What Math Should I focus/practice On the Most?

[ROBOT]

So I decided instead of getting by I would focus on what I actually will need in later classes.

I'm in precalc now but have trig and Calc 1,  Calc 2, and differential equations left. What formulas/concepts are most important?

I have physics 1 and 2 along with:

Circuit Theory 1
Circuit Theory 2
Electronics 1
Electonics 2
Microprocessors (Assembly language)
Advanced Digital Electonics
Digital and Analog Communication
Microprocessors 2
Control systems
+some undecided electives.

[Brumby]

Depends on where you're headed, but to start off....

I would say you need a high level of competence with basic algebra - and throw in some complex arithmetic for good measure.  Calculus perhaps, but nothing exotic.

This will get you grounded - and if your studies lead you into directions where something more advanced is required, those studies will make it clear what that will be.

JMHO

[daqq]

For me the most powerful tool were systems of linear equations. Once you understand what kind of a power those have (seeing as you can easily solve matrices of thousands unknowns these days on off the shelf computers) you can solve LOTS of engineering/programming problems with them.

[dannyf]

What formulas/concepts are most important?

wouldn't that depend on what you want to do?

other than that, I would say pick the ones that you lease understand and go from there.

[rstofer]

This looks a lot like a EE program.  At a minimum, you will need differential equations to get set up for Laplace Transforms and probably Fourier Series.  You will absolutely need Laplace for Control Systems.  Bottom line, engineering is ALL math.

Slinging around polynomials, particularly difficult polynomials with e^x terms will be helpful.  You'll be doing a LOT of that when dealing with Laplace and changing between the time domain and frequency domain.

Of the math courses listed, you need to be proficient in ALL of them.

May I suggest the Khan Academy videos on YouTube.  I was watching his treatment of Laplace the other day and I thought it was pretty good.  The problem is, he's a mathematician and the examples don't get grounded in hardware.  When he talks about damped harmonic motion which involves e^x and sin(x) and/or cos(x), he doesn't really spend enough time showing a physical system.  But the math is good!  For some values of 'x'...

I'm going to go back and watch his entire Calculus, Differential Equations and Laplace videos again.  I'm long retired but my grandson is just about to embark on the EE program.  I better be able to keep up!

[westfw]

Calculus is pretty fundamental to semiconductor physics and signal processing.  Also linear algebra and complex numbers.
Computer science may want some "discreet math" and other more theoretical mathematics, which can be quite shocking (I took an online class along the lines of "intro to theoretical math like math majors do in college - it's not about getting an answer.")

Do you actually have any choices?  When I got my EE degree, there was a pretty fixed set of math classes that you HAD to take, and taking any additional math would have been problematic because of the "required" structure of electives.

OTOH, if you're lucky, your Electronics, Circuit Theory, and Communications classes (what, no physics?) will all be spoon feeding you the required math as well.  (I'm having trouble figuring out how multi-variable calculus can be a 2nd year class these days, when I needed it extensively for 1st year physics...)

[f5r5e5d]

certainly depends on the academic program - its nice to get to Maxwell's Equations in a EE Physics sequence - does require Vector Calculus: Div, Grad, Curl, Green's and Stoke's Theorems

a Calculus based Probability and Statistics course is advisable for advanced Signals and Systems, any Optimization based Controls


and my personal hobby horse - if, in Robotics/Mechatronics or Computer Graphics, anyone introduces Quaternions - run straight for Hestenes "Geometric Algebra" reboot/update of Grassmann and Clifford's ideas
there's good reason Quaternions lost out to Gibbs/Heaviside Vector Algebra - if you need to extend to 3D rotations its better to use "Geometric Algebra" which keeps the modern definition of Vector

[LabSpokane]

Linear algebra is a must for a EE.

Calculus.  If you're taking pre-calc as a frosh, make sure you avail yourself of all help available.  Generally, most freshman are in Calc 1 or at least were when I was your age.  And I'm not blaming you for this.  The slacking off of the math curriculum in public schools is a problem for everyone everywhere in the US. 

Differential equations - particularly if you're destined for controls, then really get a handle on solving differential equations with s-parameters. 

Get yourself a copy of Schaum's:  https://www.amazon.com/Schaums-Outline-Mathematical-Handbook-Formulas/dp/0071795375/ref=sr_1_1?ie=UTF8&qid=1469425344&sr=8-1&keywords=schaums+mathematical+handbook+of+formulas+and+tables

It has all the math identities you'll need to know as an undergrad.  These will be mysterious until you use them for a while. 

[CatalinaWOW]

Math has a longer half life than anything else you will study in electrical engineering.  Take and LEARN all you can stand.

Engineers who started their careers on vacuum tubes, but also had Laplace, Fourier, Linear Equations, Diff. Eqs., Statistics and so on were still doing fine after vacuum tubes had passed on to transistors, and transistors passed on to integrated circuits, and with a little polishing were doing fine after the digital transformation.  Specialists in each of those technologies had much rougher times when technology moved on.  I see no reason why this pattern will change over the next 50 years. 

[rstofer]

Many differential equations aren't solvable with classic means.  But they can be modeled in Matlab with Simulink!  Or wired up on an analog computer - my favorite.  Get on a first name basis with Matlab.

