Vector calculus was actually “designed” to be applied for physics as calculus was intended to so there’s definitely stuff like “position”, “speed of a curve”(this is an archaic term) etc etc well at least latently to what’s presented in the book. A book I referred to back in the day, was the one by BS Grewal: loads of work outs
I get a kick out of the fact that you love the aroma of your older math books. I do exactly the same thing! And I'm on my way to getting a copy of "Vector Calculus" by Lindeman. Thanks for pointing me in this direction!
Just love how you take in a deep whiff of each physical book …… could not agree with you more there……I do that with every book when I first open it, no matter how many times I may have read that book before….the way that a book’s smell ages is also such an intrinsic and “living” part of that book…..❤❤❤
the smell of a book, whether with or without dust, is always great. I'm currently reading a book on vector calculus to apply to fluid dynamics, Spiegel's Vector Analysis, and I'm completely in love with it.
Vector Calculus by Marsden and Vector Calculus by Colley are two more recent books I would recommend. Marsden includes "historical notes" on notable mathematicians and physicist, which helps explain the "why".
I am from north Africa and i remember a very popular book series of "Landau lifchitz" and Feynman lectures they were recommended by our professors when we were students 15 years ago .
Love this 🙌🏻 my Calculus III instructor was good, but I took his class in the summer, so he had to skip a lot of vector calculus stuff. Unfortunately, that led to some confusion/frustration in the future, when I took Physics II, and PDEs I & II
Vector calculus was my last math class at university. Never figured out what came next. Didn't see anything offered in selections. There was the coding theory and computer stuff.
The math and physics books I enjoy the most were written in the mid-50's to the mid-70's. The books were better made, the material better presented, no need for multiple color and fancy pictures. A good explanation, simple tables and diagrams were the best tools. These don't have any new material since it is about 60 years old, give or take a decade. I'm currently reading "Equilibrium Statistical Mechanics" by Andrews (1963). So far I have found the presentation excellent. Recently, I finished "Quantum Theory for Atomic Structure Vol 1." by J.C. Slater (1966). There could not be a better explanation of quantum mechanics.
I looked this book up.. It is not available on any of the shadow libraries I know of (at least, easily).. And the few actual copies that are available are pretty much priced out of reach of many of us... Given all this, what would be really subversive to the overlords who decide what knowledge is accessible, to whom, and at what price, would be to scan your copy and make it freely available on the internet.
Would love to see a review of Advanced Engineering Mathematics by E. Kreyszig - which was a staple “bread & butter” book in the first two years of common course in our 4-yr B-Tech/5-yr Engg or Science journey back in India late 80s/early 90s (IIT-Kanput anyone c. 87-93 anyone….. 😊😊😊….?) I still believe that it was an awesome math book too, even though it was “technically” for engineering juniors and sophomores, and it’s treatment of sequences, series, Fourier series etc even from a “pure math” perspective … is still awesome One of my favorite “math methods for engg. & scientists” book …..👍👍👍
Ah yes the weighting factor resulting in the set covering all points with the tx1 + (1-t)x1 formula, and you can plug in whatever vectors you desire, that will cover all the space or boundary endpoints in between if we're restricting it. Jk. But really though, that ux + (1-u)x vector formula is a big part in fields like economics, specifically microeconomic theory when building a convex set of multiple goods that are desired I guess and they deal with vectors too surprisingly.
I took vector analysis at the University of Minnesota and I am almost certain that was the textbook we used. But as you stated, it is hard to find. I've looked through my library and while I seem to have kept all my other text books, I cannot find my vector analysis textbook.
In a course in linear algebra, we learn that the gradient is an operator consisting of an ordered list of partial derivatives of a scalar function with respect to its coordinates, which are also an ordered list of components that weight the basis vectors of a space. They are not a sum of weighted so-called "unit vectors", The vector representation in linear algebra is given by the inner product of the operator and the coordinate vector. If the basis happens to be orthonormal, fine, but it doesn't have to be. How does this book treat coordinate vectors and gradients? It seems to me that prior to a class in vector or multivariable calculus, at least an introductory course in linear algebra be given.
