@ I said relatively advanced mathematics. And it’s true. ODE is pretty advanced compared to other majors. Is it as advanced as everything a math major takes? No. But it’s RELATIVELY advanced compared to most majors, as I said
There's a grimly amusing cartoon plotting mathematical difficulty versus grade level. PDEs and all that good stuff in college. First job = spreadsheets. ;)
I have been a engineer for 20+ and i can honestly say. The most important thing is the understanding of what needs to be learned to solve a problem. 99% of all the math i do at work is Basic algebra and basic Trig for 99% of what i have done. I had to do advanced FFT for a project, but i just used a library file and it does it for me, that is a example of the understanding of what to do.
@@appleitree YES! I also opened up my Physics book over the years and look at some of my college notes and think, "I KNEW THIS" LOL!!! Understanding on what to do is the most important thing. The hands down best engineer i have ever worked with is a self taught engineer without any college degree, he would wipe the floor with ANY ENGINEER He is also the best programmer too! He just gets it and that is something you cannot teach!!!
The newer edition of the Kreyszig Book has a lot more material, including a whole new section on numerical analysis, there's even 2 solution manuals which cover each problem in detail. It's honestly amazing how much work went into creating it.
The Kreyszig book is phenomenal. I have the newest edition and several other “Advanced Engineering Mathematics” books. Kreyszig is head and shoulders above the rest.
I am a Structural Engineer. You do need to understand the math that you take in school, because you need to know what is going on, and you have to be understand the answers the black boxes(software) are spitting out to be able to use them, but day to day I only ever add, subtract, multiply and divide. Once in a while I take a square root and once in a while I might do a little algebra or trigonometry, but that’s it.
HI. future civil engineering student here. Will I be expected to hand check the answers or complex equations softwares solve for me? Or is it more like a "learn enough so much so that you can tell which answers can make some sense and which are way off the estimate" kinda thing?
@idkwhy77 the engineering checker in the company is someone who is at the senior level. Yes, that's the job of checker to ensure the accuracy and correctness of calculations - normally presented as whole report. Just check the inputs used are right and the methods of calculations used. If there is software used, engineers do the "software validation" exercise to check the accuracy of the software output. But this is done only once for every new analysis software purchase by your company. This means you will do your set of hand calculations and then compare your answers (from manual calculations) with the output of the software. Just simple engineering formulae and the common mathematical operations (+, -, ÷) are useful. If your job is in research industry, probably you will then use the complex maths.
When i read these comments it's clear the good youve done for the world. It inspires me to encourage the young electrical engineers i work with to become the best version of themself. Thanks for being a great example.
From the opening: I guess I don't have to be embarrassed to say I had to repeat Calc II, and this is my 40th year as an engineer. The series at Cal Poly Pomona was taught from Howard Anton, Calculus and Analytic Geometry. In that pre-Internet era I found the REA Problem Solver series, i.e. the Calculus volume gave me the solution examples that got me to a 'B on the second taking of the series.
@@vcv6560 I like the idea of being able to repeat a course to finally get it. For Calc II, was it just that a certain amount of work is needed to get it for some people? A constant comment from my teachers is that I’m slow to learn, but once I get it I understand it well.
I have been a mechanical engineer for 4 years now, designing ,calculating for certified lifting equipment to EN ISO and DNV standards. And never used or needed any math of any advanced level. All basis statics and dynamics are defined by formulars in for example EURO code 3, and anywhere you you need to redo the formulas is done with normal Algebra. More advanced math also come in ready to imput formulas like in DNV-0378 or EN 13001. Infact you are required to use the exact formulars in your reports to achieve certification.
One aspect I truly appreciate about your channel is the comprehensive road map you provide, which is incredibly helpful, especially for self-learners. Additionally, your insights and book introductions add significant value to the content and enhance the learning experience.
cool video, laughed everytime you smelled the books! I'm a senior now about to graduate soon but have been watching you since freshman year. It's true, no matter how hard it is you can get through it.
Computer engineering at University of California system -alegra -geometry -trig -precalc -calc 1 -calc 2 -calc 3 -linear algebra -differential equations -probability & statistics I started college after military service so my first college math course was basic algebra & had to work my way up.
I received my BSEE in 1975. I took an Advanced Calculus course in addition as my interest was in Electromagnetics (vectors come into play in E&M). I received the MSEE a year later and took the complex variable course. The linear algebra that I had as an undergrad was pretty weak. I used every bit of the mathematics that I learned from day one on the job. I went on and completed the PhD in 1986. I wish that I would have taken a few more math courses as an undergrad.
I studied civil engineering at a British university in the late ‘70s. Calculus was introduced at Year 9 at school, and ordinary differential equations and complex numbers were taught at Year 13, so they were not taught at University. The maths taught at University included vector calculus and complex analysis, statistics and numerical analysis. The civil engineering subjects themselves did not have much maths. From memory, geotechnical engineering made some use of differential equations (in theory of consolidation). After graduation (in the pre-personal computer era), all calculations were done by hand using calculators and charts, involving only simple arithmetic. In a 40-plus year engineering career, I never had to use any of the maths that I learnt at school or university.
Even it doesn't seem like I have to use that much of math in my electronics subject. They just like to make us as unhealthy as possible. I hate derivations because they have to be "memorised. "
I studied and graduated with a degree in electrical engineering... Yes the math was difficult and i want to go back and study and get a better foundation. I graduated 3 years ago and dont use my degree for my day job but hey still passed my FE. Thanks for the video!
