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This module builds on the Stage 1 Real Analysis 1 module. We will extend our knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives.
The outline syllabus includes: Continuity and uniform continuity of functions of one variable, series and power series, the Riemann integral, limits and continuity for functions of several variables, differentiation of functions of several variables, extrema, the Inverse and Implicit Function Theorems.
Total contact hours: 42
Private study hours: 108
Total study hours: 150
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 Hours 60%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.
Recommended reading:
B. S. Thomson, A. M. Bruckner, and J. B. Bruckner, Elementary Real Analysis (2nd Edition), 2008.
W. Rudin, Principles of mathematical analysis (3rd Edition), International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976.
Additional reading:
T.M Apostol, Mathematical analysis (2nd edition).. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1974.
K.G. Binmore, Mathematical analysis. A straightforward approach (2nd edition). Cambridge University Press, Cambridge-New York, 1982.
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within mathematical analysis;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the
following areas: uniform continuity of functions, sequences of functions, uniform convergences, series, power series, Riemann integration, functions of several variables,
differentiation of functions of several variables;
3 apply the concepts and principles in mathematical analysis in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.
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