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MATH2011: COMPLEX ANALYSIS II

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Type Open
Level 2
Credits 20
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Calculus I (Maths Hons) (MATH1081) or Calculus 1 (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra 1 (MATH1071) and Analysis 1 (MATH1051) [the latter may be co-requisite].

Corequisites

  • Analysis 1 (MATH1051) unless takenbefore.

Excluded Combinations of Modules

  • Mathematics for Engineers and Scientists (MATH1551), SingleMathematics A (MATH1561), Single Mathematics B (MATH1571), Mathematical Methods in Physics (PHYS2611)

Aims

  • To introduce the student to the theory of complex analysis.

Content

  • Complex differentiation.
  • Conformal Mappings.
  • Metric Spaces.
  • Series, Uniform Convergence.
  • Contour Integrals, Calculus of Residues.
  • Applications.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solveunseen problems in Complex Analysis.
  • Reproduce theoretical mathematics in the field of ComplexAnalysis to a level appropriate to Level 2.
  • Have a knowledge and understanding of this subjectdemonstrated through one or more of the following topic areas: ComplexDifferentiation.
  • Conformal Mappings.
  • Metric Spaces.
  • Contour integrals, calculus of residues.
  • Series, Uniform Convergence.
  • Applications of Complex analysis.

Subject-specific Skills:

  • In addition students will have enhanced mathematical skillsin the following areas: Spatial awareness.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lecturing demonstrates what is required to be learned and theapplication of the theory to practical examples.
  • Fortnightly homework problems provide formative assessment to guide students in the correct development of their knowledge andskills.
  • Tutorials provide active engagement and feedback to thelearning process.
  • The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures522 or 3 lectures per week on an alternating basis throughout Michaelmas and Epiphany terms and two lectures in week 211 Hour52 
Tutorials10Fortnightly for 21 weeks1 Hour10Yes
Problems Classes9Fortnightly for 20 weeks1 Hour9 
Preparation and Reading129 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 hours100Yes

Formative Assessment

One written or electronic assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment

More information

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