I don't comment on your channel much; I think only once or twice, now that I think about it. I'm studying computer engineering. With constant practice and viewing the resources on your channel and website, I've gained more confidence and I'm getting better. I used to think I was bad at math, but it turns out I just need a lot of practice and consistency. So thank you ☺️
I brought Erwin Kreyszig’s Advanced Engineering Mathematics 7th Edition in a book store in Philadelphia called The Book Trader for $9. They told that they had it there for years and was amazed that someone finally brought it! It’s a decent book for practice but you really have to be somewhat already versed in the previous maths you’ve mentioned to get through it. Also I’m glad to know that I’m not the only person who does the smell test. They (the books) do really smell amazing! Love the channel.
Love your channel. I've been an engineer for almost 40 years and I am STILL learning mathematics in order to create new designs. Always something new and interesting to learn with math! Engineers really are applied mathematicians at heart.
Tysm man, I'm still in high school but just getting ahead of the curve in terms of engineering math knowledge will certainly help, your videos are always helpful.
As an electrical engineering system in the Cal State system here’s our math curriculum: • Calc I • Calc II • Calc III • Differential Equations • Linear Algebra • Probability, Statistics, and Stochastic Modeling
No Numerical Methods & Operations Research, Trigonometry & Coordinate Geometry ? Calc 2 & 3, Maths modeling & Operations research I found difficult back then. Bad lecturers and couldn’t find a good textbook that simplifies it. These days UA-cam makes learning much easier compared to 2010 or 2013
@@lonelycubicle EE is probably the closest major to physics, almost all the lower level classes are the same in most curricula. Later, EE focuses on electromagnetism when physics focuses on other topics like special relativity. Interestingly, the majors can overlap again if either chooses optics.
Definitely covers the college level mathematics courses. This doesn’t mention the physics courses that are also required! I agree with him you eat an elephant one bite at a time though don’t be discouraged. Every course is just the next step past the previous one….stay the course
As an EE, I’d also recommend a course in Laplace and Fourier analysis. Fourier is used everywhere, and Laplace will save your butt when it comes to solving differential equations.
Absolutely agree with the part of getting up in the morning and putting in some time. I would book a tutor online to help me go over the concepts for the days lecture in the morning so I could have a foundation as we went through lecture. Makes a huge difference.
Wow, I really appreciate you introducing the book "Advanced Engineering Mathematics". It looks so handy, as a quick reference for all the math you would need in solving engineering problems. Why am I never aware of it before?!😅
From my experience in an engineering major some engineers like myself find the math easy and the physics hard in the beginning, others find math hard and the physics easy. I had a friend was good in physics and had difficulty in calc, and since I was the other way around we always tutored each other on the things the other struggled in. Worked out very well for us. Also, in our calc courses we used no calculator, but did so in physics and engineering courses. I also took a couple of discrete math courses in my curriculum bc I doubled major in comp sci.
My degree's in chemical engineering. The only math required beyond the usual 3 semesters of calculus, was O.D.E.s. However, I also took an elective, "Numerical Analysis for Scientists & Engineers," which was really great. For instance, you find out where "Simpson's Rule" came from (derivative of a Taylor Series), and plenty of ways an engineer can "cheat," and get results, without lengthy, tedious operations (which you've probably forgotten, anyway) like "Newton's Method, "Lagrange Polynomials," "Cubic Splines," etc. Also, two recommendations: "The Calculus Tutoring Book," by Robert & Carol Ash. It has lots of examples that are very well explained. And "Technical Calculus with Analytic Geometry," by Judith Gersting It feature plenty of exam[;es taken from physics and engineering.
Which in our case, as chemical engineers, makes it hard for us to really grasp process control and dynamics. Because the feedback control systems requires some complex variables analysis. I can solve the usual problems but is really challenged when interpreting complex graphs. In my experience, I've self studied Circuit Analysis to really understand frequency analysis and BODE plots and has separately studied the book by Brown and Churchill's Complex Variables and Applications. Our advanced engineering mathematics course only tackled complex variables in a very mechanical/computational approach.
@@sarutobihokage7488 I took a class, "Control Systems Engineering," which just involved D.E.s, and especially, poles & zeros on the "S" Plane. Despite the fact that they were complex numbers, there was no serious complex analysis involved. I have an electronics background and know things like Fourier Analysis, but that wasn't involved in the Control Systems class I took.
All of those books are great but if students want just one book that contains everything from the video they have to buy Mathematical methods for physics and engineering. It’s a book by Cambridge university press and it has like everything you need for your undergrad. Things like - differential and integral calculus, multiple integrals and partial derivatives , differential equations, vector and tensor calculus, calculus of variations , integral equations, complex numbers and variables, numerical methods , group theory, representation theory, quantum operators , statistics and probability- like everything you will need for physics or engineering.
There is also one by John Bird, "Understanding Engineering Mathematics", it covers every subject you need for most engineering degrees, coming from law school transitioning to engineering, it helped a lot.
@@alex-t3i9v wow that seems like a really really good book. Does it go kinda far on those topics or is it just a watered/introductory version? Saying it just because seems like 10 books in 1, but if it's good I'll give it a chance.
