Learning Objectives, MAT430: Complex Analysis
At the end of this course a student will
- Understand how complex numbers provide a satisfying extension of the real numbers;
- Appreciate how throwing problems into a more general context may enlighten one about a specific context (e.g. solving real integrals by doing complex integration; Taylor series of a complex variable illuminating the relationship between real function that seem unrelated -- e.g. exponentials and trig functions);
- Learn techniques of complex analysis that make practical problems easy (e.g. graphical rotation and scaling as an example of complex multiplication);
- Continue to develop proof techniques;
- Appreciate how mathematics is used in design (e.g. conformal mapping);
- Unlearn (if ever learned) the notion that mathematics is all about getting "the right answer";
- Hone the ability to do reality checks on calculations;
- Hone the ability to communicate mathematics.
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