All The Math You Need For Engineering: The Ultimate Guide (Step-by-Step)

In this video, I'm going to show you, step-by-step, all of the mathematics that you need in order to become an engineer. Now, there are different types of engineers, and some engineers require more math courses than others. For example, electrical engineers require typically more math than other types of engineers. But don't worry, we're actually including extra math in this video, so we're going to go through every single math subject that you need, and I'm going to go in order, step-by-step. A couple things before we get started. So first, let me just say that some of this stuff is hard, and if you're an engineer now, and you're taking classes, and you're an engineering student, and you're feeling discouraged, it's okay. It's hard. Once you get through this, you're going to be okay. When I was a student, most of my friends were engineers, and a lot of them struggled with math, and they ended up getting degrees, and now they have jobs, and they have happy lives. So they made it. As a teacher, teaching calculus for many years, most of my students have been engineers, and I've seen students struggle through my classes. They get through, they go on to their engineering classes, it gets harder, it gets a lot harder, but they survive, they make it, and they end up with degrees. So don't give up. If you're an engineer, don't give up. I'll try to leave links to these books in the description of this video. Some of them might be really cheap, some of them might not exist, and some of them might be more expensive. These are just books from my personal collection. I've got thousands of books, as you can see. So all right, let's just go ahead and get started. I'm going to start with the very, very basic. I've picked a book that covers mathematics that you would need if, like, you didn't know any math. Like, if you didn't even go to school, like, if you just barely knew anything at all, this is the type of math you would need to learn. So if you are terrible at math, this is where you begin, okay? And feel free to fast forward this video if, you know, you want to jump to the other subjects. But I'm going to go in order, step by step. So I picked this one because this book covers both beginning and intermediate algebra. I have several books, and this one is just a good, solid book. By the way, these are all textbooks here that I'm showing you. So textbooks are typically books that are used in college. In fact, all of these are college level, even this one. So they contain more information than, for example, a lot of the workbooks that you see on Amazon. So keep that in mind. Oh, I just got to smell this. I'm sorry. It's calling me. Oh, amazing. So you could use this book to learn beginning algebra and intermediate algebra. Things like factoring, adding rational expressions, things like that. And this book has answers to all of the odd number problems in the back of the book. So you could use this for self-study. What you want to do with all of these books, by the way, with any math subject, is you want to spend a little bit of time every day working on it. And that is honestly the best way to get good at it. My advice is spend some time in the morning. And we'll talk more about that at the end of the video. So basic algebra, you want to start here, right? Beginning and intermediate algebra by Alain Martin Gay. The next book is going to be a really, really good book. And this is a book that I've used to teach in college, a course called College Algebra for Many Years. It's the book by Blitzer. This book contains a lot of the mathematics that you're going to need for calculus. So a lot of the stuff you learn in this course is really, really important. Again, this one also has answers in the back of the book to all of the odd number exercises. So let's move a little faster and get to more advanced stuff. So after you get through algebra, you have to take two more courses in college, at least in the U.S. Those courses are pre-calculus and trigonometry. And typically, those courses use the same book. So for example, this book here can be used for two courses. It can be used for pre-calculus and for trigonometry. So that's kind of cool because you can get one book and it covers two courses. So pre-calculus covers a lot of things that are covered in algebra. Ooh, there's a hidden treasure in here. What did we find? Oh, California State University Chico, 1988. Oh, that's cool, right? Pretty cool. Blast from the past. Oh, this is so cool. I just want to spend some time on it, but let's keep going. Kind of a hidden treasure. I'm going to smell it. Oh, that's fun. That's fun. So I was saying, pre-calculus and trig in one book, which is super awesome. Yeah, so highly recommend getting this one. Then you go to calculus. So after you take all the prerequisites, basically you have to get through college algebra and take pre-calc and trig. You have to take the calculus sequence. Most engineers have to take calculus one, calculus two, and calculus three. Typically you use the same book for all three courses, and you're typically allowed to use a calculator. The recommended calculator, I'll leave a link in the description. It's the one I have. I can run and get it, but yeah, it's a good one. One of the TI-84s, color edition. And that's useful because you can use that to help you graph a lot of the problems, and it's just a helpful calculator. So I picked this book because this is one that you're probably