I read that book it was pretty hard to read ngl. It took a while and once I switched to learning the topics from a book dedicated to that one topic I could understand it much better. I don't really recommend it
@@SuperGlogang it’s over 1500 pages and dives deep into the topics. It’s everything you will need for your physics or engineering degree. It’s recommended in every UK university
I was a physics major and these are the Mai classes you need for a BS in physics as well. The main difference is that I took 2 mathematical physics courses.
University Physics with Modern Physics - Bauer, Westfall. A very good book. An average student would get A’s if they use this. It also has Chemical Thermodynamics in there which all engineering students take
I had those as an EE undergrad at Cal and also took “discrete mathematics”. As I continued on in my career I went back and studied abstract algebra to help understand cryptography and tensor calculus but most/all undergrads won’t need those.
Awesome suggestions! Starting with algebra makes a lot of sense since it's foundational. You could also begin by reading an introductory book on Set Theory. Set Theory is ubiquitous in applied mathematics, like Probability Theory and Statistics, and it teaches the basic language of mathematics. Patrick Suppes has a few excellent books on Logic and Set Theory. I recommend his book that's titled Axiomatic Set Theory.
In the late 1960s (undergrad) and early 1970s (grad school) I used Kreyszig for the engineering math classes I took in the Math Department and Wylie for a couple of classes I took in the Engineering departments. I also used Hamming for numerical analysis.
I currently work under the title of an engineer but i want to go back to school to actually get a degree. Im pretty scared about math again since i havent used it since high school but watching your videos i feel like i can make it through it. Thanks going to watch more videos.
The Cal State Chico assignment at 4:27 was mimeographed. It’s like photocopying. I remember that from elementary and middle school in the early/mid-80s. Nice find! Also at 5:00 I used Salas’s Calculus; solid book.
These were the engineering math I took from freshman till graduation. Freshman: 1st Semester - Algebra, Trigonometry. 2nd Semester - Analytic Geometry, Algebra 2, Solid mensuration (just measuring common shapes) Sophomore: 1st Semester - Differential Calculus, Statistics. 2nd semester: Integral Calculus Junior: 1st semester: Differential equations. 2nd semester: Advanced Mathematics. Senior: None - Every single math we learned were applied in our major robotics classes. I didn't get to learn the advanced math classes that the Math majors took that's why I'm here.
So far the classes I need to take for civil engineering as far as math are Intermediate Algebra, College Algebra, Trigonometry, Calculus 1 through 3 with analytical geometry. Also, I have to take chemistry and physics classes to include the core engineering classes.
really great advice . I was thinking what to do next exactly and it really helped a lot let me write down few things now but yeah you really helped a lot ❤
Comp Sci Software Engineer here. Stewart Calculus book is a must have. Even 25 years later i keep a copy at home and in storage. Also a fan of Serge Langs books. New editions are all yellow...
Probably my favorite book to work in is the first one you presented. I hated the Pearson software adaptation of this text book, but I did complete the class after I bit the bullet and ordered it.
Agreed on Kreyszig ……one of the jewels among textbooks in the math. Methods for Physics space….what the hell its even good as a text book in a math course………… as an overview textbook !!!!
3 courses i recommend that will be a big help when working as an engineer are applied physics, appled algebra, and appled trigonometry. These courses use problems that you might actually be having to deal with as an engineer! Consulting engineers with their own business should take a course in engineering economics and a course in small business accounting.
Talk about the math you need for AI. I have a BS in Math and MS in EE , but I forgotten most math. I'd like to hear your comments on reviewing the math for AI. thanks
Amazing list. Great video as always! I have a small suggestion. Althought it is not mathematics like "real Mathematics ", but engineers also need to learn Numerical methods. So it would be great if you would discuss a few good books on the topic. Thanks once again 😊
As a CompSci major (years and years ago), I studied with my engineering friends. They got me through the 8 credit hours of Calc 1 and 2 that I needed. No way I wanted any more of it!
You know someone is a math expert when they smell the book. My university professor made the math book we used for the entire year and he used to smell his own copy every day 😂
Hey there! 😊 I thought I'd share some of my absolute favorites as well: 1. **Calculus - A Complete Course** by Adams 2. **Differential Equations & Linear Algebra** by Edwards & Penny 3. **Linear Algebra** by Friedberg, Insel & Spence (this one's great for more advanced, proof-based courses!) 4. **Introduction to Probability** by Bertsekas & Tsitsiklis 5. **Introduction to Probability** by Blitzstein & Hwang 6. **Complex variables & its application ** by Churchill and Brown And I can't forget to mention: **Advanced Engineering Mathematics** by Kreyszig - it's a classic! I hope you find these recommendations helpful! Sorry if any names are off or if I missed any - happy reading! 📚✨
As a practicing practical electrical engineer, I frequently use basic algebra, trigonometry, and the most useful of all, statistics. I rarely need to use calculus.
I found taking Partial Differential Equations useful even though you'll see PDEs in engineering and physics. I found numerical analysis/methods to be useful too. You'll encounter integral equations depending on what you do in engineering, but that's not a commonly offered course. In graduate school, one of my mentors recommended to me Porter and Stirling's Integral Equations.
I'm more consumer math. Studied some Algebra. Was fairly more difficult than the trigonometry. For some reason, it made more sense to me... I keep trying to get back to the math, but I am more consistent with guitar.
