How Much Math is REALLY in Electrical Engineering?

so the amount of math involved in electrical engineering is quite a lot it's actually terrifying but once you understand what math is involved in each class and why it's there and how you can go about it it's actually not that bad so in this video I'm going to walk you through the math that I used in four years of electrical engineering and my bachelor's degree I'm going to walk you class by class and show you what that math actually looks like now I'm doing this mainly for my four-year bachelor degree I'll do a separate video for my masters and PhD and the math I used in my internships so stick around for that in my first year the three math intensive classes were calculus chemistry and introduction and computer science an introduction to computer science was not bad at all there's almost no math involved it was just basically learning some code and chemistry the math that was used is very simple just basic linear math to like solve for equations like PV equals nrt and you would like basically try to solve for one variable and it's just very basic algebra very simple math and calculus one however because this was calculus for engineers it was a bit more intense mainly in this class you start learning how to take derivatives and for most people it's not too bad but in my case I had the head of the mathematics Department as my professor so unfortunately we had to do a lot of math probes and a lot of extra work that we didn't really need to and this is what some of these proofs look like now in the spring however we take calculus 2 which now we start dealing with integrals and integration and we also learned about series and summations and this again not too bad and it would actually be useful later on in some of the physics classes in my case I took physics 1 mechanics which essentially just involved basic motion and forces and for example like gravitational equation so in mechanics actually the math was not too bad it was pretty straightforward we would try to solve problems like this where again you would like have some type of force action going on and you would try like isolate for one force and solve for it so again nothing too bad in my second year I took differential equations and this is very relevant because at the same time the class that I was taken is circuit analysis where you learned about how to solve electrical circuits so basically like resistors capacitors inductors and if you're just doing like voltage current resistance which is essentially like the first half of the class these equations are linear and they're pretty easy to change one variable and that other variable changes at the same rate however later on in the class when start learning about capacitors and inductors and you start learning about like charging circuits that's where the differential equations that I learned in my math class become more relevant because now the behavior is no longer linear on both ends for example if there's a capacitor in your circuit and you turn the switch and apply voltage and pass current through your circuit that change in voltage and current is not going to happen at the same rate as that charging of the capacitor there's going to be some time delay and this can be modeled with differential equations so again nothing too bad as long as you understand the concepts and you'd probably have to do a ton of problem sets just to make sure you understand the concepts really well now in that semester there's also another class digital principles which deals with binary numbers one and zeros so in this case you do a different type of math where you start breaking decimal numbers into binary so you go from base 10 to base 2 and you start doing all sorts of mathematical operations with base two numbers so you start adding two binary numbers together and that class is actually very interesting and the math use is very interesting because again it's just like basic addition subtraction things like that but now you're doing it with binary numbers which is kind of new now in the semester also there's physics 2 which is electromagnetics so you start learning about electric Fields magnetic fields and you start learning about the equations that model electric Fields model magnetic fields for example you start learning about Coulomb's law and the forces created by charges and then later on in the course you learn about for example the electromagnetic induction and the idea how like a changing magnetic field induces an electric field and exactly how much basically the energy carried out within the field so the math and electromagnetics is going to be very dependent on calculus 2 because you're going to be doing a lot of like surface integrals basically trying to sum up how much energy is within like a field at a closed boundary so again nothing too bad assuming that you did well in calc 2 and they like feels now there is also a bit of vector calculus in this class however you learn more about that in calc 3 which is in the next semester so in the second semester of your second year generally there's many math intensive classes and keep in mind this will vary on universities this is based on what the university I went to and in this semester there were four math intensive classes it was physics 3 which dealt with waves and Optics there's calculus 3 which dealt with multi-variable Calculus essentially it's taking calc 1 and making it 3D there's a class called engineering computations which teaches you like a bit of linear algebra as well as Matlab and Matlab is extremely important to learn if you're an electrical engineering and then there's also signals and systems and this class has very interesting math because you start learning about frequency domain math and it's not no longer becomes a matter of linear versus non-linear start dealing with other types of math which is imaginary and complex numbers you start learning about