not using right now. So like if you live in the U.S. or in Canada, you're probably using the book by Stewart or the book by Larson. Those books are typically more popular with colleges, I've noticed. Thomas book is used by some colleges, but more colleges use, I believe, the Stewart and Larson books. This basically covers everything you need for calc one, two, and three. And I highly recommend that if you are an engineer and you're buying any book here, get a calculus book. You want to have at least one of these big, thick calculus books. It doesn't have to be this one, but just make sure you get one of the big, thick ones like this one. So this covers everything. It's got derivatives. It's got integrals. And again, everything you need for calc one, two, three. This also has answers in the back of the book. So the odd number of exercises. So you can look in the back of the book to check your work. Yeah, this is a solid book. I know this is also used in India because I have a lot of subscribers from India and they have mentioned this book. Also, you should know that this book, notice the name, Thomas Calculus, right, 13th edition. So the original book was just called Calculus and was written by a man named George B. Thomas. And so the old version of the book is actually very different from the new version. I find that the new version has more practical examples and less theory. And the older version has some harder examples and more theory, but they have less easier ones. So I think they've changed it because the target audience, again, for most calculus classes, is mostly engineering students. That's been my experience in teaching calculus. You get some computer science students and some pre-med students, but it's heavily engineering students. So these books are kind of geared towards that. So highly recommend Thomas Calculus. It's pretty awesome. All right. So now that you have calculus, you can jump and take differential equations. This is also something that an engineering student would have to take. Differential equations is actually not that hard. Once you get through calculus two, everything else is pretty much comparatively easy until you get to some more advanced subjects, which we'll look at later in this video. But this is a good book for differential equations. This is actually the one I used when I was a student. I've taught differential equations as well in college, and the book I used for that was also good. But I chose this one because this is the one I used, and it's a little bit harder than the one I've used to teach. It's got good examples. The layout is kind of bland. It doesn't really have, like, nice colors or anything. But it has a lot of applications, and it has answers in the back of the book to the odd-numbered exercises. So differential equations would complete kind of like your core, right? You've got your Calc 1 or Calc 2 or Calc 3 or DE. And then typically, as an engineering major, your college is going to require that you take some statistics. So I've got two statistics books here. So let me just explain why I have two. So this one here is for, like, the basic stats course, OK? This is actually one that I used to teach stats in college many, many years ago. The first stats class I ever taught used this book, and then I switched and started using the book by Triola. In any case, this book is for a very elementary stats class. Engineers don't take that class. Instead, they take a harder stats class. Usually it's called something like Statistics for Engineers. And so they actually have books that are called Engineering Statistics. And I have some, but I chose this one. This one is a mathematical statistics book, which is just as hardcore as a Statistics for Engineers book. In fact, it might be a little more... I don't know. I don't know what the word is. Math-y? It might have more proofs than one for engineering. So it might be a little bit harder, a little more... I don't know. I just think it's a really good book. So this is the one. It's called Johnny Froon's Mathematical Statistics with Applications. So the key difference between the content in these books is that this book actually has examples where you need to know calculus, right? So this is a calculus-based book. You can buy this book and start learning right away and learn mathematical statistics. But you do need calculus for some of the sections. Whereas this book, the only prereq typically to take this in college is a basic intermediate algebra course. You don't even need college algebra. So as long as you know some basic algebra, you're able to take this course. Usually you use software. Sometimes you can do it by hand and use formulas. It depends on your teacher. When you study this, a lot of times you use software as well. But when you're doing self-study, it's always better to do it by hand, right? Because you can always do it by hand as a last resort. I once had a student in stats who did everything by hand and with a calculator. I don't know why she did that. She had a thing about it, and she scored a 100% on every test. That's a true story. So, yeah. So statistics is kind of like a side thing. This is connected to calculus because you do need calculus for it. But you could just jump into statistics anyways and just skip the calculus stuff as you learn. Another really core subject that is recommended and sometimes required of engineers is a subject called linear algebra. Now, there's all kinds of great linear algebra books. I chose this one because I'm