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I am going to teach a course names "Engineering Mathematics" and the topics in it, are:

  1. Fourier series and integrals; including the motivation and computational aspects and their application, and Linear Partial Differential Equations of second order; including the Laplace, Heat, and Wave Equations (both homogeneous and nonhomogeneous cases of Equations and also different kind of boundary conditions in rectangular and cylindrical and spherical domains)
  1. Complex Variables; including Complex numbers, Cartesian and Polar coordinates, Holomorphic functions, Elementary functions, Harmonic functions, Cauchy integral formulas, Taylor and Laurent series and Residue theory and its applications, and Conformal mappings and their applications.

Advanced Engineering Mathematics, Textbook by Erwin Kreyszig is my source for this course.

The previous semester, I firstly taught the Fourier series and PDEs first and the rest of the semester I taught the complex variables.

I personally think that this order is not appropriate logically. But students don't complained any more and the students were happy.

I decided to switch the order of teaching of these two topics in the following term.

I will be thankful if any one could give advice to me.

My main question is which one is mathematically correct approach?

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    $\begingroup$ I think you are asking the wrong question. Which topic are the students going to need first in their engineering courses? $\endgroup$ – Michael Renardy Sep 12 at 2:10

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