Find a machinable material that is reasonably incompressible.
Step 2. Find a string material that is reasonably non-stretchy.
Step 3: Make a cylinder out of the machinable material (perhaps ...
- 3,148
10
votes
Applications and motivation of abstract linear algebra topics for engineers
Of course it depends on how much time you're willing to spend on this. If the answer is "very little" then no chance that you can say something more than "in the future this will be useful for you"...
...
- 1,715
9
votes
How to incorporate optional higher level mathematical content in an Engineering Maths course?
In our department, large introductory math courses, such as calculus, linear algebra, and discrete mathematics, come together with little satellite courses called "advanced investigations in *", where ...
- 174
9
votes
Applications and motivation of abstract linear algebra topics for engineers
Two Four ideas:
(1) "composing linear transformations": Use rotation, scaling, and shearing. If you extend to homogenous coordinates, you can include translations. Fundamental to all computer ...
- 29.5k
7
votes
What do I study in calculus beyond the minimum required for undergraduate engineering?
There is a big old textbook Advanced Engineering Mathematics by Kreyszig. Maybe looking at its table of contents HERE will show you what mathematics he thought was useful for engineering students.
(...
- 7,369
7
votes
Introducing derivative concept and definition
It occurs to me that maybe you can approach this from the viewpoint of approximations. Briefly, I’m thinking of the kinds of approximations they likely use in practice, and which are often given in an ...
- 5,768
7
votes
Complex analysis (Applied versus pure)
First: there seems to be a traditional belief that "pure" math fusses over tiny uninteresting details that "applied" math takes for granted, etc. Sure, we can operate this way, and make "pure math" as ...
- 14.2k
7
votes
Accepted
Why does a first course in linear algebra teach QR-decomposition?
I wouldn’t feel bad about leaving it out, but I think it’s a valuable conceptual example for understanding matrix algebra. Computing the QR decomposition is equivalent to applying Gram-Schmidt ...
- 226
6
votes
Mathematics that can be worked into 8th grade engineering course
Here are two activities I have used. The second does not fit in an hour, however.
(1) Give the students maybe two different sizes and thickness of paper.
Ideally, the two are quite different.
Their ...
- 29.5k
6
votes
Teaching Mathematics to a Machine Learning Class
This may help, the labs and associated materials for a course
CSC 294: Computational Machine Learning:
github link. See course-materials/Labs/, Jupyter Notebooks:
...
- 29.5k
6
votes
How can I build a protractor without a protractor?
In mweiss' method, the outer angles ∠AOC and ∠DOB are shy of 1° by slightly more than 0.0001°, and the inner angle ∠COD exceeds 1° by slightly more than 0.0002°.
On a (huge!) one meter diameter ...
- 3,148
6
votes
What to do with "wild goose chase" or "quantum leap"-types of incorrect solutions when you ask students to prove/show something?
It's quite likely to be a consequence of the belief that they have to answer the question. When they can't work it out, when they've gone around in circles and got lost, but still they have to give an ...
5
votes
Polar form before Cartesian form when introducing complex numbers
Let me suggest the following story: if we consider $z = x+iy$ as a point in the complex plane then we have $z = (x,y)$ in the usual Cartesian coordinate notation. Since
$$ z=x+iy = x(1)+y(i) = x(1,0)+...
- 10.7k
5
votes
What do I study in calculus beyond the minimum required for undergraduate engineering?
Are you an undergrad majoring in aerospace engineering, or are you interested prerequisites from graduate programs in aerospace engineering?
In either case, the following syllabus may help you ...
- 2,075
5
votes
English book for math for (electrical) engineering similar to German "Higher Mathematics"
(edited)
I have used Kreyszig, Advanced Engineering Mathematics, fifth edition, as an undergrad, a practicing engineer, and in grad school. I love it.
(1) It is in English, composed in English, ...
- 1,812
5
votes
Complex analysis (Applied versus pure)
Since "epsilon-delta" has been mentioned a couple of times by the question asker, I just thought I'd add my opinion that the epsilon-delta business should not be seen as a divider between pure and ...
- 51
5
votes
Why does a first course in linear algebra teach QR-decomposition?
Solving least squares problems by QR factorization is much more numerically stable than solving them by Cholesky factorization of the normal equations. This can easily be demonstrated on an ill-...
- 821
5
votes
What is the best way to introduce Laplace transforms on an Engineering Mathematics course?
In a classical control theory course, Laplace transforms are used to calculate transfer functions. As suggested by @Isaiah, see what your colleagues are doing. Skipping material can be risky when ...
- 4,625
4
votes
Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"
Let's take Kreyszig as the reference case, since I'm familiar with it. In terms of next harder books, I would say:
Arfken and Weber: unfortunately I HATE this book as do many physicists. (It's ...
- 1,812
4
votes
Differential forms in mechanics?
I'd suggest having a look at Geometric Mechanics by Darryl Holm.
The theme of developing mechanics in the framework of differential geometry has a considerable record at the graduate level, as ...
- 221
4
votes
What do I study in calculus beyond the minimum required for undergraduate engineering?
You do not mention differential equations, but this is a very useful topic in engineering, aerospace included, and the list of topics/courses you have studied mean that you would be well prepared for ...
- 4,625
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
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
Accepted
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 ...
- 20.1k
4
votes
How and what to teach on a second year Engineering Mathematics?
I'm unaware of a major reform in engine math. If you look at the major selling textbooks, for instance, they remain pretty traditional. The most popular, Kreyszig, is one that I had in the mid-80s (...
- 41
3
votes
Need to learn recurrence relation discrete mathematics
I liked this Discrete Mathematics: An Open Introduction, by Oscar Levin, for generating functions, so I'm guessing it will be good for recurrence relations.
- 20.1k
3
votes
Applied ODEs for Numerical Methods
I would consider to add two items to the list, both from a systems slant:
Predator prey relations. The behavior can be graphically investigated, but the actual solution function is not analytically ...
- 31
3
votes
Introducing derivative concept and definition
A good approach for engineers might be to connect the "slope of a graph" to sensitivity: the factor by which a small change in input gets multiplied to produce a change in the output. You ...
- 3,927
3
votes
Introducing derivative concept and definition
I think you should take whatever motivation you are most excited to show them based on (a) their interests and background (b) your passion and go that way. Everyone will have a different answer to ...
- 250
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