Astronomy 615: Fall 2011

"Computational Astrophysics"

This course will provide the astronomy student with a basic knowledge of numerical methods in astrophysics. By the end of the course students should be comfortable working in a Unix environment, compiling and running codes, and employing a variety of visualization techniques to analyze the results. This process will be motivated by concrete examples of modern problems in astrophysics that demand numerical approaches.

The exact details of the material covered will depend on the existing level of computer sophistication among the class participants. However, in broad outline the major course topics will include linear algebra, root finding, least-square fitting, Monte Carlo methods, numerical integration, N-body methods, fluid dynamics, FFTs and time-series analysis.


    Instructor:  Massimo Ricotti
    Class:       room CSS 0201
    Lectures:    Tuesday and Thursday from 2:00pm to 3:15pm
    First class: Thu Sept 1 
    Last  class: Tu Dec 13

What's New?

Nov 26: Problem Set #6 posted (the last one!).
Nov 18: Problem Set #5 posted.
Nov 8: Problem Set #4 posted.
Oct 19: Problem Set #3 posted It is long, start early!
Oct 4: Problem Set #2 posted.
Sept 22: Tutorial on GNU's GDB Debugger.
Sept 20: Problem Set #1 posted.
Sept 13: Play with C examples and "Makefile mistery".
Sept 06: Survey results posted.

Contact info and Notes

Course Outline

The Syllabus is available in HTML and PDF format.

DateLectureReading (NRiC)Lecture Notes

#1Sep 01Introduction to the course--
#2Sep 06Computer architecture-class02.pdf
#3Sep 08Introduction to UNIXtutorial-
#4Sep 13Introduction to C1.1-1.2, tutorial-
#5Sep 15Introduction to C (cont.)1.1-1.2, tutorial-
#6Sep 20Introduction to visualizationtutorialclass05.pdf
#7Sep 22Data representation1.3class05.pdf
#8Sep 27Linear algebra, part 1 (Gauss-Jordan elimination)2.0-2.3class06.pdf
#9Sep 29Linear algebra, part 2 (LU & SVD decomposition)2.4-2.6class07.pdf
#10Oct 04 Root finding in 1-D9.0-9.1, 9.4, 9.6class08.pdf
#11Oct 06Root finding in multi-D, and numerical differentiation5.7class09.pdf
#12Oct 11Statistics and the K-S test14.0-14.3class10.pdf
#13Oct 13Least-squares fitting15.0-15.2, 15.4-15.5class11.pdf
--Oct 18MIDTERM----
#14Oct 20Random numbers and cryptography7.0-7.2class12.pdf
#15Oct 25Numerical integration7.6, 4.0-4.4, 4.6class13.pdf
#16Oct 27Integration of ODEs, part 1 (IVPs)16.0-16.1class14.pdf
#17Nov 01Integration of ODEs, part 2 (leapfrog)-class15.pdf
#18Nov 03Integration of ODEs, part 3 (stiff ODEs & 2-pt BVPs)16.6, 17.0class16.pdf
#19Nov 08Integration of ODEs, part 4-class17.pdf
#20Nov 10N-body techniques, part 1 -class18.pdf
#21Nov 15N-body techniques, part 2 (PP)19.0, 19.4-19.6class19.pdf
#22Nov 17N-body techniques, part 3 and 4 (PM)-class20.pdfclass21.pdf<
#23Nov 22Integration of PDEs, part 1 (ell & hyp) 19.2class22.pdf
-Nov 24no class (Thanksgiving)--
#24Nov 29 Integration of PDEs, part 2 (hyp & par)19.2class23.pdf
#25Dec 01Guest lecturer: Anton Dorodnitsyn-
#26Dec 06Fluid dynamics, part 1 (eqns)19.3class24.pdf
#27Dec 08Fluid dynamics, part 2 (methods)-class25.pdf
#28Dec 13Parallel Computing (CPU and GPU)--
-Not coveredFourier transform, part 1 (intro)12.0-12.1, 19.4class26.pdf
-Not coveredFourier transform, part 2 (FFT)12.2, 13.0-13.2, 13.4class27.pdf
-Not coveredOther topics-class28.pdf


There are no required textbooks
Numerical recipes in FORTRAN [or in C], by Press, W.H. et al.

Course Grading

Note that the homework is the most important part of the class. However, because this is a graduate class, there will be 2 questions in the qualifyer exam concerning this class. So, midterm and final are a necessary evil to prepare you for the qualifyer. In class participation is strongly encouraged.

Class Survey Results

The starting level of computer and programming competence of the students in this class (measured the first day of class) is "Novice/Beginner" as indicated by the result of the class survey. The survey results are available in HTML and PDF format. I will start the lectures with simple and, for some of you, obvious concepts and finish with more complex and challenging topics that should entertain even the most experienced students in the class.


Homework will be assigned every week or every other week. Their due dates will be announced at the time they are assigned. On the due date the students will be expected to turn in their homework in class. The homework turned in will be graded and returned to the students. I will provide solutions and discuss them in class.

Link to Numerical Recipes sources in C and in FORTRAN: it is preferable to compile the recipes as separate files rather than cut and paste the functions into your source code.

Note that in order to use NRiC routines the easiest way is to include nr.h header file and nrutil.c and nrutil.h to use vectors and matrices. You can find these files here.

Problem setDateProblem SetSolutionsExtras
#1Sept 20Sept 29HTML/PDFHTML/PDF 
#2Oct 4Oct 13HTML/PDFHTML/PDFdata
#3Oct 19Nov 3HTML/PDFHTML/PDFdata
#6Nov 26Dec 13HTML/PDFHTML/PDFmovie


Old Class Notes

    These notes were part of the "first edition" of this course (ASTR688N) in Spring 2001.

Useful Links

Debugger's Links: Using GNU's GDB Debugger Debugging Floating Point Exceptions

OpenMP links: OpenMP Tutorial

Wiki OpenMP

CUDA and GPU computing: Nvidia webpage with examples to download Wiki OpenCL Wiki CUDA

Check out the UMD Astronomy Computing Wiki!

(In the listings below, a "W" link indicates a Wikipedia entry on the topic is available.)

Online Tutorials Free Software General Stuff