MT 274 NUMERICAL ANALYSIS I
SECOND SEMESTER 2016/2017
REVISION OF BASIC CONCEPTS
If you are able to intelligently, independently, and correctly answer the following 11
questions then, you are well prepared to follow any course in numerical analysis.
Prof. Ralph W.P. Masenge
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What is a mathematical problem? Give a simple illustrative example of a mathematical
problem.
What is a mathematical algorithm? Give a simple example of a mathematical algorithm.
What is an analytical method for solving a mathematical problem? Give a simple
illustrative example of an analytical method for solving a mathematical problem.
What is a numerical method for solving a mathematical problem? Give a simple
illustrative example of a numerical method for solving a mathematical problem.
Define a direct numerical method for solving a mathematical problem and give a simple
illustrative example.
Define an iterative numerical method for solving a mathematical problem and give a
simple illustrative example.
What is the difference between an analytical solution and a numerical solution of a
mathematical problem? Give a simple illustrative example of a mathematical problem
and solve it using an analytical method and a numerical method to illustrate the
difference between the two types of solutions.
What is a mathematical error? Give a simple illustrative example of a mathematical error.
Distinguish between absolute error and relative (percentage) error, and relate the two
types of mathematical errors to the concepts of accuracy and seriousness of mathematical
errors. Give a simple illustrate example of each type of mathematical error.
What are the chief sources (causes) of mathematical errors and what type of an error does
each source or cause lead to? Give a simple illustrative example of each type of
mathematical error.
Discuss how each type of mathematical error can be reduced or minimized and, in each
case, give a simple illustrative example.
What are the desirable properties of a good numerical method? In each case explain the
underlying concept, and where possible give an illustrative example.
What do you understand by numerical analysis, and how does a course in numerical
analysis differ from a course in numerical methods?
Professor Ralph W.P. Masenge
Course Lecturer