I have yet to see a calculus book that effectively teaches the basic concepts of vectors in a way that does not scare the student. It is a mistake to mix theory with practical applications because it affects different areas of the brain, making learning more difficult for the beginning student. This seems to be the case with this book. The minimum content that a vector teaching book should have is the following: 6. Vectors 6.1. Oriented segments 6.2. Equivalent segments 6.2.1. Concept 6.2.2. Theorem 6.3. Definition of vector 6.3.1. Concept 6.3.2. Addition of vectors 6.3.3. Subtraction of vectors 6.3.4. Product of a scalar by a vector 6.3.5. Canonical form 6.3.6. Cartesian form 6.3.7. Module 6.3.8. Unit vector 6.3.9. Null vector 6.3.10. Versor of a vector 6.3.11. Relations between vectors 6.3.12. Parallel or proportional vectors 6.4. Consolidation exercises 6.5. Product scalar 6.5.1.Concept 6.5.2.Properties 6.5.3.Fixing exercises 6.6.Projection 6.6.1.Concept 6.6.2.Example 6.7.Director cosines 6.7.1.Concept 6.7.2.Example 6.8.Linear dependence 6.8.1.Linear combination 6.8.2.Linearly dependent vectors (LD) 6.8.3.Linearly independent vectors (LI) 6.8.4.Theorem 6.8.5.Important definitions 6.8.5.1.When a vector is LI or LD 6.8.5.2.When two vectors are LI or LD 6.8.5.3.When three vectors are LI or LD 6.8.6.Exercises 6.9.Vectorial product 6.9.1.Concept 6.9.2.Example 6.9.3.Observations 6.9.4.Properties 6.9.5.Calculating areas with vectors 6.9.5.1.Area of a parallelogram 6.9.5.2.Area of a triangle 6.9.6.Exercises 6.10.Mixed product 6.10.1.Concept 6.10.2.Properties 6.10.3.Geometric interpretation of the mixed product 6.10.4.Volumes of known solids 6.10.4.1.Volume of a parallelepiped 6.10.4.2.Volume of a prism with a triangular base 6.10.4.3.Volume of a tetrahedron 6.10.5.Exercises 6.11.Derivative directional 6.11.1.Concept 6.11.2.Geometric interpretation of the directional derivative 6.11.3.Examples 6.12.Gradient 6.12.1.Concept 6.12.2.Exercises
![ILLSLICK - KILLSHOT REMIX [FULL VERSION]](http://i.ytimg.com/vi/RIK8RrqIAzE/mqdefault.jpg)
Vector calculus was actually “designed” to be applied for physics as calculus was intended to so there’s definitely stuff like “position”, “speed of a curve”(this is an archaic term) etc etc well at least latently to what’s presented in the book. A book I referred to back in the day, was the one by BS Grewal: loads of work outs
I get a kick out of the fact that you love the aroma of your older math books. I do exactly the same thing! And I'm on my way to getting a copy of "Vector Calculus" by Lindeman. Thanks for pointing me in this direction!
That is so cool! 😄
Lindgren*
Just love how you take in a deep whiff of each physical book …… could not agree with you more there……I do that with every book when I first open it, no matter how many times I may have read that book before….the way that a book’s smell ages is also such an intrinsic and “living” part of that book…..❤❤❤
This book is in high demand. Prices range from $120-$240, used.
the smell of a book, whether with or without dust, is always great. I'm currently reading a book on vector calculus to apply to fluid dynamics, Spiegel's Vector Analysis, and I'm completely in love with it.
Vector Calculus by Marsden and Vector Calculus by Colley are two more recent books I would recommend. Marsden includes "historical notes" on notable mathematicians and physicist, which helps explain the "why".
I am from north Africa and i remember a very popular book series of "Landau lifchitz" and Feynman lectures they were recommended by our professors when we were students 15 years ago .
Love this 🙌🏻 my Calculus III instructor was good, but I took his class in the summer, so he had to skip a lot of vector calculus stuff. Unfortunately, that led to some confusion/frustration in the future, when I took Physics II, and PDEs I & II
Yeah that always happens! There is just so much to cover in Calculus 3.
It’s true 🤣
That looks like a fun text; however, the *thin* books can be kind of scary!
I used "Vector Calculus" (2nd edition) by Marsden & Tromba.
Hehe yes those thin books can be really tough LOL!!!
Vector calculus was my last math class at university. Never figured out what came next. Didn't see anything offered in selections. There was the coding theory and computer stuff.
you never were able to take real analysis or even matrix algebra?
The math and physics books I enjoy the most were written in the mid-50's to the mid-70's. The books were better made, the material better presented, no need for multiple color and fancy pictures. A good explanation, simple tables and diagrams were the best tools.
These don't have any new material since it is about 60 years old, give or take a decade. I'm currently reading "Equilibrium Statistical Mechanics" by Andrews (1963). So far I have found the presentation excellent. Recently, I finished "Quantum Theory for Atomic Structure Vol 1." by J.C. Slater (1966). There could not be a better explanation of quantum mechanics.
I used this when I took Vector Analysis in the late 60s.
wow that is really cool!
Very helpfull book.
I borrowed it.❤❤❤
Thanks for it ❤
You're welcome!
I looked this book up.. It is not available on any of the shadow libraries I know of (at least, easily).. And the few actual copies that are available are pretty much priced out of reach of many of us... Given all this, what would be really subversive to the overlords who decide what knowledge is accessible, to whom, and at what price, would be to scan your copy and make it freely available on the internet.
Would love to see a review of Advanced Engineering Mathematics by E. Kreyszig - which was a staple “bread & butter” book in the first two years of common course in our 4-yr B-Tech/5-yr Engg or Science journey back in India late 80s/early 90s (IIT-Kanput anyone c. 87-93 anyone….. 😊😊😊….?)