My linear algebra course was taught from the Advanced Engineering Mathmatics book. I still have the 8th edition on my shelf. That was certainly a long time ago...
pls math sorcerer do a video on math that's used by quats. How far do they go on calc, algebra, ODE, PDE, stochastic proccesses, real analysis, measure theory, etc. And background to understand all that. Ty so much
As far as I remember they heavily rely on statistics, real analysis, AI, linear algebra, vector calculus and some more specialized domains. I don’t think they’re using much OEDs or PDEs, etc.
lol same here! My (one) son is in Engineering at University. I believe you will find out very quickly if that is his path. I found that he had a strong desire to take as much math as possible and try to ace it with perfect scores……. Don’t let teachers discourage your son, they often don’t recognize the talent or are jealous.
I love the idea of studying early in the morning but I can't seem to get over the fact that I have to wake up at three thirty A.M. to go to work and don't have time for a cup of coffee. Maybe there is some optimum time during the evening when I am struggling to stay awake that is better.
Kindly make for fundamental engineering courses like Engineering Mechanics, Materials & it’s Strength, Fluid Mechanics etc. From personal experience, some American textbooks/authors are usually the best out there. The Indian books I tried to use made everything complex. Good books definitely help if the lecturers are bad 😅 I usually dozed off in class when cantilever beams & deflection were badly taught. That Mechanics - Khurmi text book for example is crap
My main objection: Complex analysis is NOT just like calculus on the real line. Having a derivative in the complex plane has many profound and unexpected consequences.
Love this! 2nd year mechanical engineering student here! I love the idea of continuous self study. Do you recommend marking up textbooks I own? It kind of hurts me to do so but let me know your thoughts, anyone for that matter. Big fan!!
I'm a physics person who has worked with many engineers both at the research/grad level and at various companies. Engineers do some basic math on paper and anything complicated its all software... Matlab, comsol, Ansys, or just plain old excel. Sadly a lot of it is 'what do I have to click on...' instead of understanding the math
I was discouraged from becoming an engineer when I was told that most engineering majors end up NOT working in the engineering field. Apparently large companies will higher pretty much every graduating student in the engineering department and then dismissing most of them after a year or two, only retaining the top 3% or so. The rest find that no one will hire then for an engineering job after that. This is why I'm looking for a curriculum in applied Math instead. Do you know of any that are good and lead to a job?
I do apologize, but I cannot seem to find the link/name of the calculator model you mentioned in the video! I'm trying to look for a good model to use for school
Engineering degrees always require some relatively advanced math, but once you actually get a job it’s literally just spreadsheets
Engineering? Advanced mathematics, Really?
@ I said relatively advanced mathematics. And it’s true. ODE is pretty advanced compared to other majors. Is it as advanced as everything a math major takes? No. But it’s RELATIVELY advanced compared to most majors, as I said
@@Katzeblow
If not engineers, besides academics, what careers require advanced mathematics?
Advanced engineering mathematics literally goes into analysis. More mathematics an engineer know the better and this same rule applies to physics.
There's a grimly amusing cartoon plotting mathematical difficulty versus grade level. PDEs and all that good stuff in college. First job = spreadsheets. ;)
I have been a engineer for 20+ and i can honestly say. The most important thing is the understanding of what needs to be learned to solve a problem. 99% of all the math i do at work is Basic algebra and basic Trig for 99% of what i have done. I had to do advanced FFT for a project, but i just used a library file and it does it for me, that is a example of the understanding of what to do.
Oh are you an electronics engineer? I have FFT, assuming fast Fourier transform so.
@@appleitree YES! I also opened up my Physics book over the years and look at some of my college notes and think, "I KNEW THIS" LOL!!! Understanding on what to do is the most important thing. The hands down best engineer i have ever worked with is a self taught engineer without any college degree, he would wipe the floor with ANY ENGINEER He is also the best programmer too! He just gets it and that is something you cannot teach!!!
To do FFT we just press a button on the machine 😂
@@johnjay6370 If your work can be done better by a self taught “Engineer” then I’m afraid what you do is not Engineering.
@ I'll bet we've all seen a Wunderkind or two. I've found they've always loved the subject and didn't wait until college to start learning.
Currently working towards an engineering degree, and your videos helped me learn the brilliance of mathematics, great video!
🔥🔥🔥
m.ua-cam.com/users/djganit
The newer edition of the Kreyszig Book has a lot more material, including a whole new section on numerical analysis, there's even 2 solution manuals which cover each problem in detail. It's honestly amazing how much work went into creating it.
The Kreyszig book is phenomenal. I have the newest edition and several other “Advanced Engineering Mathematics” books. Kreyszig is head and shoulders above the rest.
m.ua-cam.com/users/djganit
I am a Structural Engineer. You do need to understand the math that you take in school, because you need to know what is going on, and you have to be understand the answers the black boxes(software) are spitting out to be able to use them, but day to day I only ever add, subtract, multiply and divide. Once in a while I take a square root and once in a while I might do a little algebra or trigonometry, but that’s it.
HI. future civil engineering student here.
Will I be expected to hand check the answers or complex equations softwares solve for me? Or is it more like a "learn enough so much so that you can tell which answers can make some sense and which are way off the estimate" kinda thing?
@idkwhy77 the engineering checker in the company is someone who is at the senior level. Yes, that's the job of checker to ensure the accuracy and correctness of calculations - normally presented as whole report. Just check the inputs used are right and the methods of calculations used.
If there is software used, engineers do the "software validation" exercise to check the accuracy of the software output. But this is done only once for every new analysis software purchase by your company. This means you will do your set of hand calculations and then compare your answers (from manual calculations) with the output of the software. Just simple engineering formulae and the common mathematical operations (+, -, ÷) are useful.
