20 credits at level HE5
To provide an awareness of how numerical methods can be used to solve problems for which an analytical solution is either difficult or impossible to obtain;
To provide an introduction to the mathematical methods used to derive algorithms and an analysis of their accuracy and reliability;
To develop understanding of the algorithms by requiring the student to program some of the methods.
Errors and accuracy in computation:
Rounding, truncation, absolute and relative error.
Iterative methods for the solution of equations of the form f(x) = 0:
Rearrangement, Newton-Raphson, Bisection and False Position methods.
Modified Newton-Raphson method for multiple roots.
Simpson’s rule and the Trapezium rule;
Derivation of formula using the method of Undetermined Coefficients;
Use of Lagrange and Chebyshev polynomials.
Solution of simultaneous linear equations:
Jacobi and Gauss-Seidel iterative methods;
The students will be given printed notes. Approximately two-thirds of the time will be allocated to formal lectures and the remaining time will involve supervised tutorial work.
Two pieces of coursework will be set, each to be completed by a prescribed date in the students’ own time. There will be a formal closed-book examination of 2¼ hours duration at the end of the module. The weighting of the two components of assessment is as follows:
Coursework 30%, Examination: 70%.
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||Understand the basic principles of numerical analysis.||Demonstrate an appreciation of fundamental numerical methods by writing algorithms and associated Maple or Fortran codes (coursework). Demonstrate the ability to derive the alogrithms.|
|2.||Use numerical analysis techniques to solve a range of appropriate mathematical problems. Use analysis to derive measures associated with numerical methods: for example, order of convergence, error bounds.||Apply the numerical methods studied in this module to a variety of examples.|
|3.||Be able to design and write structured programs to utilise various numerical methods.||Demonstrate an ability to write well-structured Maple or Fortan codes incorporating a particular numerial method.|
Your achievement of the learning outcomes for this module will be tested as follows:
|Description||Algorithms and codes for the solution of f(x)=0.||Algorithms and codes for numerical integration.||Examination of 2.25 hours duration.|
Before taking this module you must have successfully completed the following:
No restrictions apply.
Burden R. L., Douglas-Faires J. Numerical Analysis London : Brooks/Cole Publishing, 1997
Gerald, Curtis F. & Whalley, Patrick O. Applied Numerical Analysis, 7th ed., Addison-Wesley, 2003.
Matthews, John H. Numerical Methods for Mathematics, Science and Engineering, 2nd ed., Prentice Hall, 1992.
Shampine, L.F. Fundamentals of Numerical Computing, Wiley, 1996.
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