Im a rising junior in the US starting my upper division physics classes. I have an opening this quarter and want to take an applied math course, but cannot decide between these two: In the mathematics department: "Applied complex anlysis Introduction to complex functions and their applications to engineering and science. Complex numbers, elementary functions; analytic functions; complex integration; power series; residue theory; conformal maps; applications." In the mechanical engr department "Introduction to Engineering Analysis Analytical methods in engineering. Nonhomogeneous linear ordinary differential equations. Variable coefficient linear ordinary differential equations. Eigenfunction expansions. Laplace transforms. Introduction to Fourier transforms. Linear partial differential equations." I havent decided on my research interest too much, but materials, spectroscopy and signal processing have caught my interest. I was thinking about taking an elemtary analysis course my senior year so I could study Fourier analysis a little more--something i know that would have relevance to both quantum and signal processing. I have no idea if i can handle the theorem-proof method of learning mathematics though. If anyone has any input on which class they would recommend, please tell me. I cannot take both classes, unfortunately. It's possible I could take once class this year and the other one next year. Also: the applied complex analysis course is a pre req for an upper div continuous signal processing class in the EE department (but not the discrete signal processing class). EDIT: these are both upper division classes. i've already taken all my lower division math classes (linear algebra, differ eq, etc).