16
votes
Computational topology for engineers
I'm just finishing up a graduate course in computational topology which could be adapted very effectively for this purpose. We're focusing on topological data analysis and computational homology. All ...
- 1,665
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"...
...
- 1,637
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 ...
- 27.9k
9
votes
Accepted
Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"
I am unaware of standard mathematical texts for engineers at a level beyond that of the usual advanced engineering mathematics texts. Perhaps the closest thing in some sense might be Strang's classic ...
- 4,308
9
votes
Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"
Not certain this satisfies your set of criteria, but...
This is a challenging but wonderful book. Arnold emphasizes
the geometry of manifolds throughout:
differential forms,
Riemannian geometry, ...
- 27.9k
8
votes
Computational topology for engineers
Wow, thanks for the recent shout-out. I hope this is the right place for me to add a few references that might be useful and haven't already appeared in the answers.
Rob Ghrist has just written a ...
- 181
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 ...
- 13.3k
7
votes
New math. teaching assistant facing big problems, what to start with?
I would start with a discussion with the Engineering department about what it is they want the students to learn. Teaching different skills will need different methods, so you might as well start with ...
- 5,540
7
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 ...
- 154
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 ...
- 5,129
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.
(...
- 6,141
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 ...
- 27.9k
6
votes
Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"
Geometric Methods and Applications for Computer Science and Engineering, by J. Gallier, does the job for what concerns classical differential geometry.
Elasticity and Geometry by Audoly-Pomeau ...
- 1,637
6
votes
Complex analysis (Applied versus pure)
This may not be a direct hit, but since you mentioned "emphasis on visualization," may I suggest you investigate Tristan Needham's Visual Complex Analysis. E.g., see this MSE answer:
&...
- 27.9k
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:
...
- 27.9k
5
votes
What Should be there in a Single Variable Calculus course for Engineers?
I strongly agree with Douglas Zare that it is highly dependent on what incoming students are prepared for in terms of their mathematical background beforehand. As far what is the minimum calculus ...
- 2,513
5
votes
Reference requests: Is there a text that is even more advanced than books on "advanced engineering mathematics"
Surprisingly not yet mentioned is
Advanced Mathematical Methods for Scientists and Engineers by Carl M. Bender and Steven A. Orszag
Below are some comments about this book I made in a 10 January 2007 ...
- 5,129
5
votes
New math. teaching assistant facing big problems, what to start with?
I think you need to build a support network locally. Even if it means going outside the university to a nearby university, you will need mentors, fellow TA's, administrators, and others to help you ...
- 2,518
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
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, ...
- 1,758
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)+...
- 9,982
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 ...
- 2,008
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-...
- 696
5
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 ...
- 16.9k
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 ...
- 4,308
4
votes
New math. teaching assistant facing big problems, what to start with?
"What is my mission when I teach math for engineering students?"
I think it is possible to zig-zag between applications and appreciation of
the history and the beauty of the mathematics underlying ...
- 27.9k
4
votes
Linear algebra for engineers
I learned linear algebra (decades ago) as an "adjunct" to "engineering mathematics."
The focus of most engineering students is "systems of equations." As long as you remember that, you're fine. So ...
- 1,500
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
Accepted
Are there more modern or computation oriented applications of complex analysis in science and engineering?
In computer science, specifically in combinatorics (much used in algorithm analysis) one important task is to derive asymptotic behaviour of sequences, which in turn are easiest to get in form of a ...
- 12k
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