Assessment - Math 29142

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The summative assessment for the course consists of two parts.

• 20% Coursework Test in Week 7 (An online test administered via Blackboard covering the course material through week 6.)
• 80% Final Exam (A two-hour on-campus exam covering all of the intended learning outcomes. Details to follow.)

You will be assessed on the course's intended learning outcomes.

Intended Learning Outcomes

The formal goals of the course are codified in the intended learning outcomes listed below, which describe what you will be able to do at the end of the course.

1. Prove the Cauchy-Riemann Theorem and its converse and use them to decide whether a given function is holomorphic.
2. Use power series to define a holomorphic function and calculate its radius of convergence, and perform computations with such series. Define elementary holomorphic functions such as sin. cos. sinh. cosh. exp. log.
3. Define the complex integral and use a variety of methods (the Fundamental Theorem of Contour Integration, Cauchy’s Theorem, the Generalised Cauchy Theorem and the Cauchy Residue Theorem) to calculate the complex integral of a given function.
4. Use Taylor’s Theorem and Laurent’s Theorem to expand a holomorphic function in terms of power series on a disc and Laurent series on an annulus, respectively.
5. Identify the location and nature of a singularity of a function and, in the case of poles, calculate the order and the residue.
6. Apply techniques from complex analysis to deduce results in other areas of mathematics, including proving the Fundamental Theorem of Algebra and calculating infinite real integrals, trigonometric integrals, and the summation of series.