ASTR-5540, Fall 2022

Instructor:	Steven R. Cranmer   (email, web page)
Instructor's Office:	Duane Physics D111 (main campus), LASP/SPSC N218 (east campus)
Course Times:	Fall 2022, Mon./Wed./Fri., 10:10-11:00 am
Location:	Duane Physics, Room E126
Office Hours:	Tuesdays, 11:00-11:30; Fridays, 1:30-2:00 (usually Zoom)
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 below on this page as the semester progresses. Other resources for this course include:

• A brief set of notes about grading that say a bit more than the syllabus about how total course grades will be computed.
• 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 2022).
• 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 & example topics for the final 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 22: 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., August 31.

2. Wed., August 24: Algebraic techniques & computing.
   • Python notebook illustrating roundoff error accumulation.

3. Fri., August 26: Algebraic techniques & computing.

4. Mon., August 29: Algebraic techniques & computing.

5. Wed., August 31: Linear algebra & applications.
   • Homework 1 due.
   • Homework 2 (problem set) assigned, due Wed., September 14.

6. Fri., September 2: Linear algebra & applications.
   • Lecture notes (02) for linear algebra and its applications.

     [Mon., September 5 is Labor Day; no classes.]

7. Wed., September 7: Linear algebra & applications.

8. Fri., September 9: Linear algebra & applications.

9. Mon., September 12: Linear algebra & applications.

10. Wed., September 14: Integrals, numerical quadrature, & special functions.
    • Homework 2 due.
    • Homework 3 (problem set) assigned, due Fri., September 30.
    • Lecture notes (03) for integration techniques and special functions.

11. Fri., September 16: Integrals, numerical quadrature, & special functions.

12. Mon., September 19: Integrals, numerical quadrature, & special functions.

13. Wed., September 21: Integrals, numerical quadrature, & special functions.

14. Fri., September 23: Integrals, numerical quadrature, & special functions.

15. Mon., September 26: Ordinary differential equations (analytic methods).
    • Lecture notes (04) for analytic methods to solve ODEs.

16. Wed., September 28: Ordinary differential equations (analytic methods).

17. Fri., September 30: Ordinary differential equations (analytic methods).
    • Homework 3 due.
    • Homework 4 (problem set) assigned, due Fri., October 14.

18. Mon., October 3: Ordinary differential equations (analytic methods).

19. Wed., October 5: Ordinary differential equations (analytic methods).

20. Fri., October 7: Ordinary differential equations (analytic methods).

21. Mon., October 10: Ordinary differential equations (analytic methods).

22. Wed., October 12: Ordinary differential equations (numerical methods).
    • Lecture notes (05) for numerical methods of solving ODEs.

23. Fri., October 14: Ordinary differential equations (numerical methods).
    • Homework 4 due.
    • Take-home midterm exam assigned (see Canvas), due Fri., October 21.

24. Mon., October 17: Ordinary differential equations (numerical methods).

25. Wed., October 19: Ordinary differential equations (numerical methods).

26. Fri., October 21: Ordinary differential equations (numerical methods).
    • Take-home midterm exam due.
    • Homework 5 (problem set) assigned, due Fri., November 4.

27. Mon., October 24: Integral transforms & discrete Fourier transform.
    • Lecture notes (06) for integral transforms.

28. Wed., October 26: Integral transforms & discrete Fourier transform.

29. Fri., October 28: Integral transforms & discrete Fourier transform.

30. Mon., October 31: Integral transforms & discrete Fourier transform.

31. Wed., November 2: Partial differential equations (analytic methods).
    • Lecture notes (07) for analytic methods of solving PDEs.

32. Fri., November 4: Partial differential equations (analytic methods).
    • Homework 5 due.
    • Homework 6 (problem set) assigned, due Fri., November 18.

33. Mon., November 7: Partial differential equations (analytic methods).

34. Wed., November 9: Partial differential equations (analytic methods).

35. Fri., November 11: Partial differential equations (analytic methods).
    • See also auxiliary lecture notes (lec07AUX) for additional example applications of ODE/PDE solutions.

36. Mon., November 14: Partial differential equations (analytic methods).

37. Wed., November 16: Partial differential equations (example applications).

38. Fri., November 18: Partial differential equations (example applications).
    • Homework 6 due.

      [November 21-25: Fall Break & Thanksgiving; no classes.]

39. Mon., November 28: Partial differential equations (numerical methods).
    • Lecture notes (08) for numerical methods of solving PDEs.

40. Wed., November 30: Partial differential equations (numerical methods).

41. Fri., December 2: Partial differential equations (numerical methods).

42. Mon., December 5: Partial differential equations (numerical methods).

43. Wed., December 7: Integral & integro-differential equations?
    • Final project due.

      [Fri., December 9: Reading Day. Final Exam Week: December 10-14.]