Analysis

Subject 620-252 (2009)

Note: This is an archived Handbook entry from 2009. Search for this in the current handbook

Credit Points: 12.50
Level: 2 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2009:

Semester 1, - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable

Lectures and practice classes.

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 one-hour lectures (three per week), 11 one-hour practice classes (one per week)
Total Time Commitment: 120 hours total time commitment.
Prerequisites:

One of

  • 620-122 (prior to 2008)
  • 620-142 (prior to 2009)
  • 620-192 (prior to 2006),
  • 620-194 (prior to 2006),
  • 620-211 (prior to 2008);

and one of

  • 620-113 (prior to 2008),
  • 620-123 (prior to 2008),
  • 620-143 (prior to 2009),
  • 620-193 (prior to 2006).
Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects: Students may only gain credit for one of 620-221 (prior to 2009) and Analysis.
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit.

Coordinator

Dr Omar Foda
Subject Overview:

This subject deals with convergence of sequences and series; elementary topology of the real line; the fundamentals of continuity, and differentiability of functions of several real variables; analytic functions of a complex variable; complex derivative; power and Laurent series in complex variables; basic topological concepts in the complex plane; and Cauchy's theorem and its applications. Students completing this subject develop the ability to determine the convergence or otherwise of sequences and series; differentiate functions of a complex variable; calculate contour integrals; work with analytic functions in the cut plane; and apply Cauchy's integral formula and the residue theorem. The subject demonstrates the differences between functions of a real and a complex variable; and the role of complex analytic methods in solving important problems in science and engineering.

Sequences and series topics include standard sequences and series, Cauchy convergence, ratio and nth root tests, absolute and conditional convergence, re-arrangements and power series. Continuity topics include continuity and differentiability of functions of several real variables. Functions of a complex variable topics include elementary functions of a complex variable, branches, differentiation, analytic functions and Cauchy-Riemann equations. Integration topics include line and contour integrals, and Cauchy's integral theorem; Laurent series; singularities, poles and Liouville's theorem; and residue theorem, limiting contours, and evaluation of integrals using contour integration.

Objectives: .
Assessment:

Up to 36 pages of written assignments due during the semester (0% or 15%); a 3-hour written examination in the examination period (85% or 100%). The relative weighting of the examination and the total assignment mark will be chosen so as to maximise the student's final mark.
Prescribed Texts: None
Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Notes:

This subject is available for science credit to students enrolled in the BSc (pre-2008 degree only), BASc or a combined BSc course.
Related Majors/Minors/Specialisations: Mathematics && Statistics Major

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