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Learn Vector Calculus

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My Courses: www.freemathvi... || In this video I show you a wonderful book on vector Calculus. It was written by Susan Jane Colley.
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29 авг 2024

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Комментарии : 56

@SabrinaMarquez-rw2xb 9 месяцев назад

Susan Colley’s book is amazing. I am in love with the book. She really cares about making sure you understand multivariable calculus. But I also like how she connects the subject to linear algebra. Which puts it all into context.

@waltercoady-jz2rf 9 месяцев назад

In Alberta Canada we took four calculus courses. Vector calculus was taught in the fourth. My major was in the meteorological sciences so vector calc was super important.

@TheMathSorcerer 9 месяцев назад

Oh wow very nice !!

@robcleaver4964 4 месяца назад

I have a fourth edition of this excellent book plus a companion book giving full solutions to all the exercises which is perfect for self study and I have enjoyed working through it. Highly recommended.

@TheMathSorcerer 4 месяца назад

Sounds great!

@aesmon 9 месяцев назад

Vector Calculus, Linear Algebra, and Differential Forms by Hubbard is a good one

@calebuic4310 9 месяцев назад

Indeed

@CumeBait 9 месяцев назад

Yeah, it's strange at my university because our Cal 3 course is more of the mix-and-match course, where we discuss vectors and some other concepts that are fairly similar to a few of the later linear algebra topics, but then our Cal 4 course covers multivariable calculus.

@TheMathSorcerer 9 месяцев назад

It's so good that you have a Calc 4 course, many schools don't offer that 👍

@akirahagiya2144 9 месяцев назад

Calc 4 is a weird beast, in my uni it's just a complex analysis course. It's not even needed for any other classes, most everyone struggles to get through it and it's just to check it off the list for graduating

@thomasblackwell9507 9 месяцев назад

Marsden and Tromba has a great book on Vector Calculus!

@douglasstrother6584 9 месяцев назад

I still have my 2nd Edition. Tony Tromba was my Calc 1 & 2 professor back in the day.

@niteman555 9 месяцев назад

Columbia University goes to Calc 4, focusing on just two chapters of the Stewart book: Multiple Integrals and Vector Calculus. When I took the course 10 years ago, our professor had some time left over so also started teaching some complex variables, going into topics like the nth roots of 1.

@adriantuesta1012 9 месяцев назад

Is it possible a student could pass calc 1-3 and not know what a derivative is or does but by just knowing formulas and how to solve the problems he passes the class but has no good conceptual understanding of the material? I feel like if you want to be an engineer in the later classes the test are designed in a way that if you don't really understand what the material means you likely won,t pass especially with things like calc based phyiscs 2 if you don,t really understands for example what a capacitor is or does you will not do well in the test.

@markprange2430 9 месяцев назад

Helps to draw the picture, diagram, or graph. The derivative function is taught on about Chapter 3 in Calculus. Study it with any interest at all, and understanding it will not be a problem.

@KMMOS1 9 месяцев назад

Mentioning relations among vectors, matrices, and ordered lists brings one closer to a bowl of STEM stew at an engineering department picnic or department dinner, a possible basis to mingle and socialize among students and/or faculty.

@terencemeikle534 9 месяцев назад

A lovely looking book. I hadn't known about this one. Really full treatments. 👌

@PhillipRhodes 9 месяцев назад

On a related note, do you have any familiarity with / thoughts on, "Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach" by Hubbard and Hubbard? I've heard really good things about it and have it queued up to start working on soon.

@SabrinaMarquez-rw2xb 8 месяцев назад

The biggest strength of Colley’s book is that she teaches multivariable calculus with a lot more emphasis on linear algebra. Which helps everything make perfect sense. Because for whatever reason most modern calculus books don’t do this and it makes the multivariable chapters the weakest part of of those books. I remember first learning calculus through Stewart and the multivariable chapters were so bad. It made me hate it. But Colley really made me love the subject.

@BUY_YOUTUB_VIEWS_186 9 месяцев назад

This video was so important, thank you for speaking up.