I still believe that it was an awesome math book too, even though it was “technically” for engineering juniors and sophomores, and it’s treatment of sequences, series, Fourier series etc even from a “pure math” perspective … is still awesome
One of my favorite “math methods for engg. & scientists” book …..👍👍👍
The author, Bernard "Bernie" Lindgren (1924~2012), was known for statistics and peanut brittle.
The age of vanilla extract from the trees, how great it is! Got that explanation from math sorcerer himself in a past video.
Ah yes the weighting factor resulting in the set covering all points with the tx1 + (1-t)x1 formula, and you can plug in whatever vectors you desire, that will cover all the space or boundary endpoints in between if we're restricting it. Jk. But really though, that ux + (1-u)x vector formula is a big part in fields like economics, specifically microeconomic theory when building a convex set of multiple goods that are desired I guess and they deal with vectors too surprisingly.
I took vector analysis at the University of Minnesota and I am almost certain that was the textbook we used. But as you stated, it is hard to find. I've looked through my library and while I seem to have kept all my other text books, I cannot find my vector analysis textbook.
Another interesting video, thank you.
In a course in linear algebra, we learn that the gradient is an operator consisting of an ordered list of partial derivatives of a scalar function with respect to its coordinates, which are also an ordered list of components that weight the basis vectors of a space. They are not a sum of weighted so-called "unit vectors", The vector representation in linear algebra is given by the inner product of the operator and the coordinate vector. If the basis happens to be orthonormal, fine, but it doesn't have to be. How does this book treat coordinate vectors and gradients? It seems to me that prior to a class in vector or multivariable calculus, at least an introductory course in linear algebra be given.
I have yet to see a calculus book that effectively teaches the basic concepts of vectors in a way that does not scare the student. It is a mistake to mix theory with practical applications because it affects different areas of the brain, making learning more difficult for the beginning student. This seems to be the case with this book. The minimum content that a vector teaching book should have is the following:
6. Vectors
6.1. Oriented segments
6.2. Equivalent segments
6.2.1. Concept
6.2.2. Theorem
6.3. Definition of vector
6.3.1. Concept
6.3.2. Addition of vectors
6.3.3. Subtraction of vectors
6.3.4. Product of a scalar by a vector
6.3.5. Canonical form
6.3.6. Cartesian form
6.3.7. Module
6.3.8. Unit vector
6.3.9. Null vector
6.3.10. Versor of a vector
6.3.11. Relations between vectors
6.3.12. Parallel or proportional vectors
6.4. Consolidation exercises
6.5. Product scalar
6.5.1.Concept
6.5.2.Properties
6.5.3.Fixing exercises
6.6.Projection
6.6.1.Concept
6.6.2.Example
6.7.Director cosines
6.7.1.Concept
6.7.2.Example
6.8.Linear dependence
6.8.1.Linear combination
6.8.2.Linearly dependent vectors (LD)
6.8.3.Linearly independent vectors (LI)
6.8.4.Theorem
6.8.5.Important definitions
6.8.5.1.When a vector is LI or LD
6.8.5.2.When two vectors are LI or LD
6.8.5.3.When three vectors are LI or LD
6.8.6.Exercises
6.9.Vectorial product
6.9.1.Concept
6.9.2.Example
6.9.3.Observations
6.9.4.Properties
6.9.5.Calculating areas with vectors
6.9.5.1.Area of a parallelogram
6.9.5.2.Area of a triangle
6.9.6.Exercises
6.10.Mixed product
6.10.1.Concept
6.10.2.Properties
6.10.3.Geometric interpretation of the mixed product
6.10.4.Volumes of known solids
6.10.4.1.Volume of a parallelepiped
6.10.4.2.Volume of a prism with a triangular base
6.10.4.3.Volume of a tetrahedron
6.10.5.Exercises
6.11.Derivative directional
6.11.1.Concept
6.11.2.Geometric interpretation of the directional derivative
6.11.3.Examples
6.12.Gradient
6.12.1.Concept
6.12.2.Exercises
🖐I'll check it out. Yeah It's a rare book. Interesting one indeed. Thanks brother. 🤜🤛👍
No problem 👍
just sent in a request to my library to borrow it, thank you!
That’s awesome! 👍
2:57 he couldn't resist the urge 😂😂
We must complement the calculations as part of the rule for vector spaces.
10 hours after video upload... all copies on amazon sold out... come on.
There was only 1 copy I think ? It’s a rare book
Hey are you a math teacher? (In school)?
I brought an old math book from 1907 today (:
yes math sorcerer the lost art of type setting 😞
Yikes! It’s $240!
❤❤❤❤
Iam glad Im not the only one who gets high on huffing books
I’m 0!*3!!!!!! Yeah!!!
Math sorcerer waiting for your reply, few weeks ago i had mailed you😢
I'm second! From India
i, j, k.
First 😊