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 | MATHEMATICS | ||
Code | MATH186 | ||
Coordinator |
Prof DI Jack Mathematical Sciences Dij@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2016-17 | Level 4 FHEQ | Second Semester | 15 |
Aims |
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• To consolidate and extend the mathematics required by physical scientists. • To assist students in acquiring the skills necessary to use the mathematical techniques developed in the module. |
Learning Outcomes |
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be able to manipulate matrices with confidence and use matrix methods for solving simultaneous linear equations;
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have an introductory knowledge of vector algebra, functions of several variables and vector calculus; |
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be familiar with some methods of solving first and second order differential equations in one variable. |
Syllabus |
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1 |
Matrices: Addition, multiplication. Determinant, inverse. Solutionsof linear equations by matrix methods. Introduction to vector calculus: Vector and scalar fields. Grad,Div, Curl in Cartesian co-ordinates. Applications including work done, moment of a force, angular momentum, gravitational and electromagnetic fields. Differential equations: First and second order differential equations in one variable. Separable equations, integrating factors, homogeneous. Applications involving different boundary conditions, electrical circuits, damped and forced vibrations, gravitational motion. (Mention of Laplace''s and Poisson''s equations and different co-o rdinatesystems). Series solutions. LegendrePolynomials (Mention of Spherical Harmonics and Schrödinger''s equation). Fourier Series and Transforms: Fourier Series, periodic functions, even and odd expansions. Fourier integrals, non periodic functions. Fourier Transforms. (Mention some of the applications). |
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. Explanation of Reading List: |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH181 |
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: |
Programme:FZ61 Year:1 Programme:F100 Year:1 Programme:F102 Year:1 Programme:FZ11 Year:1 |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Unseen Written Exam | 150 | Second semester | 90 | Yes | Standard UoL penalty applies | Assessment 2 Notes (applying to all assessments) 10% for homework of 10 Problem Sheets Candidates should answer the WHOLE of Section A and THREE questions from Section B. Section A carries 55% of the available marks. |
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Coursework | Second semester | 10 | No reassessment opportunity | Standard UoL penalty applies | Assessment 1 There is no reassessment opportunity, |