Linear Algebra and MV Calculus

In summary, the conversation discussed the importance of taking linear algebra and multivariable calculus, with some people debating whether or not the order in which they are taken matters. The general consensus was that while linear algebra is helpful for understanding multivariable calculus, it is not a prerequisite. Suggestions for rigorous linear algebra textbooks were also given, including "Linear Algebra" by Hoffman and Kunze, "Introduction to Linear Algebra" by Strang, and "Linear Algebra" by Shilov. The conversation also mentioned the importance of solid proof-writing skills and the potential for the order of classes to matter in certain cases.
  • #1
Aciexz
5
0
Do you need one before the other or does the order not matter?
 
Physics news on Phys.org
  • #2
There was a discussion about this before. Some people prefer doing LA first, but it doesn't really matter in most cases. Nabeshin summed it up nicely
Nabeshin said:
Linear Algebra gives you a little more intimate knowledge of vectors, which play a key role in multivariable calc. So, while the two subjects deal with vastly different domains of mathematics, it is nonetheless beneficial to have taken linear algebra.

That said, LA is by no means a prerequisite. It helps, but not significantly enough to be a pre or even co requisite. You shouldn't worry about going into multivar having not taken calc III, as the classes are about 95% independent of each other.
 
  • #3
Thanks, and now for the real point of this post, after getting someone to confirm what I wanted to hear, I need a suggestion for a first LA book. ^_^ I'm not really into applications, lots of rigor and proofs is what I want, as long as it's plausible considering I've had nothing past Calc. II. This will be for self-study.

So basically I want the most rigorous LA I book. Thanks a bunch. :]
 
  • #4
Try Linear Algebra by Hoffman and Kunze. Very rigorous and good book on the subject.
 
  • #5
Hoffman and Kunze was written for 3rd year math majors at MIT so it definitely fits your description of rigorous but be warned.

Alternatives include Introduction to Linear Algebra by Strang and linear algebra by Shilov.
 
Last edited:
  • #6
Hoffman & Kunze looks great, but is the latest version from '71? Would that matter?

And what about Friedrich? It also seems highly praised, and has a 2002 edition.
 
  • #7
Aciexz said:
Hoffman & Kunze looks great, but is the latest version from '71? Would that matter?

And what about Friedrich? It also seems highly praised, and has a 2002 edition.

If you can handle Hoffman & Kunze then it's a good textbook regardless.
 
  • #8
This is pretty much my exact situation(also from physicsforums):

Yowhatsupt
Mar2-07, 12:36 AM
I'm planning on teaching myself linear algebra over the summer and was wondering what text to grab.

Thoughts, suggestions, recommendations etc are all appreciated.:redface: :smile:

morphism
Mar6-07, 02:13 AM
Hoffman-Kunze or Friedberg are the way to go. (I personally lean towards Friedberg because of the amount of material covered in that book, as well as the plethora of exercises.)

But I've also read that Friedberg is for a second course. If that's the case does it matter?
(like how it wouldn't matter what calculus book you get because all calc II books are calc I-II books)

What are everyone's thoughts about Friedberg?
 
  • #9
It seems like the OP has already made up his mind, but I would like to mention that sometimes the order in which the classes are taken does matter. My college has two versions of multivariable calculus, one with and one without a linear algebra prerequisite. I would have not wanted to take the more rigorous version without a strong background in linear algebra and solid proof-writing skills.

But I guess it is safe to say that the order does not matter as long as neither is a prerequisite for the other.
 
  • #10
We used "Linear Algebra and It's Applications", by David C. Lay.

Linear%20Algebra%20and%20its%20Applications.jpg


For Multivariate (Calculus III) we finished the mega-text "Calculus", by McCallum, Hughes-Hallett, and Gleason.
We also used this text for Calculus I & II (it's over 1000 pages).

I'm now reading "div grad curl and all that" to cement those topics, and the electromagnetics examples are great since I'm doing EE.

-----

And just to round it out, I'm finishing up in the Math department this semester with "Differential Equations" by Blanchard, Devaney, and Hall. It's turning out to be a pretty good text.
 
Last edited:

1. What is the difference between Linear Algebra and Multivariable Calculus?

Linear Algebra is a branch of mathematics that deals with linear equations and their representations in terms of matrices and vectors. On the other hand, Multivariable Calculus is a branch of mathematics that deals with the study of functions of several variables, including their derivatives and integrals. While both subjects involve the use of vectors and matrices, Linear Algebra focuses on the algebraic manipulation of these objects, while Multivariable Calculus deals with the geometric interpretation and analysis of functions of multiple variables.

2. What are the basic concepts in Linear Algebra?

Some of the basic concepts in Linear Algebra include vectors, matrices, determinants, eigenvalues and eigenvectors, linear transformations, and systems of linear equations. These concepts are essential in understanding the properties and operations of linear equations and their representations.

3. What is the significance of Linear Algebra in machine learning and data science?

Linear Algebra plays a crucial role in machine learning and data science by providing the mathematical framework for representing and manipulating data. Vectors and matrices are used to represent data points and perform operations such as dimensionality reduction, clustering, and classification. Additionally, Linear Algebra is also used in developing algorithms for tasks such as regression and optimization.

4. What are the applications of Multivariable Calculus?

Multivariable Calculus has various real-life applications, including physics, engineering, economics, and computer graphics. It is used to model and analyze complex systems with multiple variables, such as motion, forces, and optimization problems. In computer graphics, Multivariable Calculus is used to define and manipulate three-dimensional objects and their motion.

5. How can I improve my understanding of Linear Algebra and Multivariable Calculus?

To improve your understanding of Linear Algebra and Multivariable Calculus, it is essential to practice solving problems and working through exercises. Additionally, reading textbooks and watching online lectures can also help in gaining a deeper understanding of the concepts. Collaborating with others and discussing the material can also aid in clarifying any doubts and solidifying your understanding.

Similar threads

Replies
20
Views
2K
  • STEM Academic Advising
Replies
5
Views
633
  • STEM Academic Advising
Replies
11
Views
1K
  • STEM Academic Advising
Replies
15
Views
281
Replies
2
Views
765
  • STEM Academic Advising
2
Replies
60
Views
3K
  • STEM Academic Advising
Replies
6
Views
1K
Replies
1
Views
836
  • STEM Academic Advising
Replies
4
Views
767
  • STEM Academic Advising
Replies
9
Views
1K
Back
Top