Course Information

You can find details of what is covered in the course on the course syllabus page.

All timetable information for the unit can be found on https://my.manchester.ac.uk.

Succeeding in the Course Unit

What do I need to do to succeed in this course unit?

Learning outcomes are statements that describe significant and essential learning that you will have achieved, and can reliably demonstrate, at the end of a course unit. In other words, learning outcomes identify what you will know and be able to do by the end of a course or program. The learning outcomes of the course unit are:

• prove the Cauchy-Riemann Theorem and its converse and use them to decide whether a given function is holomorphic;
• use power series to define a holomorphic function and calculate its radius of convergence;
• 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;
• define and perform computations with elementary holomorphic functions such as sin, cos, sinh, cosh, exp, log, and functions defined by power series;
• 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;
• identify the location and nature of a singularity of a function and, in the case of poles, calculate the order and the residue;
• 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.

During this course unit you need to acquire the knowledge and develop the skills to demonstrate that you can achieve these outcomes.

How do I acquire the knowledge and develop the skills to succeed in this course unit?

Lectures and tutorials will provide guidance on what you need to study. Course materials and additional resources are available from the Course home page. To see the feedback opportunities, go to the Assessment & Feedback page.

How will I know I have the acquired the knowledge and skills to succeed in this course unit? (Self-assessment)

There are opportunities throughout the course unit to assess your own learning. For example, working through the course Exercises and checking your understanding against the Solutions. You should have a serious attempt at the exercises before referring to the solutions. In addition, within lectures and tutorials there will be opportunities for you to have your questions answered and discuss your progress on a regular basis.

How will I demonstrate that I have the acquired the knowledge and skills to succeed in this course unit? (Assessment)

You can find full details of the assessment on this course unit on the course syllabus page and coursework information and details about course unit feedback on the Assessment & Feedback page.