If your job is in research industry, probably you will then use the complex maths.
When i read these comments it's clear the good youve done for the world. It inspires me to encourage the young electrical engineers i work with to become the best version of themself. Thanks for being a great example.
From the opening: I guess I don't have to be embarrassed to say I had to repeat Calc II, and this is my 40th year as an engineer. The series at Cal Poly Pomona was taught from Howard Anton, Calculus and Analytic Geometry.
In that pre-Internet era I found the REA Problem Solver series, i.e. the Calculus volume gave me the solution examples that got me to a 'B on the second taking of the series.
I've had to revisit some "old friends" and make new ones as well, due to my current work assignments.
@@vcv6560
I like the idea of being able to repeat a course to finally get it. For Calc II, was it just that a certain amount of work is needed to get it for some people? A constant comment from my teachers is that I’m slow to learn, but once I get it I understand it well.
@lonelycubicle a lot of material is covered in 10 weeks. I needed more time to work through the various integration methods
We used Anton, too, at Syracuse University forty years ago. Absolutely loved that book and highly recommend it.
@@KurtColville I used the 2nd edition, and a few years ago went to Thriftbooks to get a 1st edition, to have it on the shelf 😆
I have been a mechanical engineer for 4 years now, designing ,calculating for certified lifting equipment to EN ISO and DNV standards. And never used or needed any math of any advanced level. All basis statics and dynamics are defined by formulars in for example EURO code 3, and anywhere you you need to redo the formulas is done with normal Algebra. More advanced math also come in ready to imput formulas like in DNV-0378 or EN 13001. Infact you are required to use the exact formulars in your reports to achieve certification.
That's very true. Practicing engineers can't even deviate the formulae stated in the code/standards. It's all simple maths.
One aspect I truly appreciate about your channel is the comprehensive road map you provide, which is incredibly helpful, especially for self-learners. Additionally, your insights and book introductions add significant value to the content and enhance the learning experience.
cool video, laughed everytime you smelled the books! I'm a senior now about to graduate soon but have been watching you since freshman year. It's true, no matter how hard it is you can get through it.
I am an engineer for a while, and guess what? I'm still looking for the math or psychic books. Never stop learning!!
Computer engineering at University of California system
-alegra
-geometry
-trig
-precalc
-calc 1
-calc 2
-calc 3
-linear algebra
-differential equations
-probability & statistics
I started college after military service so my first college math course was basic algebra & had to work my way up.
I received my BSEE in 1975. I took an Advanced Calculus course in addition as my interest was in Electromagnetics (vectors come into play in E&M). I received the MSEE a year later and took the complex variable course. The linear algebra that I had as an undergrad was pretty weak. I used every bit of the mathematics that I learned from day one on the job. I went on and completed the PhD in 1986. I wish that I would have taken a few more math courses as an undergrad.
I studied civil engineering at a British university in the late ‘70s.
Calculus was introduced at Year 9 at school, and ordinary differential equations and complex numbers were taught at Year 13, so they were not taught at University.
The maths taught at University included vector calculus and complex analysis, statistics and numerical analysis.
The civil engineering subjects themselves did not have much maths. From memory, geotechnical engineering made some use of differential equations (in theory of consolidation).
After graduation (in the pre-personal computer era), all calculations were done by hand using calculators and charts, involving only simple arithmetic.
In a 40-plus year engineering career, I never had to use any of the maths that I learnt at school or university.
Even it doesn't seem like I have to use that much of math in my electronics subject. They just like to make us as unhealthy as possible. I hate derivations because they have to be "memorised. "
You're not alone (who never used complex maths in real engineering jobs).
I studied and graduated with a degree in electrical engineering... Yes the math was difficult and i want to go back and study and get a better foundation. I graduated 3 years ago and dont use my degree for my day job but hey still passed my FE. Thanks for the video!
I don't comment on your channel much; I think only once or twice, now that I think about it. I'm studying computer engineering. With constant practice and viewing the resources on your channel and website, I've gained more confidence and I'm getting better. I used to think I was bad at math, but it turns out I just need a lot of practice and consistency. So thank you ☺️
I am SO GLAD to hear this! Keep it up!!
m.ua-cam.com/users/djganit
I brought Erwin Kreyszig’s Advanced Engineering Mathematics 7th Edition in a book store in Philadelphia called The Book Trader for $9. They told that they had it there for years and was amazed that someone finally brought it! It’s a decent book for practice but you really have to be somewhat already versed in the previous maths you’ve mentioned to get through it. Also I’m glad to know that I’m not the only person who does the smell test. They (the books) do really smell amazing! Love the channel.
Love your channel. I've been an engineer for almost 40 years and I am STILL learning mathematics in order to create new designs. Always something new and interesting to learn with math! Engineers really are applied mathematicians at heart.
I have several of those books in my library; completely invaluable books to have at-the-ready.
I love that you have these books! 🔥
Tysm man, I'm still in high school but just getting ahead of the curve in terms of engineering math knowledge will certainly help, your videos are always helpful.
Keep at it dawg 💪
Same senior future engineer here😂
Friends and me are thinking about becomming an engineer.
This comes at just the right time!
Thank you
Thanks I'm a mechanical engineer PhD and after I finish Im starting math over from algebra to grad probability for fun
practice makes perfect.