a big fan of Serge Lang. This is Linear Algebra by Serge Lang. This is actually the first edition. I'll leave a link to a newer edition which has more content and is probably a better book and more modernized. This is a great book. It covers linear algebra and it covers it well. Smells amazing. So you do a lot of stuff with matrices and linear mappings and systems of equations, stuff like that. So very useful to take linear algebra as an engineer. So if it's not required for your major, which it probably is, I highly recommend that you take at least a computational course in linear algebra. Most colleges offer two courses, a computational course and a proof-based course. A math major would take both. An engineer would just take a computational course. This book here is really old so I think it was written before the time when they even had two separate courses. It was just linear algebra back then and I think it was all proof-based. So yeah, a solid book. I'll leave a link in the description in case you want to check it out. I've got a couple more topics here. I picked two more topics and I'll save the best for last. I'm going to hide it. So this is Complex Variables. This is the one by Brown and Churchill. This is a very famous book on complex variables. That's why I picked this one. Also, you can find copies really inexpensively. I bet if you click the link that I leave it shouldn't be too expensive for this one, at least for a used copy because this book has been reprinted so many times. This book is very standard in the content so it covers all the material that's typically covered in a Complex Variables course in college. And it's good about that. I've got to give it a whiff. I'm sorry. Oh, it smells amazing. So I actually bought this book for a course that I took but, it's a long story but I actually already used some Complex Variables when I took the course so I didn't really need the book and I had another book so that's why it actually looks so new. But I actually did use this for a course in college even though it looks like I didn't even read it. That's because I used another book. yeah, because I already knew some Complex Variables but it's very similar to the other book I used which is the one by Saf and Snyder. So most Complex Variables books are very, very similar. Basically in Complex Variables you basically do Calculus again but you do it with Complex Numbers. That's pretty much what you do. So a lot of it's a lot of it is like review so it's actually pretty simple. So it's a good elective class. So if you're like an engineer and you have Calc 1, 2, 3, D, E I highly recommend if you have to take an elective or if you want to get like a math minor you take Complex Variables because it's like an easy transition you know what I mean? You already know Calculus sure there's some baby proofs but it's a pretty easy transition. So Linear Algebra and Complex Variables would probably be my two recommendations for extra math courses if they're not requirements for your engineering degree. And last and certainly not least I almost forgot about this one I wanted to include this one in the video because this is an epic book. So this one is called Advanced Engineering Mathematics and we're going to take a look at the contents of this book because it's just epic and it's by Irwin Kreizig. I know we didn't look at the contents of the other ones but let's let's take a look at this one I'm gonna smell it here this is epic. This book is awesome the worst thing about this book is the price it's never inexpensive I've looked like you always have to pay a decent amount of money for this it's never cheap no matter what edition you get. It's one of those books that's always in demand right? Because it's such a good book so 1962-1967 so yeah this is this is the second edition and look what it says here let's briefly read the preface so you can see what it says this book is intended to introduce students of engineering and physics to those fields of mathematics which from the modern point of view seem to be the most important in connection with practical problems. Topics are chosen according to the frequency of occurrence and applications. Cool right? Let's look at the topics the topics are so exciting look at this this is a really fun book check this out so it starts with review of some topics from algebra and calculus so it's really fun it's like we'll look at that in a minute then it teaches you differential equations that's right so this is like basically you know what I teach in differential equations when I teach it in college this is like the beginning of the course and then you've got some more differential equations yep and then you've got series solutions differential equations and then Laplace transforms and you use those to solve differential equations as well there's an entire differential equations course there plus more then you've got some calc 3 stuff here so you're learning calc 3 and then you've got more calc 3 and you've got linear algebra right I mean it's just ridiculous Fourier series and integrals every time I'm just blown away PDEs right partial differential equations and then you've got some complex variables right like the Brownian Tertial book we talked about and then more complex variables more complex variables calc 2 right calc 2 so a lot of the stuff here oh let's keep going this is going to be Laurent series is complex variables this is complex variables probably complex variables complex variables probability theory probability