convolution and you start learning about the Fourier transform which looks like this and this is a class where a lot of people struggle because the math just becomes really weird because complex and imaginary numbers are not really intuitive the concept of the frequency domain is not very intuitive so things get pretty ugly in there but it's pretty interesting stuff so usually that class is a weed out if you can make it through signals and systems that means you should be okay for the rest of the degree now in those first two years the math is extremely intensive because you're essentially trying to build a good foundation and how to do basic math and when I say basic math I don't mean algebra or like addition subtraction I mean like basically being able to calculate rates of change and being able to integrate and being able to solve differential equations and being comfortable with complex and imaginary numbers and being comfortable with binary numbers that's basic math for electrical engineers so then in your third year you start taking more of the application oriented classes and you start applying a lot of this math for example in electronic circuits class which is usually like a follow-up of circuit analysis but with the introduction and that you deal with like some linear and non-linear devices you start dealing with amplifiers start dealing with diodes and other components that have behavior that is more complicated than just basic resistors capacitors inductors you also learn about transistors and their modes of operation which has some mathematics involved and this semester you also take applied electromagnetics which is basically electromagnetic physics on steroids applied to electrical engineering you start learning a lot more about wave guides and transmission lines start learning about Smith charts that's actually its own math Branch where again you're spending some time in the phaser domain and you're trying to understand how the phase of a signal relates to its amplitude now you can design circuits in such way that you can track that phase if you have no idea what this means don't worry you'll learn it in time time but in this class again you don't learn any like new math you just use what you already knew from your previous classes to get a better understanding of electromagnetics in the context of electrical engineering for example in terms of like designing antennas or waveguides and then there's probability and statistics class which is very math intensive start learning about basic probability events expectation mean standard deviation variance and all these basic concepts you'd expect in a probability class but then you'd also start applying it to electrical engineering scenarios for example modeling noise in a communication system and then finally in the spring you do take a communication systems class and let you model that noise but as well as doing some other things like modulation theorem and applying some of the concepts from signals and systems to learn how communication systems operate actually this class is quite nice because you get to learn things on a system level so you get some block diagrams that explain to you what goes on but then inside those block diagrams you could choose some math that is similar to the systems and signals math which again like frequency domain stuff time domain frequency domain multiplication because essentially like in modulation theorem all you're doing is you're just multiplying the two signals together and you're seeing and you're equipping the message signal onto the carrier signal and again if you don't know what that means don't worry you'll learn it in time but essentially the math that you're going to be using is actually a lot simpler than in the previous classes this is going to be the foundation that you learn in signals and systems there's also fundamentals of energy systems our Power Systems and I think the math in that class is pretty straightforward because you're essentially dealing with just like efficiently transferring energy from point A to point B and you're dealing with pretty large numbers so I'd actually say the math in there is pretty easy it looks something like this and then finally there's embedded systems which you're essentially dealing with microcontrollers and you're kind of dealing more with computer engineering Concepts so in that class there's not really much like calculations or derivations or anything like that it's pretty much just like learning how to program a microcontroller what is a microcontroller and what applications you could use it for so that's more like a project oriented class and then finally in your senior year besides the electives that you can take which will involve different math but you also take HDL or Hardware descriptive language or essentially digital design classes and again those are just piggybacking the concepts you learned in digital principles and being able to hard code them like through your computer so not much new math to learn there so really the hardest math you learn is in like your first and second year and a lot of it is just built on like a calculus and differential equations foundation so if you do really well in your Calculus and differential equations classes and linear algebra uh you should be good to go in terms of knowing how to do the math and all the other classes and actually the math and the later classes would make more sense and actually be more fun because you know how to do the math but you get to actually apply it to things that are interesting now if you're curious about these classes in terms of how difficult they are I did make a video ranking which ones I thought was were the easiest and which ones I thought were the hardest you can check it out over here

Channel: Ali the Dazzling

Views: 37,459

Keywords: electrical engineering math

Id: zF2BHIjmznE

Length: 8min 40sec (520 seconds)

Published: Tue Nov 22 2022