Literally doing same the thing as structural engineer PhD :D
m.ua-cam.com/users/djganit
For engineering mathematics
As an electrical engineering system in the Cal State system here’s our math curriculum:
• Calc I
• Calc II
• Calc III
• Differential Equations
• Linear Algebra
• Probability, Statistics, and Stochastic Modeling
Very nice!!
Useful Maths are simplified (aka dumbed down) versions of transforms and polynomials which are taught in engineering classes instead of math courses.
No Numerical Methods & Operations Research, Trigonometry & Coordinate Geometry ? Calc 2 & 3, Maths modeling & Operations research I found difficult back then. Bad lecturers and couldn’t find a good textbook that simplifies it. These days UA-cam makes learning much easier compared to 2010 or 2013
@@JT15C
Thanks for posting. Would any of those courses be different if one wanted to be a physics major instead of engineering?
@@lonelycubicle EE is probably the closest major to physics, almost all the lower level classes are the same in most curricula. Later, EE focuses on electromagnetism when physics focuses on other topics like special relativity. Interestingly, the majors can overlap again if either chooses optics.
Definitely covers the college level mathematics courses. This doesn’t mention the physics courses that are also required! I agree with him you eat an elephant one bite at a time though don’t be discouraged. Every course is just the next step past the previous one….stay the course
This is the video I was waiting for!
Thomas' Calculus is always a must, I have no doubt of it, such a great deal.
As an EE, I’d also recommend a course in Laplace and Fourier analysis. Fourier is used everywhere, and Laplace will save your butt when it comes to solving differential equations.
I would include Numerical Methods as well.
Chemical engineer here !!! The math was the easy part, chemical engineering was hard. All that thermodynamics and kinetics 😂
Absolutely agree with the part of getting up in the morning and putting in some time. I would book a tutor online to help me go over the concepts for the days lecture in the morning so I could have a foundation as we went through lecture. Makes a huge difference.
Waking up at 7 am... How cute. I've had my second cup of coffee by 7am
Wow, I really appreciate you introducing the book "Advanced Engineering Mathematics". It looks so handy, as a quick reference for all the math you would need in solving engineering problems. Why am I never aware of it before?!😅
From my experience in an engineering major some engineers like myself find the math easy and the physics hard in the beginning, others find math hard and the physics easy. I had a friend was good in physics and had difficulty in calc, and since I was the other way around we always tutored each other on the things the other struggled in. Worked out very well for us. Also, in our calc courses we used no calculator, but did so in physics and engineering courses. I also took a couple of discrete math courses in my curriculum bc I doubled major in comp sci.
Nice! What was your second major/ which ENGR degree?
I found the math easy and some physics easy. I struggled with mechanics but was fine with Electromagnetism and thermodynamics.
Don't forget the fundamental theorem of Engineering: sin(x) = x. And its corollary: cos(x) = 1.
ROFL
ROFL WTX😮 DOES THAT MEAN WIZ?
e = pi = 3
π² = g, and ≈ = =
It only applies for a very small x. But yeah i get what you mean
And here he comes as a saviour!!!
My degree's in chemical engineering. The only math required beyond the usual 3 semesters of calculus, was O.D.E.s. However, I also took an elective, "Numerical Analysis for Scientists & Engineers," which was really great. For instance, you find out where "Simpson's Rule" came from (derivative of a Taylor Series), and plenty of ways an engineer can "cheat," and get results, without lengthy, tedious operations (which you've probably forgotten, anyway) like "Newton's Method, "Lagrange Polynomials," "Cubic Splines," etc.
Also, two recommendations: "The Calculus Tutoring Book," by Robert & Carol Ash. It has lots of examples that are very well explained. And "Technical Calculus with Analytic Geometry," by Judith Gersting It feature plenty of exam[;es taken from physics and engineering.
Which in our case, as chemical engineers, makes it hard for us to really grasp process control and dynamics. Because the feedback control systems requires some complex variables analysis. I can solve the usual problems but is really challenged when interpreting complex graphs. In my experience, I've self studied Circuit Analysis to really understand frequency analysis and BODE plots and has separately studied the book by Brown and Churchill's Complex Variables and Applications. Our advanced engineering mathematics course only tackled complex variables in a very mechanical/computational approach.
@@sarutobihokage7488 I took a class, "Control Systems Engineering," which just involved D.E.s, and especially, poles & zeros on the "S" Plane. Despite the fact that they were complex numbers, there was no serious complex analysis involved. I have an electronics background and know things like Fourier Analysis, but that wasn't involved in the Control Systems class I took.
We have numerical analysis, interpolation and approximation in the course itself
All of those books are great but if students want just one book that contains everything from the video they have to buy Mathematical methods for physics and engineering. It’s a book by Cambridge university press and it has like everything you need for your undergrad. Things like - differential and integral calculus, multiple integrals and partial derivatives , differential equations, vector and tensor calculus, calculus of variations , integral equations, complex numbers and variables, numerical methods , group theory, representation theory, quantum operators , statistics and probability- like everything you will need for physics or engineering.
Oh and btw the book covers also - linear algebra and Fourier series.
There is also one by John Bird, "Understanding Engineering Mathematics", it covers every subject you need for most engineering degrees, coming from law school transitioning to engineering, it helped a lot.
@@alex-t3i9v wow that seems like a really really good book. Does it go kinda far on those topics or is it just a watered/introductory version? Saying it just because seems like 10 books in 1, but if it's good I'll give it a chance.
