# Extra math classes for a math minor

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## Main Question or Discussion Point

I am a double major in EE and physics. I have taken all of the courses required of me (calc 1-3, DiffEQ, advanced engineering math, prob/stats) and I am considering taking 3 more math classes for a mth minor.

I am looking at taking linear alg (of course), advanced calculus, and PDE.

Below are the course descriptions:
Line and surface integrals, Green's theorem, Stokes' theorem, Divergence Theorem. Topics from differential and integral calculus theory. Power series solution of differential equations. Bessel functions, Leg endre's equation. Lecture 3 hrs.

MCS 3863 - Linear Algebra
Systems of linear equations, matrices, determinants, eigenvalues, eigenvectors, Finite-dimensional vector spaces, linear transformations and their matrices, Gram-Schmidt orthogonalization, inner product spaces. Lecture 3 hrs.

MCS 3733 - Partial Diff Equations
Orthogonality, orthonormal bases, Fourier series, Fourier integral. Solution techniques for first and second order equations. Solutions of homogeneous and non-homogeneous boundary value problems. Sturm-Liouville theory. Lecture 3 hrs.

Are these the typical topics covered in these types of courses at most universities? Would these be beneficial to a physicist/engineer? Do these extra math courses appeal to grad schools?

Thanks.

Really -- All of these would be useful in different ways.
I'm partial to partial differential equations myself.

But -- grad admissions usually won't be appealed to just by extra coursework/minors. Sometimes a double major might mildly impress, but usually what admissions committees will want to see is that you've done research. There's lots of recent threads on the forum about that.

leright said:
I am a double major in EE and physics. I have taken all of the courses required of me (calc 1-3, DiffEQ, advanced engineering math, prob/stats) and I am considering taking 3 more math classes for a mth minor.

I am looking at taking linear alg (of course), advanced calculus, and PDE.

Below are the course descriptions:
Line and surface integrals, Green's theorem, Stokes' theorem, Divergence Theorem. Topics from differential and integral calculus theory. Power series solution of differential equations. Bessel functions, Leg endre's equation. Lecture 3 hrs.

MCS 3863 - Linear Algebra
Systems of linear equations, matrices, determinants, eigenvalues, eigenvectors, Finite-dimensional vector spaces, linear transformations and their matrices, Gram-Schmidt orthogonalization, inner product spaces. Lecture 3 hrs.

MCS 3733 - Partial Diff Equations
Orthogonality, orthonormal bases, Fourier series, Fourier integral. Solution techniques for first and second order equations. Solutions of homogeneous and non-homogeneous boundary value problems. Sturm-Liouville theory. Lecture 3 hrs.

Are these the typical topics covered in these types of courses at most universities? Would these be beneficial to a physicist/engineer? Do these extra math courses appeal to grad schools?

Thanks.
At your University, PDE and linear algebra is not required for physics major?

morphism
Homework Helper
I also fail to see how those three courses aren't already required by both your EE and physics programs.

Yeah, I am required to take 2 algebra semesters and 3 differential equations semesters. Where are they handing out these physics degrees?!

In my school, business major requies Linear Algebra already. Linear Algebra is basis of everything.

quasar987
Homework Helper
Gold Member
I am temped to say "take linear algebra" because it really is the basic of the basic. On the other hand, if you've gone through what 2 years in your double major, you've probably learned most of linear algebra by osmosis! So my ultimate recommandation is to pick up a linalg book at fill in the gaps of your knowledge.

I wouldn't bother with advanced Calculus as they don't prove things in this type of course and if you've gone through E&M 1, you've learned by osmosis what they're gonna "teach" you. Power series solutions to ODE is a triviality; suppose you have an ODE, you say "ok let's try a series solution. You set y=$\sum a_nx^n$, insert that into your ODE and see if the ODE "transforms" into a recurence relation for a_n. If it does then u just arrange to find the explicit expression for a_n and that is your series solution! Bessel, Legendre, Tchebichev, Hankel, Hermite and Laguerre functions are only names for the series solutions you get by solving the particular ODEs bearing the respective names. Thank me, you've just learned all you'd have learned in that class.

