The subject-matter of this course is the numerical rendering of problem with the aim to construct algorithmic procedures for their solution. Such algorithmic solution must also be implementable on a computing tool. The modern computing tool is the digital computer. Specifically, therefore, we will discuss the theoretical basis of computable and solvable numerically rendered problems. The topics that will be considered include;
- The character of the computing instrument;
Error and error propagation in the process of problem solving;
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The role of methods and machine in error generation and propagation;
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Precaution to handling and treating error so as to prevent the manifestation of errors from compromising the final solution computed;
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Discuss how methods for solving problems described using non-linear and linear models can be solved precisely;
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Discuss how methods for solving dynamic problems described using ordinary and partial differential equation and models can be solved precisely;