Complex Analysis and Diff Equations

[YAHA]

Hello,

I am wondering what I should brush up on for a class in Complex analysis and Diff Equations. I am planning to take these in the fall and this will be by far the toughest math I will have had. I took a 4 credit Calc II with a solid A. Currently taking Calc III (through Green, Stokes and Divergence theorems and surface and line integrals) and Linear Algebra and feeling very comfortable.

Course description says that Complex analysis will study: The theory of functions of a single complex variable. Complex numbers, elementary complex functions, differentiation and integration of complex functions, complex series and residue theory

and Diff Equations: study of the techniques and theory of solving ordinary differential equations. Topics may include series solutions, numerical methods, Fourier and Laplace transforms, linearization, stability theory, periodic orbits, and bifurcations and chaos.

I tried contacting the prof, but haven't gotten a response.

Much appreciated.

 

[anonymity]

Complex analysis (at my school) is a graduate level course, requiring, at the very least, a full year of real analysis.

I am not sure how it is possible for you to be in this course without any proof-based mathematics experience (it is clearly done differently at your school), so i will not presume to know what you should do.

As far as differential equations go, you should brush up on your calculus I and calculus II info (calc III will be largely useless). Sequences, series, and integration techniques will be the most important things to remember. You could also breeze through the differential equations chapter/sections in your calculus textbook. It will be basic stuff, but still valuable.

 

[capandbells]

Complex analysis (at my school) is a graduate level course, requiring, at the very least, a full year of real analysis.

Many schools have an "Applied Complex Analysis" that covers analytic functions of complex variables, contour integration, residues, conformal mapping and other topics in complex analysis, with a focus on applications to physics, engineering, etc. Generally these courses require little to no proof-writing and only a background up to multivariable calculus and maybe differential equations.

edit: In response to the OP, you will be probably fine in both classes if you can are very comfortable with the calculus you've had so far.

 

[fluidistic]

Many schools have an "Applied Complex Analysis" that covers analytic functions of complex variables, contour integration, residues, conformal mapping and other topics in complex analysis, with a focus on applications to physics, engineering, etc. Generally these courses require little to no proof-writing and only a background up to multivariable calculus and maybe differential equations.

edit: In response to the OP, you will be probably fine in both classes if you can are very comfortable with the calculus you've had so far.

I agree with you. I'm a physics undergraduate student and my complex analysis course was meant for physicists, although it was FULL of proofs. I guess the mathematics major course is even more formal than the course I took.
About the comment "(calc III will be largely useless)", it wasn't my experience. In fact calculus III (still proof based in my university) helped me with the limits of functions of several variables. It helped me in complex analysis for limits of complex functions.
The OP seems to be doing fine in all his courses, I don't think he needs to "brush up" anything as he will take his courses soon enough.

 

[Chunkysalsa]

I think he meant that calc III will be largely useless for a course on Differential Equations and not Complex Analysis.

 

[fluidistic]

I think he meant that calc III will be largely useless for a course on Differential Equations and not Complex Analysis.

You're right. In this case I agree with him.

 

[anonymity]

The OP seems to be doing fine in all his courses, I don't think he needs to "brush up" anything as he will take his courses soon enough.

I agree. A quick review in the weeks preceding the start of classes hasn't ever hurt anyone, though; and chances are that over the course of an academically inactive summer things will be forgotten.

 

[creepypasta13]

Hello,

I am wondering what I should brush up on for a class in Complex analysis and Diff Equations. I am planning to take these in the fall and this will be by far the toughest math I will have had. I took a 4 credit Calc II with a solid A. Currently taking Calc III (through Green, Stokes and Divergence theorems and surface and line integrals) and Linear Algebra and feeling very comfortable.

If you were comfortable with those, then I doubt complex analysis and this DE class will be that tough. I'd worry a lot more about upper-div physics or proof-based math

 

[YAHA]

Thank you everyone for your replies. Every one has been helpful. In my school, this CA class differs from the Real Analysis (proof based) class by one digit (both 400 senior level classes). It maybe that CA is proof based - I am going to find out

As to the DE, can someone tell me if ODE class would normally lead to PDE? My concern is that Quantum Mechanics is only offered in the spring and I would like to have finished (or take concurrently, at worst) the PDE class before QM. Now, the question is whether QM is doable without PDEs under one's belt? Lastly, I will be taking a class called Math Methods for Physics (series, complex #'s, Fourier, Laplace, etc) next spring together with QM. I am just trying to get a general guidance (thus the name of the subforum ) and optimize my schedule and study program.

 

[anonymity]

You'll have to check your school's course catalog, but ODEs should be the only prerequisite for PDEs.

As far as quantum mechanics is concerned, you'll have to wait, but I do know that it is a prerequisite at my school.

edit: wait for someone else to answer, that is.

 

[creepypasta13]

Thank you everyone for your replies. Every one has been helpful. In my school, this CA class differs from the Real Analysis (proof based) class by one digit (both 400 senior level classes). It maybe that CA is proof based - I am going to find out

As to the DE, can someone tell me if ODE class would normally lead to PDE? My concern is that Quantum Mechanics is only offered in the spring and I would like to have finished (or take concurrently, at worst) the PDE class before QM. Now, the question is whether QM is doable without PDEs under one's belt? Lastly, I will be taking a class called Math Methods for Physics (series, complex #'s, Fourier, Laplace, etc) next spring together with QM. I am just trying to get a general guidance (thus the name of the subforum ) and optimize my schedule and study program.

You just need lower-div ODE for PDE. That ODE class you listed is not necessary to take prior to PDE. In fact, I wouldn't even bother to take it as it won't help for physics, unless you haven't learned Laplace and Fourier transforms before or you just are interested in the math content in that class

I doubt the CA class is proof-based. All the undergrad CA courses I've heard of are not

I think QM is doable without PDE...as long as you can self-teach yourself separation of variables. I learned that from my lower-div ODE and it was more than sufficient for upper-div E&M. I took PDE before QM, but it was a waste as I didn't learn anything useful, as I had already mastered separation of variable