By far, Precalculus is the most important and the most difficult math subject simply because it covers a lot of territory.  The calculus courses are pretty easy, in comparison.

[westfw]

Many differential equations aren't solvable with classic means.

In general, I find  that the "qualitative" understanding of calculus I have as a result of my EE education is more valuable than the actual mechanics that most calculus classes will have you go through.  I mean, these days you can use a symbolic or numeric math package to get actual solutions, but you have to be able to understand how to set them up, and you need to know what they mean.  Even in my day, there was Macsyma (now available as Maxima, I believe...)  (OTOH, I haven't actually been doing much EE-like stuff.  I spent most of my career writing software, and never touching a floating point number!  YMMV)

[tggzzz]

Math has a longer half life than anything else you will study in electrical engineering.  Take and LEARN all you can stand.

Engineers who started their careers on vacuum tubes, but also had Laplace, Fourier, Linear Equations, Diff. Eqs., Statistics and so on were still doing fine after vacuum tubes had passed on to transistors, and transistors passed on to integrated circuits, and with a little polishing were doing fine after the digital transformation.  Specialists in each of those technologies had much rougher times when technology moved on.  I see no reason why this pattern will change over the next 50 years.

Seconded.

[tggzzz]

Many differential equations aren't solvable with classic means.

In general, I find  that the "qualitative" understanding of calculus I have as a result of my EE education is more valuable than the actual mechanics that most calculus classes will have you go through.  I mean, these days you can use a symbolic or numeric math package to get actual solutions, but you have to be able to understand how to set them up, and you need to know what they mean.  Even in my day, there was Macsyma (now available as Maxima, I believe...) 

Seconded.

[ROBOT]

OTOH, if you're lucky, your Electronics, Circuit Theory, and Communications classes (what, no physics?) will all be spoon feeding you the required math as well.  (I'm having trouble figuring out how multi-variable calculus can be a 2nd year class these days, when I needed it extensively for 1st year physics...)

I hope so. It's really hard to apply use cases with these horrible Pearson text books and Mymathlab.

For example when I would need to determine the vertex of a parabola. The textbook just says how but never says when I would need such a thing.

[IanB]

When you said you were doing precalc and trig I assumed you were in high school. But then you listed other courses that suggested you were in college.

Generally speaking mathematics is a prerequisite for engineering, so you should be aiming to learn as much analysis, calculus, linear algebra and related areas as possible. Unfortunately, proficiency doesn't come from learning formulas, it comes from practice and application, and a lot of it. If you need/want to teach yourself, look around for good texts (not necessarily the ones your college uses) and make sure to do the exercises at the end of each chapter.

[rs20]

I hope so. It's really hard to apply use cases with these horrible Pearson text books and Mymathlab.

For example when I would need to determine the vertex of a parabola. The textbook just says how but never says when I would need such a thing.

If x is time and y is height, you're finding the peak altitude of the flight of the Vomit Comet, essential to ensuring that the plane can stand up to those pressures.
If x and y are position, and the parabola is the shape of a satellite dish, then you're finding the centreline of a satellite dish. Bonus question: find the focus (as opposed the vertex) of the parabola -- that's where you need to put the transmitter, or else the dish won't do its job properly.

Slightly contrived examples, but the more general understanding -- basics like dy/dx = 0 at the maxima and minima (plus other places!) -- is pretty essential if you want to know the maximum voltage your components will experience, and how they need to be rated.

As a more general comment, if you do electronics as a hobby, you'll run into maths soon enough. Maybe if you work your way into the maths that way, you'll find it more engaging.

[tggzzz]

For example when I would need to determine the vertex of a parabola. The textbook just says how but never says when I would need such a thing.

Determining the vertex of a parabola is a tool in your armoury, just like a  Torx T15 bit is a tool in your toolbox.

Provided you know a tool exists and how to use it, you only use it when appropriate.

 You wouldn't expect a textbook to tell you when to use a T15 bit, would you.

[rstofer]

Here's a simple algebra problem than can be solved INSTANTLY with first semester calculus:

What are the dimensions of a rectangular area that can be fenced with 32 feet of fabric having the maximum possible area.
One side is x, the other is 16-x so when you add two of each side, the x's drop out and you have 32 feet of fence - what you started with.

From first semester calculus, we're going to find the vertex of the area curve and the area is x * (16-x) or 16x - x^2.  Differentiate the expression to find the point where the slope is zero (the peak) and you wind up with 2x = 16 or x = 8.  So, the maximum area is 8 x 8 or 64 square feet.  In the algebra class they solved the problem by creating a table of values and looking for the maximum.  But they didn't know, nor could they prove, that they had found the absolute maximum.  But calculus does prove it.  The vertex of a parabola is a point and it occurs exactly where the slope is 0.

So, yes, calculus is important!  For engineers, of any kind, math is everything.  Engineering is math!

[ivan747]

Laplace and Fourier transformations and, respectively s and frequency domains can simplify a TON of things, they are useful. I'd focus on using them rather than learning their formulas. Inverse transforms are a pain in the ass. Luckily we have computers in our pockets all the time.


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