We're left with Partial Diff Equations then it seems. This is the real stuff anyway. Hopefully for you, you will see the real theory of Fourier series and transform (with Fejer's kernel and all). Familiarity with the concepts of orthogon/normality in function spaces are useful for QM. A Sturm-Liouville differerential equation is a second order ODE in which appears an unspecified constant $\lambda$ such that the ODE can be rewrited in operator form as $\mathcal{L}(f)=-\lambda f$. So it is an eigenvalue problem. I.e. solving the ODE means finding the values of f and $\lambda$ that satifie the S-L equation. The Sturm-Liouville operator $\mathcal{L}$ involves differentials operators and 3 functions r(x),p(x), s(x) such that when specified in certain ways, the resulting S-L equation takes the names Bessel, Legendre, Chebichev, Hankel, Hermite and Laguerre and their solutions are the corresponding polynomials you'd have covered in "Advanced Calc". The material in this course relies heavily on Linear Algebra, so make sure you know your stuff before diving in.

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I also have a hard time believing that linear algebra isn't a requirement. If you don't understand linear algebra, you can never really grok most of physics, or EE.

And a lack of linear algebra might hurt you in PDE's or vector calc. (I cannot believe also how vector calc isn't a requirement! Nearly all of electromagnetism is based on those theorems - how can you deal with Maxwell's equations without them?)

I would say, though, that with a strong background in linear algebra and multivariable calculus, the vector calculus should be a cakewalk.

linear alg IS required for physics, but not for EE. My mistake. (they are trying to get linear alg. to be a requirement in EE though....but all of the linear alg necessary in EE is covered in the EE courses)

And no physics degree program that I have seen REQUIRES PDE and real analysis.

I need 2 additional math courses.

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jbusc said:
I also have a hard time believing that linear algebra isn't a requirement. If you don't understand linear algebra, you can never really grok most of physics, or EE.

And a lack of linear algebra might hurt you in PDE's or vector calc. (I cannot believe also how vector calc isn't a requirement! Nearly all of electromagnetism is based on those theorems - how can you deal with Maxwell's equations without them?)

I would say, though, that with a strong background in linear algebra and multivariable calculus, the vector calculus should be a cakewalk.
I am required to take CALC 3, which is VECTOR CALCULUS. Calc 3 covers nearly all of the things covered in adv. calc, but with less rigor.

quasar987
Homework Helper
Gold Member
I'm having trouble seeing what this advanced calc class will look like. Surely it is not absolutely rigourous (spivak's calculus on manifold level) otherwise there'd be analysis prerequistes to the course.

So what is "more rigourous than calc 3" but not "completely rigourous"? quasar987 said:
I'm having trouble seeing what this advanced calc class will look like. Surely it is not absolutely rigourous (spivak's calculus on manifold level) otherwise there'd be analysis prerequistes to the course.

So what is "more rigourous than calc 3" but not "completely rigourous"? don't know...I was hoping someone here might know.

I looked up the course description and that's what was shown.

But I wondered the same thing myself, since most of that stuff was covered in calc 3.

leright said:
And no physics degree program that I have seen REQUIRES PDE and real analysis.
Most physics programs in canada i have seen requires PDE and Complex Analysis. Real Analysis is required if you're doing mathematical physics.

my physics degree requires a mathematical physics course which is about 1/3 PDE's and power series solution of ODE's, and one course fully dedicated to ODE's. These are both 4-unit semester-long courses.

jbusc said:
my physics degree requires a mathematical physics course which is about 1/3 PDE's and power series solution of ODE's, and one course fully dedicated to ODE's. These are both 4-unit semester-long courses.
I had a full ODE course (3 credits) and an advanced engineering math course (3 credits), which was basically complex analysis. No PDE.

Maybe I will take that PDE course then.

My physics degree requires 1 full ODE course, 1 full PDE course, 1 full numerical techniques course and 1 full applied differential equations course.

Isnt physics just bunch of ODE & PDE to model nature? In the book of Methods of Mathematical Physics by Courant and Hilbert, it is nothing but bunch of DE floating around.

vsage
Hello. I am an EE major as well and have just completed a minor in math. I found Advanced Calculus to be a little off-kilter with what engineers do. The course I took was almost entirely boring theory and painstakingly stressed basic things. Not worth the time for an engineer, in my opinion. I suggest taking complex analysis as well as a numerical methods class if you're interested in electrical engineering.

It's always good to know the theory that is so sorely lacking in your engineering classes, I suppose. My numerical methods class recently derived the concept of a fourier series from a matrix, which I thought was interesting, and was something my engineering classes (I've had about four classes on the DSP-signals path now) would never have time to teach.

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