ASTR-5540, Fall 2024

Instructor:	Steven R. Cranmer   (email, web page)
Instructor's Office:	Duane Physics D111 (main campus), LASP/SPSC N218 (east campus)
Course Times:	Fall 2024, Mon./Wed./Fri., 10:10-11:00 am
Location:	Duane Physics, Room E126
Office Hours:	Mondays, 2:30-3:00, and Thursdays, 12:00-12:30 (Duane D111)
Syllabus:	See the most up-to-date PDF version.

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Summary

This is an applied mathematics course designed to provide the necessary analytical and numerical background for courses in astrophysics, planetary science, plasma physics, fluid dynamics, electromagnetism, and radiation transfer. Topics include linear algebra, integration techniques, ordinary and partial differential equations, special functions, integral transforms, and integral equations. We aim to keep the course grounded in research applications and illustrative examples from the areas of physics listed above. This is a core required course for APS graduate students, and it is the same course as ATOC-5540.

Course Material

The primary "required readings" are my lecture notes, which will be posted on Canvas as the semester progresses. Other resources for this course include:

• A list of other online books and lecture notes that supplement my own material.
• Handout: useful math/physics formulae & constants that you're free to use for any work in this course (revised for Fall 2024).
• For background & review: undergraduate lecture notes from ASTR-2100 that cover:
  • trigonometry, vectors, coordinate systems, basic ODEs
  • partial derivatives, gradients, multiple integrals, div & curl, basic PDEs
• Some resources for scientific computing with Python.
• Guidelines and example topics for the Midterm Project.

Schedule

Below is a detailed schedule that will list the material covered in each class session, links to electronic copies of any handouts and problem sets, and various course deadlines.

1. Mon., August 26: Introductory lecture; syllabus summary. Begin discussion of algebraic techniques & computing.
   • Lecture notes (01) for course intro; algebraic techniques & computing.
   • Homework 1 (problem set) assigned, due Wed., September 4.

2. Wed., August 28: Algebraic techniques & computing.

3. Fri., August 30: Algebraic techniques & computing.

     [Mon., September 2 is Labor Day; no classes.]

4. Wed., September 4: Algebraic techniques & computing.
   • Homework 1 due.
   • Homework 2 (problem set) assigned, due Wed., September 18.

5. Fri., September 6: Linear algebra, eigenvalue problems, & applications.
   • Lecture notes (02) for linear algebra and its applications.

6. Mon., September 9: Linear algebra, eigenvalue problems, & applications.

7. Wed., September 11: Linear algebra, eigenvalue problems, & applications.

8. Fri., September 13: Linear algebra, eigenvalue problems, & applications.

9. Mon., September 16: Linear algebra, eigenvalue problems, & applications.

10. Wed., September 18: Linear algebra, eigenvalue problems, & applications.
    • Homework 2 due.
    • Homework 3 (problem set) assigned, due Wed., October 2.

11. Fri., September 20: Integrals, numerical quadrature, & special functions.
    • Lecture notes (03) for integration techniques and special functions.

12. Mon., September 23: Integrals, numerical quadrature, & special functions.

13. Wed., September 25: Integrals, numerical quadrature, & special functions.

14. Fri., September 27: Integrals, numerical quadrature, & special functions.

15. Mon., September 30: Ordinary differential equations (analytic methods).
    • Lecture notes (04) for analytic methods to solve ODEs.

16. Wed., October 2: Ordinary differential equations (analytic methods).
    • Homework 3 due.
    • Homework 4 (problem set) assigned, due Wed., October 16.

17. Fri., October 4: Ordinary differential equations (analytic methods).

18. Mon., October 7: Ordinary differential equations (analytic methods).

19. Wed., October 9: Ordinary differential equations (analytic methods).

20. Fri., October 11: Ordinary differential equations (analytic methods).

21. Mon., October 14: Ordinary differential equations (analytic methods).

22. Wed., October 16: Ordinary differential equations (numerical methods).
    • Lecture notes (05) for numerical methods of solving ODEs.
    • Homework 4 due.
    • Homework 5 (problem set) assigned, due Wed., October 30.

23. Fri., October 18: Ordinary differential equations (numerical methods).

24. Mon., October 21: Ordinary differential equations (numerical methods).

25. Wed., October 23: Ordinary differential equations (numerical methods).

26. Fri., October 25: Integral transforms & discrete Fourier transform methods.
    • Lecture notes (06) for integral transforms.

27. Mon., October 28: Integral transforms & discrete Fourier transform methods.

28. Wed., October 30: Integral transforms & discrete Fourier transform methods.
    • Homework 5 due.
    • Midterm Project assigned, due Wed., November 13.

29. Fri., November 1: Integral transforms & discrete Fourier transform methods.

30. Mon., November 4: Integral transforms & discrete Fourier transform methods.

31. Wed., November 6: Partial differential equations & applications (analytic methods).
    • Lecture notes (07) for analytic methods of solving PDEs.

32. Fri., November 8: Partial differential equations & applications (analytic methods).

33. Mon., November 11: Partial differential equations & applications (analytic methods).

34. Wed., November 13: Partial differential equations & applications (analytic methods).
    • Midterm Project due.
    • Homework 6 (problem set) assigned, due Wed., December 4.

35. Fri., November 15: Partial differential equations & applications (analytic methods).

36. Mon., November 18: Partial differential equations & applications (analytic methods).

37. Wed., November 20: Partial differential equations & applications (analytic methods).

38. Fri., November 22: Partial differential equations & applications (analytic methods).

      [November 25-29: Fall Break & Thanksgiving; no classes.]

39. Mon., December 2: Partial differential equations (numerical methods).
    • Lecture notes (08) for numerical methods of solving PDEs.

40. Wed., December 4: Partial differential equations (numerical methods).
    • Homework 6 due.

41. Fri., December 6: Partial differential equations (numerical methods).

42. Mon., December 9: Integral equations: analytic & numerical methods.
    • Lecture notes (09) for solving integral equations.

43. Wed., December 11: Integral equations: analytic & numerical methods.

      [Fri., December 13: Reading Day. Final Exam Week: December 14-18.]