I read that book it was pretty hard to read ngl. It took a while and once I switched to learning the topics from a book dedicated to that one topic I could understand it much better. I don't really recommend it
@@SuperGlogang it’s over 1500 pages and dives deep into the topics. It’s everything you will need for your physics or engineering degree. It’s recommended in every UK university
I'm like you, love to smell my books from 40 yrs ago, (Engineering, Physics and Math)! I'm now helping my son who is also an Engineering Major.
It really warms my heart to hear that. It sounds like such a beautiful experience, and I'm so glad you shared that
Please make one for physics too! Thank you so much🙏
I was a physics major and these are the Mai classes you need for a BS in physics as well. The main difference is that I took 2 mathematical physics courses.
@ Oh thank you for sharing that!
University Physics with Modern Physics - Bauer, Westfall. A very good book. An average student would get A’s if they use this. It also has Chemical Thermodynamics in there which all engineering students take
I had those as an EE undergrad at Cal and also took “discrete mathematics”. As I continued on in my career I went back and studied abstract algebra to help understand cryptography and tensor calculus but most/all undergrads won’t need those.
Awesome suggestions! Starting with algebra makes a lot of sense since it's foundational.
You could also begin by reading an introductory book on Set Theory. Set Theory is ubiquitous in applied mathematics, like Probability Theory and Statistics, and it teaches the basic language of mathematics.
Patrick Suppes has a few excellent books on Logic and Set Theory. I recommend his book that's titled Axiomatic Set Theory.
😂 when you're so good in math that you can smell out equations ❤.
In the late 1960s (undergrad) and early 1970s (grad school) I used Kreyszig for the engineering math classes I took in the Math Department and Wylie for a couple of classes I took in the Engineering departments. I also used Hamming for numerical analysis.
Nice!!!
This video is a Christmas present!
I currently work under the title of an engineer but i want to go back to school to actually get a degree. Im pretty scared about math again since i havent used it since high school but watching your videos i feel like i can make it through it. Thanks going to watch more videos.
The Cal State Chico assignment at 4:27 was mimeographed. It’s like photocopying. I remember that from elementary and middle school in the early/mid-80s. Nice find! Also at 5:00 I used Salas’s Calculus; solid book.
Very cool information, thank you for sharing this!!!!
I know I love finding old things in books:)
As a cs student we have quite a bit of maths too
Cal 1,2,3
Differential equations or cal 3
Discrete
Linear algebra
Probability and statistics
These were the engineering math I took from freshman till graduation.
Freshman: 1st Semester - Algebra, Trigonometry. 2nd Semester - Analytic Geometry, Algebra 2, Solid mensuration (just measuring common shapes)
Sophomore: 1st Semester - Differential Calculus, Statistics. 2nd semester: Integral Calculus
Junior: 1st semester: Differential equations. 2nd semester: Advanced Mathematics.
Senior: None - Every single math we learned were applied in our major robotics classes.
I didn't get to learn the advanced math classes that the Math majors took that's why I'm here.
So far the classes I need to take for civil engineering as far as math are Intermediate Algebra, College Algebra, Trigonometry, Calculus 1 through 3 with analytical geometry. Also, I have to take chemistry and physics classes to include the core engineering classes.
really great advice . I was thinking what to do next exactly and it really helped a lot let me write down few things now but yeah you really helped a lot ❤
Comp Sci Software Engineer here. Stewart Calculus book is a must have. Even 25 years later i keep a copy at home and in storage.
Also a fan of Serge Langs books. New editions are all yellow...
Probably my favorite book to work in is the first one you presented. I hated the Pearson software adaptation of this text book, but I did complete the class after I bit the bullet and ordered it.
great tutorial!!!! Thanks
Agreed on Kreyszig ……one of the jewels among textbooks in the math. Methods for Physics space….what the hell its even good as a text book in a math course………… as an overview textbook !!!!
3 courses i recommend that will be a big help when working as an engineer are applied physics, appled algebra, and appled trigonometry. These courses use problems that you might actually be having to deal with as an engineer!
Consulting engineers with their own business should take a course in engineering economics and a course in small business accounting.
Talk about the math you need for AI. I have a BS in Math and MS in EE , but I forgotten most math. I'd like to hear your comments on reviewing the math for AI. thanks
Amazing list. Great video as always! I have a small suggestion. Althought it is not mathematics like "real Mathematics ", but engineers also need to learn Numerical methods. So it would be great if you would discuss a few good books on the topic. Thanks once again 😊
I recommend Thomas's Calculus it's quite good for beginners like from start to finish
Surprised no vector analysis books were talked about which was a big part of my studies.
As a CompSci major (years and years ago), I studied with my engineering friends. They got me through the 8 credit hours of Calc 1 and 2 that I needed. No way I wanted any more of it!
You know someone is a math expert when they smell the book. My university professor made the math book we used for the entire year and he used to smell his own copy every day 😂
Hey there! 😊
I thought I'd share some of my absolute favorites as well:
1. **Calculus - A Complete Course** by Adams
2. **Differential Equations & Linear Algebra** by Edwards & Penny
3. **Linear Algebra** by Friedberg, Insel & Spence (this one's great for more advanced, proof-based courses!)
