Intro Complex Analysis, Lec 14, Preimages, Mathematica, Maximum Principle (Harmonic), Polynomials

Long division, synthetic division, rational functions and partial fractions decomposition included in the content as well.

Lecture 14. (0:00) Mathematica project ideas. (4:12) Preimages of rectangles under a mapping are regions between level curves of u and v. (14:36) Maximum principle for harmonic functions and an example over a disk, including optimization analysis along the boundary of the disk. (30:09) Polynomial roots and factorizations. (32:50) Example of a cubic with complex coefficients. Do polynomial long division and synthetic division if you are given one of the roots.

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