Classical Mechanics: Understanding Calculus & Linear Algebra Use

[Brahmajala]

So hi everyone, I'm a freshman in Physics and in a couple weeks I'm going to start my second semester, with Chemistry and two exams of Classical Mechanics (Theoretical and Practical).
In our first semester we had Calculus, Linear Algebra and C Programming. Since our Calculus program went as far as Multivariable Calculus I'd like to know how much I will use it, together with Linear Algebra.
Will it be mostly multivariable or single variable calculus the one used? And then Linear Algebra, when will I get to really use Matrix Diagonalization and Vector Duality?

 

[Student100]

So hi everyone, I'm a freshman in Physics and in a couple weeks I'm going to start my second semester, with Chemistry and two exams of Classical Mechanics (Theoretical and Practical).
In our first semester we had Calculus, Linear Algebra and C Programming. Since our Calculus program went as far as Multivariable Calculus I'd like to know how much I will use it, together with Linear Algebra.
Will it be mostly multivariable or single variable calculus the one used? And then Linear Algebra, when will I get to really use Matrix Diagonalization and Vector Duality?

What do you mean, "how much I will use it?" What class?

 

[Brahmajala01]

I mean, how much I will use those topics in Classical Mechanics

 

[Vanadium 50]

I mean, how much I will use those topics in Classical Mechanics

Six.

Seriously, how do you expect us to tell this from only the name of the class. And even if we knew, how do we answer it. If one person says "a lot", how do you know that's the same as another person's "a lot"? Or your own "a lot"?

You need to talk to your academic advisor and the professor teaching the class.

PS "Gonna" isn't a word. It's not even slang. It's baby talk.

 

[Brahmajala01]

Six.

Seriously, how do you expect us to tell this from only the name of the class. And even if we knew, how do we answer it. If one person says "a lot", how do you know that's the same as another person's "a lot"? Or your own "a lot"?

You need to talk to your academic advisor and the professor teaching the class.

PS "Gonna" isn't a word. It's not even slang. It's baby talk.

I'm sorry, I didn't know that since I'm not native in English and I'm prone to such errors, I'm baby talking.
Then multivariable calculus is quite clear as a concept I think, as linear algebra is.

 

[Vanadium 50]

You still need to talk to your academic advisor and the professor teaching the class.

 

[Incand]

Like others have said It depends on the course.
However a typical first course in CM doesn't require that much math except single variable calculus (differentiation, integrations, simple ode) and knowing the dot and cross product but you need to know this well. You may see some multiple variable calculus as well with vector valued functions and double/triple integrals for things like center of mass. Matrices may show up (things like inertia for example) but probably not much more. The difficulty in CM is imo usually not the math.

But again I'm only describing what is typical since we know nothing about the course, perhaps you know the course literature that will be used?

 

[johnnyTransform]

Firstly, the rigor and scope of the class is up to your particular professor, so this question is hard to answer.

However, the best general advice I could give would be to not worry too much about the mathematics of a first course in CM. Like the above poster said, you'll probably just run into some relatively basic differentiation and integration, and perhaps some introductory ordinary differential equations (which you may not even be expected to solve, but rather just set up). Linear algebra, multivariable calc, and more advanced topics in ODEs probably won't be utilized too greatly. So, in terms of mathematics, single-variable calc is probably what you should be primarily concerned with.

However, again, this is a much better question for the professor of your class. Good luck!

 

[mpresic]

Your question, "When will I need to use matrix diagonalization or vector duality?" I will give you a direct answer. Possibly your first exposure to diagonalization will be when you try to solve a question regarding the general motion of two coupled simple harmonic oscillators (Jr. undergraduate level physics psbl sophomore level engineering or honors sophomore physics). Or you may need to find the general motion of a body around an axis that is not one of the principle axes of the body. You may need to find the principle axes of fhe body, and proceed accordingly JR-Sr level physics, to graduate physics. You may need to change bases in Jr or graduate level quantum mechanics and use Clebsch Gordon Coefficients. All told, matrix diagonalization is one of the most used tools I ever learned in physics.
Vector Duality, comes up in quantum mechanics. The bra and ket spaces are dual spaces. This is important for learning and applying the postulates of QM.

It is tempting to think you will never have to use the "abstract" math you learn as a freshman. However, college freshman are still very early in their academic career. You should assume unless otherwise warned that the math you learned will be important in many if not most areas as you progress.