@anthonyjulianelle6695 9 месяцев назад

Instead of flipping through many pages so quickly, how about showing fewer pager but pausing on them so that the viewer can actually see what is written?

@pizza-tv9282 9 месяцев назад

On a different topic, from your experience, what are the key differences between Algebra by Serge Lang and Abstract Algebra by Dummit and Foote?

@austingubbels 9 месяцев назад

They are both graduate level but serge Lang embraces the categorical perspective while dummit and foote relegates categories to the appendix. Serge Lang is also much more terse and covers a ton more content. Both are great texts

@michaelglidewell1524 9 месяцев назад

Introduction to Vector Analysis by Davis and Snider and Div Grad Curl and All That by Schey are two good books on this topic.

@user-rw1ko1lr4u 9 месяцев назад

Thanks! Vector Analysis by Davis and Snider has answers to all the problems. Great!

@rich_in_paradise 9 месяцев назад

You can never have too much calculus 😉

@g5647 9 месяцев назад

except the dental kind

@gaborhadhazy6172 9 месяцев назад

How much time do you think it takes to go from pre-calc to vector calculus? I'm 16 years old and I'm learning math for machine learning and data science, and I have been going through pre-calculus in order for me to really understand everything in terms of machine learning and ai I would need to have a really good math foundation. I think that it can even take years to build that up, so I think I'll go with the approach where I learn mathematics while building machine learning models and such things. I love math and passionate about programming and machine learning, so I wonder what advice would you give to me in regards of mathematics. Thanks :)

@juliusfucik4011 9 месяцев назад

A typical bachelor's degree in engineering has about two years of math at this level. I detested it but managed to do it in about 2,5 years. I am sure you would do well if you keep the passion and do all the exercises. Also, be brutally honest with yourself. I remember these years and specifically one incident. I was going home on a train and was doing math. A woman opposite me did not say anything until she got up to get out at her stop. She then told me : "Whatever you do, never give up!". I never forgot these words. I always remind myself of it. I can only assume she gave up and regretted it later in life. So... go for it. Never give up. Be honest with yourself regarding your abilities and you will be fine. Ps. I am a research scientist in machine learning. You do not actually need a lot of math except for the obvious. Start learning Python asap.

@gaborhadhazy6172 9 месяцев назад

@juliusfucik4011 Thanks very much for your answer, I really appreciate it. My plan would be to do it progressively, I do have a lot of resources that I can get started for example I'm sure you know, Andrew Ng Introduction to machine learning course also I have a TON of books about the mathematics and machine learning in general. Once I've read those books I will do very simple projects, like linear regression or something easy and understand it as deeply as I can. I already have a good experience with python, my concern is about mathematics but in my opinion doing it progressively as I go through and build stuff would be the best. If I'm learning something new and I don't know the mathematics then I can stop and learn it. Also there is no end in terms of mathematics(you are always improving and there is always one more mountain to climb), so that's why I think doing it progressively would make sense, because you are learning mathematics that you can apply and you need. I have a really big advantage which is that I have time, I'm only 16 and I already have realised my passion so starting it from a young age I think is extremely beneficial. Thanks for you r advice and reply, I really appreciate it. Ps. I assume you have discord, you don't have to but I'm a big believer in networking and meeting with new people, so feel free to drop your discord. Thanks. !

@leolrg2783 9 месяцев назад

depends on how deep u want to go into deep learning. If you want to just use models and kindof understand what it does u don't even need calc3 u just need to know some basics such as differentiation and gradient and then a chapter of linear algebra

@markprange2430 9 месяцев назад

5 semesters? (Precalculus, Linear Algebra, Calc I, II, & III, Advanced Engineering Math.) Linear Algebra can overlap somewhere after College Algebra or Precalculus. After Calc II, also take Differential Equations. Some of this can be self-taught beforehand. Look in college libraries for self-teaching books. I've seen them for Precalc and Calculus. Even for Differential Equations. There are books full of just Calculus tests. "Div, Grad, Curl & All That" is for vector calculus. You may sit in on college lectures, too. --Might help to do that, in courses near your level. [Partial fraction decomposition is taught before Calculus. Get it figured out: it shows up in Calc II and in Differential Equations. Be very good with systems of equations: that shows up in Diff. Eq., too.]

