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    Mathematical Analysis
    MATH S216
      More information: Course Guide
    Mathematical Analysis
    Course Start Date
    Aut 2019
    Course Level
    Middle
    Length in Terms
    1 term
    Credits
    5
    Language
    English
    Fees ($) (including lab fees)
    5,850
    Future Terms
    Aut 2020
    Quota and Schedule
    Course
    Start Date
    Course Level Length in Terms Credits
    Language
    Fees ($)
    (including lab fees)
    Future Terms
    Aut 2019
    Middle 1 term 5
    English
    5,850
    Aut 2020

    Course Coordinator: Dr Douglas Ng, BSc (1st Hons), MPhil, PhD (HK PolyU); CMath; CSci; CEng; FIBMS

    Course Developer: The Open University, UK, Course Team

    This course is intended to provide a conceptual understanding of the theory of mathematical analysis. The course deals with the basic theory of analysis in real-valued functions in single variables. It provides students with a good foundation for higher-level courses in mathematical studies. The course is made up of six study units. Topics include series, continuity, limits, differentiation, integration and power series. MATH S216 is one of the compulsory middle-level courses in the BSc and BSc (Hons) in Mathematical Studies, and an elective middle-level course in the BSc (Hons) in Statistics and Decision Science.

    MATH S216 forms an excluded combination with MATH S203/MATH S213.

    This course is presented at 12-month intervals.

    Advisory prerequisite(s)
    You are advised to have already studied one of the foundation mathematics courses MATH S101, MATH S111, MATH S112, MATH S121 or MATH S122.

    Aims
    This course aims to:

    • Introduce some basic concepts in mathematical analysis;

    • Develop students’ competence in series and continuity;

    • Develop students’ ability in handling basic skills for testing the convergence of series;

    • Develop students’ knowledge of the limiting processes of real valued functions of one variable;

    • Develop students’ rigour in writing proofs.

    Contents
    The course covers the following topics:

    • Series — convergent series, test for convergence and its proof, non-null test and alternative test, absolute convergence

    • Continuity — continuity of functions, the local rule, the glue rule and the restriction rule, the intermediate value theorem, the extreme value theorem, the inverse functions and inverse function rule

    • Limits — rules for limits and one-sided limits, asymptotic behaviour of functions, uniform continuity

    • Differentiation — differentiable functions and test for differentiability, rules for differentiation and proofs, Roll’s theorem, local extremum theorem, the mean value theorem, L’Hôpital’s rule

    • Integration — Riemann integral, the fundamental theorem of calculus, inequalities for integrals, Wallis’s formula, integral test, Stirling’s formula for n!, Riemann’s criterion for integrability and proof

    • Power series — Taylor’s polynomials and theorem, approximation by Taylor’s theorem, convergence of power series, radius of convergence, approximate derivative using power series

    Learning support
    There will be six two-hour tutorials and three surgeries.

    Assessment
    There will be two assignments and a final examination.

    Online requirement
    This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, you will need to have access to the Internet. The use of the OLE is required for the study of this course and you can use it to submit assignments.

    Equipment
    Students will need access to a personal computer or other electronic devices with an Internet connection, and a television to watch the course-related programmes broadcast on Sunday mornings.

    Set book(s)
    There are no set books for this course.

    Students with disabilities or special educational needs
    The audio and visual components of this course may cause difficulties for students with hearing or vision impairments. You are encouraged to seek advice from the Course Coordinator before enrolling on the course.

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