I am not sure where i read about this (gil strang linear algebra probably?) idr now, it's been years) but there's a concept of refraction matrix/ray transfer matrix.

You can probably read about it. Idr it anymore tbh.

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For example, if I am designing a controller for a quadcopter drone, it might oscillate or spin out of control. You can keep tuning the controller parameters by trial and error until it does what you want but this takes time and money. You also don't know if you really can make it work. With control theory, you can prove if something will be stable or unstable and show how much robustness it has. I also first thought that control theory was just people playing with math but when you start building things and it doesn't do what it is supposed to do, you want explanations and you need control theory for that.

1. Doing analysis such as open loop analysis, closed loop responses, and others
2. Using model (mathematical formulae) in simulation to see responses before using real model in the system
3. Some advanced controller such as Model Predictive Controller uses Model to calculate the control variable, which is then used to controller the real system

Most control systems of significant complexity are tested and tuned in simulation. The simulation relies on an “accurate enough” mathematical model.

Nearly all ADAS, braking and steering controllers are developed based on vehicle dynamics models of varying sophistication.

A comprehensive answer to your question is unfortunately not possible due to the complexity of the algorithms, but in terms of the modelling aspects, they're often chosen based on the most common scenarios and operational design domains (ODD) -- a general dynamic model is unfortunately too complex to be useful for most conventional, non-AI/ML or non-data-driven control design techniques, so simplifying assumptions are nearly always applied based on specific scenarios.

Here's a more concrete example.

https://www.mathworks.com/help/driving/ref/bicyclemodel.html

From my experience, these are uses for mathematical modeling of systems and control laws:

• explicitly state the plant model to enable more advanced control law design (nonlinear controllers, dynamic optimizations, etc)
• design the controller before a physical plant is available
• optimization of the controller law parameters
• optimization of plant behavior to make it more controllable
• study the impact of sensor noise, placement, bias
• study the impact of actuator dynamics, range, error
• study the impact of plant variations
• serve as an agreement between the plant and controls team on how things behave
• help debug real world plant control issues by testing hypotheses on what occurred during an excursion
• I’m sure there are a lot more

f(x) = a * t^2 + vi * t + xi es una ecuación diferencial resuelta.

La matemática que estas viendo ahora si no se usa de manera directa se va a usar en otra materia del próximo año para explicar conceptos fisicos/quimicos.

Buenas yo laburo como científico de datos, las matemáticas del área son mas que nada optimizacion y probabilidad estadística, de forma directa no e usan casi nunca ya que cuando programas usas muchas cosas ya implementadas, sin embargo si es MUY importante y muchas veces las bases matemáticas y el saber porqué y cuando funciona cada modelo es lo que hace la diferencia

Depende la ingeniería pero hay diversos fenómenos físicos (como se distribuye el calor en algún metal, electromagnetismo, mecánica, hidrodinámica) en los cuales se explican con ecuaciones diferenciales, sabiendo eso se puede modelar y simular sistemas en donde se apliquen esos.

Por ejemplo, en electrónica se elaboran sistemas de control para x problemas (diseñar un brazo robótico o sistema de calefacción) que para poder modelarlos necesitas usar sus ecuaciones diferenciales (aunque existen técnicas ,como la transformada de Laplace, para abstraerte de usarlas y resolverlas como ecuaciones no diferenciales ). Me la jugaría que en aeronáutica también la usan pero no soy de ese rubro.

Ahora si estudias ingeniería en sistemas puedo decirte que es al pedo o si terminas trabajando como técnico, nos las vas a usar. Pero si sos de los que diseñas probablemente las vas a necesitar.

you can think of differential equations as just incrementally closing in on a solution using results from the previous iteration. thats engineering in a nutshell. not too many complex physical phenomena are described by closed loop equations, so differential equations are needed to approximate whats going on. fluid flows for example

Neutronic calculations in reactor cores can involve many very complex equations, like the dimensional diffusion. A lot of heat transfer phenomena in thermohydraulic calculations as well. Honestly if you aren't programming the stuff or doing research and developing the formulas you use a computer to come up with your solutions. I hated all that math because it didn't make sense which might be what you are struggling with, but the classes do teach you about problem solving and helping to see things differently. It's not great advice but push through to the stuff you enjoy and learn to preserve when it sucks, it'll make you a better engineer.

1. Calculating: geometric shapes [e.g. chute geometry, conveyor curve, and gallery chamber], and trajectories, and
2. Calculating a conveyor with a hydraulic drive [that was braked by fluid passing through an orifice] stopping duration, and a beam's deflection.

I designed an acid gas scrubber and wanted to optimize my design for economic reasons. The gas had to remain in the scrubber for a quantity of time (also referred to as residency time) for the reaction to take place. The quantity of time it stayed in the scrubber was related to the velocity of the gas and the length of the scrubber. Since the gas velocity is a function of the diameter and total cost of the scrubber is proportional to the amount of material used to make it (this was a nickel alloy unit) I used differential calculus to minimize surface are while holding my retention time to my lower limit.

I'm a computer programmer and probably not the best to answer about physical engineering.