@Cpt.Zenobia 9 месяцев назад

At my school there is also the topic of Integral Transforms (Laplace, Fourier, z, convolution,...) that was thrown in with calculus 3, which really felt out of place. Besides their application in automatic control & electronics, I never knew where they fit in mathematics, how, why were they developed or which subfield they belong to.

@carultch 9 месяцев назад

It's usually a part of differential equations, because integral transforms are methods of solving differential equations. Not sure about Z-transform, I think it's main use is in statistics.

@hxc7273 9 месяцев назад

In my school, calc 4 was differential equations.

9 месяцев назад

Hi, I'm currently exploring the field of mathematical optimization. Can you recommend some introductory books relating to optimization techniques? (like some convex optimization, linear non-linear programming... related resources?)

@jperez7893 9 месяцев назад

can you do a solution to a classical dynamics problem using vector calculus? imagine 2 spools of a cassette of constant tape length and thickness, if the two spools 1 & 2 are separated by a constant distance d, a point p on the tape intersecting a vertical line through d/2, if the driver spool 2 spins at a constant angular velocity of omega sub 2, find the instantaneous velocity of point p at any time t, the acceleration of point p at any time t, the angular velocity and angular acceleration of point p at any time t and length of the tape given a total running time tau

@Alexander-Abood12 9 месяцев назад

Hey. How may I contact you for some help regarding Physics and Mathematics? I’d need someone to verify my calculations to see if I’m correct or not as a preparation for high-school exams and beyond.

@yanntal954 9 месяцев назад

This class is our Calc 4 actually 😯

@StaticBlaster 9 месяцев назад

Aren't vectors and 3-dimensional space associated with Calc 3? Because from what I remember I learned a lot of vector and multivariable calculus in Calc 3.

@maxpercer7119 9 месяцев назад

Learning (advanced) vector calculus with the math sorcerer would be better ;p , or real analysis - there are already excellent youtube videos on such topics as greens theorem (which i have in my history somewhere), we should organize these useful calculus 3 and calculus 4 videos , this is the point where textbooks aren't as useful anymore and visualizations can be better (of course we need the textbook for the rigorous mathematical statement) A real analysis or complex number analysis course, of course (pun intended). Also i like how you do not seem easily offended as a math teacher. Nice video.

@byronwilliams7977 9 месяцев назад

I honestly didn't have any difficulties with calculus after calculus 1, I had way more difficulty with linear algebra and set theory. I got murderized in set theory.

@Dom89_ 9 месяцев назад

A little off topic from the video, but do you have any suggestions for books about game theory or mathematical modeling? Would love to know, thank you!

@juliusfucik4011 9 месяцев назад

I remember having to prove multiplying a vector by zero results in the zero vector, which at the time seemed obvious, but oh well.... Vector and matrix math is very important and my experience is that professors are not very proficient at explainin it.

@walter274 5 месяцев назад

I think vector calculus probably gets short changed a bit since it's near the end of calc 3. I haven't taught calc 3, but i always end up never doing the end of the course justice.

@estherbrown4084 9 месяцев назад

Since there's a compilation of computer science books on Amazon, what about any books on the Lua programming language?

@randydiffenderfer7793 9 месяцев назад

4th edition seems to be latest on Amazon

@thinkinghashim Месяц назад

Do you have vector calculus by m. Lovric?

@amerikanracer3301 9 месяцев назад

I used Stewart book… James Stewart book to learn vector calculus. He did a good job when. Teaching the vector calculus

@josefelix9077 9 месяцев назад

Hey man is there any book that you know of that is as rigorous as the spivak but for multivariable and vector calculus?

@user-qy8ib4ef1g 9 месяцев назад

Which game theory book do you recommend?

@muhammadmustafa2946 9 месяцев назад

Dear Math Sorcerer, in many of your videos you leave out the "p" in "depth" and say "deth." If your search it up in dictionaries they say the "p" in the word. Just thought I'd let you know