4. **Introduction to Probability** by Bertsekas & Tsitsiklis
5. **Introduction to Probability** by Blitzstein & Hwang
6. **Complex variables & its application ** by Churchill and Brown
And I can't forget to mention:
**Advanced Engineering Mathematics** by Kreyszig - it's a classic!
I hope you find these recommendations helpful! Sorry if any names are off or if I missed any - happy reading! 📚✨
As a practicing practical electrical engineer, I frequently use basic algebra, trigonometry, and the most useful of all, statistics. I rarely need to use calculus.
I found taking Partial Differential Equations useful even though you'll see PDEs in engineering and physics. I found numerical analysis/methods to be useful too. You'll encounter integral equations depending on what you do in engineering, but that's not a commonly offered course. In graduate school, one of my mentors recommended to me Porter and Stirling's Integral Equations.
I'm more consumer math. Studied some Algebra. Was fairly more difficult than the trigonometry. For some reason, it made more sense to me... I keep trying to get back to the math, but I am more consistent with guitar.
My linear algebra course was taught from the Advanced Engineering Mathmatics book. I still have the 8th edition on my shelf. That was certainly a long time ago...
Came for the seeing what maths to focus on, stayed for him getting high off sniffing math books
pls math sorcerer do a video on math that's used by quats. How far do they go on calc, algebra, ODE, PDE, stochastic proccesses, real analysis, measure theory, etc. And background to understand all that.
Ty so much
As far as I remember they heavily rely on statistics, real analysis, AI, linear algebra, vector calculus and some more specialized domains. I don’t think they’re using much OEDs or PDEs, etc.
Surprised not to see a Ken Stroud publication there.
Thank you for this! I am just a Dad hoping my son might become an engineer.
lol same here! My (one) son is in Engineering at University. I believe you will find out very quickly if that is his path. I found that he had a strong desire to take as much math as possible and try to ace it with perfect scores……. Don’t let teachers discourage your son, they often don’t recognize the talent or are jealous.
Python & SQL programmers should make a video like this please. In order of difficulty 😅
I love the idea of studying early in the morning but I can't seem to get over the fact that I have to wake up at three thirty A.M. to go to work and don't have time for a cup of coffee. Maybe there is some optimum time during the evening when I am struggling to stay awake that is better.
Kindly make for fundamental engineering courses like Engineering Mechanics, Materials & it’s Strength, Fluid Mechanics etc. From personal experience, some American textbooks/authors are usually the best out there. The Indian books I tried to use made everything complex. Good books definitely help if the lecturers are bad 😅 I usually dozed off in class when cantilever beams & deflection were badly taught. That Mechanics - Khurmi text book for example is crap
Please prof, one video "math for biology/biotechnology step-by-step" and "math for chemistry step-by-step"
Not a fan of the smelling breaks, but great and useful content. Thank you very much!
My main objection: Complex analysis is NOT just like calculus on the real line. Having a derivative in the complex plane has many profound and unexpected consequences.
12:10 I honestly never thought there would be a trend throughout the video 😂 relatable though
I learned engineering . I had to take PDE, numerical analysis, Fourier
Sehr gut, take the chance
Can you do a video like this for someone who wants to become an actuary in the USA?
The computer and A.I. just about eliminates the heavy math. What is need is to know how to ask the question properly so,A.I. can give the answer.
No numerical analysis, vibration analysis? Also reading statics and dynamic problems
Hey! Can you please do a video of reviewing the book of Mathematics for Economists? Or explain what PhD level econ consists of?
Or even econometrics!
Could make a similar resource for Machine learning & big data?
At around the 9:50 mark in your video you say it's always good to do things "by hand" what do you mean by that?
do you have a step by step math learning guide for programmers?
Yes
Sir please do one for physists
Physists usually are bad spellors did you no that?
Would love a video for physicists
🔥🔥🔥🔥🔥🔥
me too
Love this! 2nd year mechanical engineering student here! I love the idea of continuous self study. Do you recommend marking up textbooks I own? It kind of hurts me to do so but let me know your thoughts, anyone for that matter. Big fan!!
Can you do math for Computer science or any tech related? I'm willing to give it a try!
Lots of books with lots of authors.
TOP One for: ODE and BVP is Boyce and Diprima
GREAT CHOICE!!
I used that book when I took differential equations in the 1970s. It is still close to hand on my bookshelf.
I'm a physics person who has worked with many engineers both at the research/grad level and at various companies. Engineers do some basic math on paper and anything complicated its all software... Matlab, comsol, Ansys, or just plain old excel. Sadly a lot of it is 'what do I have to click on...' instead of understanding the math
Yes, because no one will pay u for solving it by hand.
Can you do the same video for physics instead of engineering please?
Also add "Numerical Analysis/Methods for Engineers by Chapra" and "Probability and Random Variables for Engineers by Garcia "
I was discouraged from becoming an engineer when I was told that most engineering majors end up NOT working in the engineering field. Apparently large companies will higher pretty much every graduating student in the engineering department and then dismissing most of them after a year or two, only retaining the top 3% or so. The rest find that no one will hire then for an engineering job after that. This is why I'm looking for a curriculum in applied Math instead. Do you know of any that are good and lead to a job?
the reason so many have degrees and don't get a job within engineering is just because they need someone who can solve problems, usually engineers
You need to signals and systems to be an EE.
Dirac delta function
I do apologize, but I cannot seem to find the link/name of the calculator model you mentioned in the video! I'm trying to look for a good model to use for school
Partial derivative
Can we lump Land Surveying in with engineers?
Whats the difference between pre algebra, intro/basic algebra, intermediate and advanced?