Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | METRIC SPACES AND CALCULUS | ||
Code | MATH241 | ||
Coordinator |
Dr NT Pagani Mathematical Sciences Nicola.Pagani@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2019-20 | Level 5 FHEQ | First Semester | 15 |
Aims |
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To introduce the basic elements of the theory of metric spaces and calculus of several variables. |
Learning Outcomes |
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(LO1) After completing the module students should: Be familiar with a range of examples of metric spaces. Have developed their understanding of the notions of convergence and continuity. Understand the contraction mapping theorem and appreciate some of its applications. Be familiar with the concept of the derivative of a vector valued function of several variables as a linear map. Understand the inverse function and implicit function theorems and appreciate their importance. Have developed their appreciation of the role of proof and rigour in mathematics. |
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(S1) Problem solving skills |
Syllabus |
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Metric spaces: Examples of metric spaces: R^n, the discrete metric, metric of uniform convergence on C[a, b]. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Assessment 2 Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When): First semester | 2.5 hours | 80 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Assessment 1 Assessment Schedule (When): First semester | 20 |