Recommended books for linear algebra and multi-variable calculus

[SP1999]

hey everyone just started university and the jump i feel is huge from a level and was just wondering if you guys knew of any books that had linear algebra and/or several variable calculus in them but displayed and explained stuff in a clear simple way? or if anyone has any websites that do the same thing?

 

[Buffu]

For maths or physics ?

 

[Demystifier]

Or engineering?

 

[SP1999]

sorry i guess its for maths

 

[ibkev]

There are some really nice "How to Self Study" guides that make lots of suggestions on how to approach learning these topics and what to read. They were put together by micromass (I wonder what happened to him?)

https://www.physicsforums.com/insights/?s=How+to+Self-study

Also, my own personal recommendation for linear algebra is Linear Algebra Step by Step. I find his approach fits with my style of learning pretty well (lots of fully worked out examples and FAQ style question/answer sections through out.)
https://www.amazon.com/dp/0199654441/?tag=pfamazon01-20

 

[SP1999]

thank you i will check them out

 

[Buffu]

There are lots and lots of good Linear algebra books.

Linear Algebra : Done right,
Linear Algebra : Done wrong (Free; Have better problems than other books)
Introduction to linear algebra by Strang,
Introduction to linear algebra by Lang,
Linear algebra and its applications by Strang,
Linear algebra and its applications by David C Lay,
Linear algebra by Lang,

And there is a problem book on Linear algebra by Halmos.

For multivariable calculus you can try 2nd volume of Apostol's calculus and/or J. Hubbard and B. Hubbard.

 

[SP1999]

There are lots and lots of good Linear algebra books.

Linear Algebra : Done right,
Linear Algebra : Done wrong (Free; Have better problems than other books)
Introduction to linear algebra by Strang,
Introduction to linear algebra by Lang,
Linear algebra and its applications by Strang,
Linear algebra and its applications by David C Lay,
Linear algebra by Lang,

And there is a problem book on Linear algebra by Halmos.

For multivariable calculus you can try 2nd volume of Apostol's calculus and/or J. Hubbard and B. Hubbard.

Thank you very much i'll definitely give these a look

 

[mathwonk]

These notes may be too condensed to be of use to you but they are free. The first 3 pages of text give a complete summary of the whole elementary theory of linear transformations and their canonical forms, such as Jordan and rational canonical form, plus the basic spectral theorems. Those 3 pages are necessarily quite dense since they summarize the content of books of some 300-400 pages, but you might benefit from reading them several times. In particular they make the observation, not always made clear in books, that diagonalizing matrices, although handy theoretically, is usually not feasible in practice, even in cases where it is theoretically possible. In particular the step of factorizing the characteristic polynomial, in the process of attempted diagonalization, is not actually feasible for most matrices. The moral is that for many applied purposes, methods of approximation should be learned as well. Those methods are not treated here however in this more theoretical essay. However, it is made clear exactly which calculations are feasible "by hand", and which ones are not. E.g. it is quite feasible to compute both the characteristic and minimal polynomials for any matrix, as well as the invariant factors and the rational canonical form, although not the Jordan [or diagonal] form in general.

http://alpha.math.uga.edu/%7Eroy/laprimexp.pdf

as far as recommendations go, I second most of Buffu's suggestions, especially Sergei Treil's LA Done wrong.

 

[SP1999]

These notes may be too condensed to be of use to you but they are free. The first 3 pages of text give a complete summary of the whole elementary theory of linear transformations and their canonical forms, such as Jordan and rational canonical form, plus the basic spectral theorems. Those 3 pages are necessarily quite dense since they sumamrize the content of books of some 300-400 pages, but you might benefit from reading them several times. In particular they make the observation, not always made clear in books, that diagonalizing matrices, although handy theoretically, is usually not feasible in practice, even in cases where it is theoretically possible. In particular the step of factorizing the characteristic polynomial, in the process of attempted diagonalization, is not actually feasible for most matrices. The moral is that for many applied purposes, methods of approximation should be learned as well. Those methods are not treated here however in this more theoretical essay. However, it is made clear exactly which calculations are feasible "by hand", and which ones are not. E.g. it is quite feasible to compute both the characteristic and minimal polynomials for any matrix, as well as the invariant factors and the rational canonical form, although not the Jordan [or diagonal] form in general.

http://alpha.math.uga.edu/%7Eroy/laprimexp.pdf

as far as recommendations go, I second most of Buffu's suggestions, especially Sergei Treil's LA Done wrong.

Thank you, i'll give this a read