The material in this section is standard theory which may be found in many textbooks, for example which I follow closely. Much more comprehensive accounts are given in, which are rightly regarded as classic accounts of the subject. My goal in these lectures is not to describe new research, but to provide students with the basic knowledge needed to follow the later and more advanced courses. However, in the third lecture I indulge myself somewhat by describing spectral theory from a computational point of view which will be familiar to numerical analysts, but not to most mathematicians and mathematical physicists. This lecture contains recent research material.
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