ƫ΢·Ö·½³ÌºÍ·ÇÏßÐÔ±à³ÌÔÚ½ðÈÚÁìÓòÊÇÔõôӦÓõģ¿

ÏëÁ˽âÒ»ÏÂÔÚ½ð¹¤ÁìÓòÕâÁ½·½ÃæµÄ֪ʶ¶¼ÊÇÔõôӦÓõÄÄØ¡£ÃÀ±¾Êýѧϵѡ¿Î£¬ÕâÁ½ÃÅ¿ÎÏÂѧϰ2Ñ¡1£¬²»ÖªµÀÄĸö»á±È½ÏÓÐÓá£
¿Î³Ì½éÉÜ£º
ƫ΢·Ö·½³Ì£ºIntroduces partial differential equations, emphasizing the wave, diffusion and potential (Laplace) equations. Focuses on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Includes fundamental solutions and transform methods for problems on the line, as well as separation of variables using orthogonal series for problems in regions with boundary. Covers convergence of Fourier series in detail.

·ÇÏßÐÔ±à³Ì£ºIterative and analytical solutions of constrained and unconstrained problems of optimization; gradient and conjugate gradient solution methods; Newton's method, Lagrange multipliers, duality and the Kuhn-Tucker theorem; and quadratic, convex, and geometric programming.

л¹ý¸÷λ´óÉñÃÇÁË

Won't be using knowledge from either of the courses much in the industry. At least in my risk analytics group, we mostly use proprietary/internal models to analyze exposure. I graduated from Duke math, but feel that unless you aim for research, math beyond calculus can only provide you a sense of analytical logic when it comes to real projects in the industry. From the course description you posted, PDE focuses upon theories and pencil-and-paper application of tricks. NLP teaches you essentials tools in optimization problems but I bet they focus on theory more than industrial application.
In all, if you are really interested in math or financial engineering, take both. But you should expect the least that classroom knowledge can be directly applied to your non-research career. If you are really interested in Financial Mathematics, take stochastic calculus and read books by Shreve on the topic. Also, programming is an essential part of daily jobs thus I encourage you to know programming especially Python and C++. Linux is a plus too.
Hope it helps.