CHEN30102
Mathematical Methods 3
10
Semester 1
Undergraduate
Level 3
David Silvester
Unit coordinator
School of Mathematics
1
FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors '
European Credit Transfer & Accumulation System Rating : 5.0
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<ol>
<li>
Systems of nonlinear equations. Methods of solution including Newton-Raphson method in the case of two or more variables.</li>
<li>
Optimisation of functions. Bisection-type and Golden-Ratio methods for minimisation of functions of a single variable. Search techniques for functions of many variables. Graphical techniques for minimisation of linear functions of two variables subject to constraints.</li>
<li>
Numerical solution of systems of ordinary differential equations. Revision of Euler’s method for a single equation. Solving systems of ordinary differential equations using high-order Runge-Kutta schemes. Shooting methods for boundary-value problems.</li>
<li>
Legendre polynomials and Bessel functions. Solutions of Legendre’s Equation. Legendre Functions of the first and second kinds. Properties and recurrence relations. Solutions of Bessel’s equation.</li>
<li>
Partial Differential Equations. Characterisation of solutions. Solution by separation of variables. Fourier series solutions. Separation of variables in three or four dimensions. Coordinate systems and reduction to Bessel and Legendre equations.</li>
<li>
Numerical approximation of partial differential equations. Explicit schemes for initial value problems. The Crank-Nicolson method for the heat equation. Solution of elliptic boundary-value problems.</li>
</ol>
</div>
</div>
<p> </p>
<div style="margin-left: 18pt">
<div style="margin-left: 18pt">
<ol>
<li>
Systems of nonlinear equations. Methods of solution including Newton-Raphson method in the case of two or more variables.</li>
<li>
Optimisation of functions. Bisection-type and Golden-Ratio methods for minimisation of functions of a single variable. Search techniques for functions of many variables. Graphical techniques for minimisation of linear functions of two variables subject to constraints.</li>
<li>
Numerical solution of systems of ordinary differential equations. Revision of Euler’s method for a single equation. Solving systems of ordinary differential equations using high-order Runge-Kutta schemes. Shooting methods for boundary-value problems.</li>
<li>
Legendre polynomials and Bessel functions. Solutions of Legendre’s Equation. Legendre Functions of the first and second kinds. Properties and recurrence relations. Solutions of Bessel’s equation.</li>
<li>
Partial Differential Equations. Characterisation of solutions. Solution by separation of variables. Fourier series solutions. Separation of variables in three or four dimensions. Coordinate systems and reduction to Bessel and Legendre equations.</li>
<li>
Numerical approximation of partial differential equations. Explicit schemes for initial value problems. The Crank-Nicolson method for the heat equation. Solution of elliptic boundary-value problems.</li>
</ol>
</div>
</div>
<p> </p>
<div>
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<ul>
<li>
Introduce the students to mathematical topics at a suitably advanced level.</li>
<li>
Teach students to carry out the relevant techniques but also have enough appreciation to apply the techniques in slightly different situations.</li>
<li>
Ensure that students have an appreciation of the application of such techniques in Chemical Engineering and related disciplines.</li>
</ul>
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</div>
<p> </p>
<p> </p>
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<p align="center">Knowledge and understanding</p></td>
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<p>Carry out problems and examples using the appropriate mathematical techniques as mentioned in the syllabus.</p><p> </p></td>
</tr>
<tr>
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<p align="center">Intellectual skills</p></td>
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<p>Have an appreciation of the basic methods and be able to adapt and generalise the underlying ideas.</p><p> </p></td>
</tr>
<tr>
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<p align="center">Practical skills</p></td>
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<p> </p><p>Develop a working knowledge of associated computational algorithms.</p><p> </p></td>
</tr>
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<td style="width: 158px">
<p align="center">Transferable skills and personal qualities</p></td>
<td style="width: 482px">
<p>Appreciation of the role of numerical methods in Chemical Engineering and associated subjects.</p><p> </p></td>
</tr>
</tbody>
</table>
<p> </p>
<p> </p>
<table border="1" cellpadding="0" cellspacing="0" width="640">
<tbody>
<tr>
<td style="width: 158px">
<p align="center">Knowledge and understanding</p></td>
<td style="width: 482px">
<p>Carry out problems and examples using the appropriate mathematical techniques as mentioned in the syllabus.</p><p> </p></td>
</tr>
</tbody>
</table>
<p> </p>
<p> </p>
<table border="1" cellpadding="0" cellspacing="0" width="640">
<tbody>
<tr>
<td style="width: 158px">
<p align="center">Intellectual skills</p></td>
<td style="width: 482px">
<p>Have an appreciation of the basic methods and be able to adapt and generalise the underlying ideas.</p><p> </p></td>
</tr>
</tbody>
</table>
<p> </p>
<p> </p><p>Develop a working knowledge of associated computational algorithms.</p>
<p> </p>
<table border="1" cellpadding="0" cellspacing="0" width="640">
<tbody>
<tr>
<td style="width: 158px">
<p align="center">Transferable skills and personal qualities</p></td>
<td style="width: 482px">
<p>Appreciation of the role of numerical methods in Chemical Engineering and associated subjects.</p><p> </p></td>
</tr>
</tbody>
</table>
<p> </p>
<div>
<div>
<p>Two or three hours of lectures every week for eight weeks. Fortnightly examples class</p><p>including one-to-one support for students working on tutorial sheet questions.</p></div>
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<p> </p>
0
Other
100%
<p> </p>
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<p align="center">Assessment task</p></td>
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<p align="center">Length</p></td>
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<p align="center">Weighting within unit (if relevant)</p></td>
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<p>Examination</p><p>Mid-Semester Test (week 7)</p></td>
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<p>1.5 hours</p><p>1 assignment</p></td>
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<p>80%</p><p>20%</p></td>
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<p> </p><p> </p>
BEng(Hons) Chem Eng
BEng(Hons) Chemical Engineerin
Third Year
Mandatory
MEng (Hons) Chem Eng
MEng Chemical Engineering
Third Year
Mandatory
MEng (Hons) Chem Eng w Bio
MEng Chem Eng with Biotech
Third Year
Mandatory
MEng (Hons) Chem w Env. Tech
MEng Chem Eng w Env. Tech
Third Year
Mandatory
MEng Chem Eng w Energy & Env
MEng Chem Eng with Energy
Third Year
Mandatory
N
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<div>
<p> </p>
<div>
<p>Erwin Kreyszig : Advanced Engineering Mathematics : Wiley (2010, 10th Edition)</p><p>David Griffiths, John Dold, David Silvester : Essential Partial Differential Equations: Springer</p><p>Undergraduate Mathematics Series ( 2014)</p></div>
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</div>
<p> </p>
Lectures
18
Tutorials
6
0
76
<p> </p>
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<p>Contact hours</p></td>
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<p>24</p></td>
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