Calculus teaching suggestion

[Deidara]

I want to communicate to the math educators through this forum. Today most calculus books introduce differentiation and integration first and then introduce vectors later usually in a second calculus course in the college. I want to bring this fact to light that this approach is counter-intuitive. It makes no deep sense to learn calculus without vectors. Calculus is for vectors, about vectors and from vectors. Ideas of calculus can be separated from vectors but as i said earlier that is counter-intuitive. Some "early vectors" versions of calculus texts do follow this authentic approach but that should be the norm not the exception.
On behalf of all the smart students of the world i can assure the educators that we breeze through the rich, cohesive and elegant theory of vector calculus but are uneasy with the non-vector calculus when it is taught first as most of it appears contrived and inorganic.

 

[Mutakalim]

I want to communicate to the math educators through this forum. Today most calculus books introduce differentiation and integration first and then introduce vectors later usually in a second calculus course in the college. I want to bring this fact to light that this approach is counter-intuitive. It makes no deep sense to learn calculus without vectors. Calculus is for vectors, about vectors and from vectors. Ideas of calculus can be separated from vectors but as i said earlier that is counter-intuitive. Some "early vectors" versions of calculus texts do follow this authentic approach but that should be the norm not the exception.
On behalf of all the smart students of the world i can assure the educators that we breeze through the rich, cohesive and elegant theory of vector calculus but are uneasy with the non-vector calculus when it is taught first as most of it appears contrived and inorganic.

In engineering we have two courses of Calculus and a separate course for vector and tensor analysis. I think it was 3D geometry and Vector calculus.

 

[CriticalThought]

Vector calculus requires concepts of linear algebra, topology, and an appreciation of a tangent space. The student would be left utterly confused if you introduced all this without building an understanding of derivative as the tan theta of the tangent at a point, limits as mappings of open sets to open sets, and dimensionality of a vector space as the number of basis vectors. Even the way it was discovered was when Newton and I think Laplace simultaneously described it for the one dimensional case.

Btw, I am not a teacher.

 

[Providence]

Getting geometric interpretations of differentitaion and integrations requires some healthy knowledge of what comprise a continuous function and how are limits defined. These concepts require special attention and has nothing to do with vectors.

Hence a separate course logically.

However, practical applicability of calculus knowledge can be realised only with complete comprehension of concepts like divergence/del operators etc which happens in vector calculus !

 

[Hamza913]

Meh. It's not that hard so I couldn't really care. Although tbh, I don't find Maths hard at all though so I may be a little biased.

Chemistry on the other hand, oh boy, I could rant about that BS all day, especially the damn experiments. I can get everything done right except for the experiments, I always mess those up.

 

[Providence]

Meh. It's not that hard so I couldn't really care. Although tbh, I don't find Maths hard at all though so I may be a little biased.

Chemistry on the other hand, oh boy, I could rant about that BS all day, especially the damn experiments. I can get everything done right except for the experiments, I always mess those up.

I was good at Chemistry/Physics/Maths all of them

At one point, I could name all elements in periodic table, their possible valence states, most common salts, do all sorts of equilibrium questions etc

 

[Hamza913]

I was good at Chemistry/Physics/Maths all of them

At one point, I could name all elements in periodic table, their possible valence states, most common salts, do all sorts of equilibrium questions etc

I'm not suggesting I'm bad per say, rarely ever got anything less than an A. I just had to do a lot more studying for Chemistry than Physics or Maths, since Maths and Physics just come naturally to me.