Welcome to Sturm-Liouville and Dirac operators, a course hosted by the Taught Course Center of Bath-Bristol-Imperial-Oxford-Warwick and Swansea. This page summarizes all key information of the module and contains all course materials, most importantly our weekly schedule.
Key organizational information:
Instructor: Thomas Bothner
Office: 2A.15, Fry Building
Contact: thomas.bothner@bristol.ac.uk and +44 117 455 2070
Meeting times: Thursday 10:00am-12:00noon via Microsoft TEAMS (starting January 22nd, 2026)
There is no exam for this course. If you are taking the module for credit you must complete the posted reading assignment/exercises and email me your report/solutions in LaTeX typeset by the due date written on the assignment sheet. Please let me know if you wish to earn credit for this module!
This course is offered exclusively to PhD students and Postdocs at the Universities of Bath, Bristol, Oxford, Warwick, Swansea and Imperial College London. If you are eligible and interested in this course please sign up via tcc@maths.ox.ac.uk with your MS Teams email address or contact me directly if there are any issues. The course will run for 8 consecutive weeks, see the weekly schedule below.
Course materials (click the links):
Welcome to Sturm-Liouville and Dirac operators - Introductory Slides
Lecture Notes (March 11th, 2026 version - let me know about typos)
Reading assignments/Exercises (February 14th, 2026 version)
Weekly schedule:
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Week 1, January 22nd, 2026 from 10:00-12:00 Bristol time:
Topics: What will we be studying? Spectral theory in the regular case (part 1)
Materials: Lesson Notes
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Week 2, January 29th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the regular case (part 2)
Materials: Lesson Notes
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Week 3, February 5th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the regular case (part 3)
Materials: Lesson Notes
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Week 4, February 12th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the singular case (part 1, decreasing potentials)
Materials: Lesson Notes
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Week 5, February 19th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the singular case (part 2, decreasing potentials)
Materials: Lesson Notes
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Week 6, February 26th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the singular case (part 3, decreasing potentials)
Materials: Lesson Notes
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Week 7, March 4th, 2026 from 10:00-12:00 Bristol time:
Topics: Spectral theory in the singular case (part 4, Weyl's method)
Materials: Lesson Notes
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Week 8, March 12th, 2026 from 10:00-12:00 Bristol time:
Topics: Inverse problems on a finite interval
Materials: