A good math course?
Hello. This question may be hard to desribe for people who do not go to my school and know the courses but i will try. I am going to include course descriptions from the coursebook below.
Anyway, i am a sophmore physics major at Carnegie Mellon University. Let me add that i am doing an applied physics track and an engineering studies minor. I have always liked engineering and may end up there but i wanted to do undergrad in physics regardless.
Anyway, as part of the physics curriculum, i take a course called Physical Analysis and later Mathematical Methods of Physics. They cover almost all of the math needed post-calculus for physics. The thing is, i need to take another math course. I could take Diff EQ but Phys Analysis covers that. I could take Matrix Algebra but Math Mathods should cover that. Most other courses require me to have a pre-req that i do not want (an intro to mathematical proofs). Does anybody have suggestions? I was thinking of partial differential equations but i am not sure.
Here are descriptions for the courses in the physics department where i will be learning math:
Physical Analysis: This course aims to develop analytical skills and mathematical
modeling skills across a broad spectrum of physical phenomena,
stressing analogies in behavior of a wide variety of systems.
Specific topics include dimensional analysis and scaling in
physical phenomena, exponential growth and decay, the harmonic
oscillator with damping and driving forces, linear approximations
of nonlinear systems, coupled oscillators, and wave motion.
Necessary mathematical techniques, including differential
equations, complex exponential functions, matrix algebra, and
elementary Fourier series, are introduced as needed.
Math Methods: This course introduces, in the context of physical systems, a
variety of mathematical tools and techniques that will be needed
for later courses in the physics curriculum. Topics will include,
linear algebra, vector calculus with physical application, Fourier
series and integrals, partial differential equations and boundary
value problems. The techniques taught here are useful in more
advanced courses such as Physical Mechanics, Electricity and
Magnetism, and Advanced Quantum Physics. transformations, four-vectors, invariants, and applications to
Anyhelp would be great
I always thought a differential geometry class would be interesting, if one is offered. Or, how about complex analysis? PDEs may be good, but I have been told by many people that graduate E&M (say, using Jackson) will teach you all the PDE techniques you need.
this all depends on wether you were taught calculus with proofs or you took a real analysis class, which is usually not a physics requirement. If you're good with proofs take a Diff geometry class. From the physics point of view i would suggest a class on complex variables. A math topic i personally find profoundly interesting is formal language theory, you won't regret it taking that one.
A course in PDEs is ultimately essential in applied physics/engineering. Complex analysis as well. These two should be covered a bit in math methods courses in the physics dept., but if you have to take another math course, these are good. I don't know about CM, but in my second year of college I took a semester of ordinary differential equations and a semester of linear algebra, the latter introducing the basis of proofs. These were requirements for a physics major in addition to the mathematical techniques taught within the physics department. Then courses in the math department beyond these require better understanding of proofs, though useful calculational techniques are still present for partial differential equations and complex analysis. Good luck.
past ordinary/partial differential equations and linear algebra all the classes that aren't applied math classes require proofs.
Hehe, even my applied math classes require proofs.
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