Deep neural networks are known to be optimised via multivariate calculus. I could always use some library and not worry about the math but I've realised its very useful to know its math to able to debug it properly. You might be training a classifier and not know why your loss wouldn't go down.

But tbh I study math because it's beautiful. I've been studying some partial differential equations recently to be able to solve the Schrodinger's equation. I'll probably not used this anywhere but the realisation that I'm studying the language of the universe is a strong feeling.

unless you are doing advanced control system design or orbital mechanics, you will likely not use it at all in your professional career. it’s one of those things that is very valuable to learn for critical thinking and problem solving, as i think it helped my ability to work through problems of all kinds, but doesn’t really show up in its pure technical form.

In practice, you will not be required to solve diff eqs by hand in the vast majority of applications. However, when you are building a model for something, you will need to know how to build a system of differential equations using the governing phenomena and constraints. To solve the system, you’ll probably use a modeling or programming tool like simulink or matlab. As an example application, consider designing a controller to drive and aircraft surface actuator. You can model the actuator dynamics using these equations. Then design and test your controller to work with the actuator model before fielding it with actual hardware.

See my answer to your question on r/askengineers

I have not done so much as done basic calculus since the day I graduated.

Never had to used those sons of b* since graduation

Pardon me for asking, what specific field of engineering? (Other than Basket Weaving - Isn't that more of a math/topology thing?)

Ohm's Law, P=VI, voltage divider, parallel resistances(Rtot=1/((1/R1)+(1/R2)+...) or Rtot=(R1R2)/(R1+R2), Volume of solid shapes, Area of flat shapes, Surface area of solid shapes, skin depth, c=f*lamda, Friis Link Equation, power gain in dB, convert power from Watts to dBm

Kind of funny how that equation is literally the basis of thermo, fluid and circuits (KCL)

in*25.4=mm

mm/25.4=in

Those are my most used by a Longshot, sometimes also do some area or volume calcs

The most important math is adding up my hours at the end of the pay period

Plates can be difficult to program in, you might be better off implementing something like a rigid diaphragm where you interconnect all of your nodes with rigid links (these could just be rigid beam elements) and apply a load to this assembly or even just fixing the vertical degree of freedom at the top-most nodes, enforcing an equal vertical displacement, and back-solving for the force applied using virtual work.

A simpler approach - which will effectively be the same as putting on a rigid plate atop your origami assembly - would be to use master-slave links (also known as a displacement constraint link).

Controversial naming aside - Basically you constrain a set of slave nodes (in this case, the nodes at the top of your structure) to all have the same displacement (and rotation if required) as an arbitrary independent node (the master node) of your choosing. If you imagine that in figure (a) on the top-left of your snapshot the point P is connected to all other points on that figure by imaginary lines - these lines are effectively master-slave links where point P is your master node and all other points are your slave nodes.

Any load applied to the master node gets distributed down to the slave nodes in a manner that satisfies static equilibrium. These are quite frequently used to simulate rigid constraints in finite element models.

Here's a book on FEA that goes through this in excellent detail (see chapter 8) : https://vulcanhammer.net/wp-content/uploads/2017/01/ifem.pdf

Btw this is effectively the rigid diaphragm approach that another user has mentioned elsewhere

Look into deployable structures in aluminium. Several of these were done for various purposes worldwide in the past 40 years

You are going to have to mesh the plates. Try to keep the mesh as simple as possible - ideally triangles or rectangles.

They have their own stiffness matrices that you can find online as a function of cross-section area, Young's modulus etc.

You will have to add these to the stiffness matrix of the structure and then analyse. Basically the stiffness of paper will contribute to the stiffness of the structure.

In fact, you probably don't even need bar elements just triangles for a folded sheet of paper!

on a day to day level, probably very little, this would be more in the research level of things.

Wireless applications using MIMO and Massive MIMO is all linear algebra... the higher the rank of the channel matrix, the more independent info streams it can carry.

A lot of stuff in industry in this area is 5G oriented, bit it's all directly applicable back to wi-fi applications.

Routing algorithm development and queuing theory both are backed by rigorous math. In operations I can’t think of anytime I’ve used anything above multiplication or division. Even in the wireless world

x (Broken application) + y (Bad application owner) = z (Network issue)

if you can count to 255, you can be an NE! although somethings will require counting to FF

Network engineering tends to involve implementing technologies built on the work of researchers that developed the technology. As engineers, we don't really get very far into the weeds of the math behind how the technology works.

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For example, I work on cellular tech as part of my job, the math behind how cellular tech works is very intensive. However, all these math problems were solved by the clever folks that built the technology. I just deploy the technology and accept that whatever math involved works.

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I build custom SCADA solutions as part of my job, which can sometimes be very math heavy. Trying to take some strange sensor output and turn that into meaningful information can at times require some reasonably advanced math. I imagine a lot of large scale data analysis and forecasting would require some pretty heavy duty math. I build smaller scale versions of that sort of stuff, but I am rarely doing anything crazy enough to require more than a high school understanding of math.

You do know people usually pay a lot of money for that kind of work, don't you?