and statistics right here we talked about that earlier as well so you see and then answers to odd number problems so something amazing just happened right we just basically we talked about all the subjects though I think we just hit every subject except algebra which algebra is an obvious prereq for all of this stuff right so but basically we've got calculus we've got differential equations we've got linear algebra we've got statistics and we've got complex variables we have all five subjects that we touched on while it's pretty cool and you know what I'm just I'm kind of just realizing this now but that's pretty epic right so fun really fun that this book actually contains the same subjects that I picked for this video I did not do that on purpose I promise that's pretty cool that's pretty cool I feel honored that Erwin Kreizig and all the calculus classes I've taught and so I know exactly I know exactly what they studied for mathematics but this book is awesome this book is awesome look at some of the problems are actually easy so you can do them find the first partial derivatives of the following functions you know what I mean some of these books are hard this book gets harder it does have some answers too in the back of the book let me show you let me go to the back here I'm going to show you one more thing too after this so yeah you do have some answers in the back that's pretty cool right oh I gotta smell it I'm sorry it's just following me so what I wanted to say is you know how do you how do you put all this together right so so let's say you buy one of these books and I'll leave links in the description and you say alright I want to start learning math so what do you do so my advice is is to get up early this is I'm just going to tell you what I would do I can talk about this for like ever but here's here's one one way to do it get up early so like let's say that you normally get up at 7 a.m. right so what you want to do is you want to get up like at 6 a.m. right and then that gives you time to you know wake up a little bit and then you want to spend maybe 30 minutes or so right doing mathematics whatever you're working on every day you do it you just think about it just think about tomorrow just do it right and then when you do it you're going to look back and you're going to be really happy that you did it and if you just keep doing it every day becomes a routine and next thing you know you you've learned some math the biggest thing in doing this is willpower right it just depends how badly you want to learn math you know like if you really really want to learn math then you'll do it if you don't care that much then you won't do it and I think that when you realize that the only way you will learn math is if you actually sit down and do math then then that's really when you have to do it or when you have a class and you have a test that really puts the pressure on but self-study should be fun but I do think if you're trying to incorporate some extra math studying into your life that's the best way and the reason I say to get up early in the morning is because by getting up early in the morning you're not taking time out from the rest of your day right so like if if instead you do it in the morning in the middle of the day you're going to have to sacrifice something else and if you're an engineering student time is super super precious right I mean engineering is hard I personally think and a lot of people disagree I think engineering is possibly the hardest major I think it might be harder than a math degree people really struggle with math proofs but like it's one thing right engineering it's like I don't know in some of those books I've seen some of those engineering books yeah yeah anyways there is I'll leave links in the description also I have math courses that cover all almost all of these things not all but several of these subjects they're on Udemy but if you get them use the links from the description of this video because I've lowered the prices to the bare minimum and so when you click the links you should get a low price plus if you use the link it also helps me a lot or you can use the links from my website it's math sorcerer dot com or freemathbids dot com and I've got courses there on college algebra I've got a stats course but you need stat crunch for it so watch out for that you can buy stat crunch so college algebra stats trig calc one calc two calc three I have a couple different calc one and calc three courses they just have different videos but similar topics and I've got advanced calculus course and an abstract algebra course and then I have some very specific courses like I have a course on proof writing like for sets and functions and some other like weird things that I need so yeah you can check those out if you want but key takeaway from this video is you can learn this stuff right these books are all really really good this one's the most fun so this is where you get your money's worth right it's got a lot this has a lot of content this has everything all the book this has everything all the other books have right as you saw which again was just a huge shock to me because you know I picked these books for the video and I thought oh what about this one so I had to go find this one and and I didn't pick it because I thought this had all these topics I picked the topics first so kind of fun that Kreising and I agree I'm in the company of a legend pretty cool anyways take care I hope it's been helpful good luck