Learning and Computing Resources
Textbook(s)
For lectures, I will use my own
lecture slides (complemented by real-time tablet annotation) that will be posted
here. I will not follow any specific textbook per se, however, you
will need to complement the lectures and my slides with additional
reading depending on your background. This will not only give you a broader perspective but it
will also give you a different perspective, which is very
important.
As the primary textbook that I will point you to for additional reading, I recommend Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greenbaum & Timothy P. Chartier (library call number QA297.G15 2012). This book is available to you freely in electronic format via NYU's library (permalink). Codes can be found at the author's website.
A secondary optional textbook is Fundamentals of numerical computation by Tobin Driscoll (QA297.D75 2018), see additional resources including codes/slides in Matlab/Julia/Python. This book is not available freely but an electronic copy can be purchased via google play -- if you wish to purchase a hard copy use this discount flier. This textbook is very applied and hands on with Matlab and more elementary in some respects.
A more advanced text that is not a first textbook on numerical methods but has very nice case studies demonstrating applications of scientific computing in various disciplines can be found in the book Scientific Computing with Case Studies by Dianne P. O'Leary (library call number QA401.O44 2009), also available freely to you in PDF format. Additional case studies can be found here.
Some of the lectures will be more closely based on a draft of a textbook Principles of Scientific Computing by my colleagues Jonathan Goodman and David Bindel, to be found here as one PDF or as individual chapters.
As the primary textbook that I will point you to for additional reading, I recommend Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greenbaum & Timothy P. Chartier (library call number QA297.G15 2012). This book is available to you freely in electronic format via NYU's library (permalink). Codes can be found at the author's website.
A secondary optional textbook is Fundamentals of numerical computation by Tobin Driscoll (QA297.D75 2018), see additional resources including codes/slides in Matlab/Julia/Python. This book is not available freely but an electronic copy can be purchased via google play -- if you wish to purchase a hard copy use this discount flier. This textbook is very applied and hands on with Matlab and more elementary in some respects.
A more advanced text that is not a first textbook on numerical methods but has very nice case studies demonstrating applications of scientific computing in various disciplines can be found in the book Scientific Computing with Case Studies by Dianne P. O'Leary (library call number QA401.O44 2009), also available freely to you in PDF format. Additional case studies can be found here.
Some of the lectures will be more closely based on a draft of a textbook Principles of Scientific Computing by my colleagues Jonathan Goodman and David Bindel, to be found here as one PDF or as individual chapters.
Computing
Computing on your own will form an
essential part of the learning process and your own applied
mathematics training. Matlab is available to all NYU students via
our ITS
software service. You can install it on your personal laptop
without a charge.
You are encouraged to submit reports as PDFs produced using LaTex
(latex), as a good practice in learning how to use mathematical
typesetting software for future papers and thesis reports. I
recommend trying out the LyX word
processor as a front-end GUI to LaTex, especially if you are
new to LaTex.
Also see these resources listed by my colleague David Bindell. In particular, some coding advice that may be useful in general.
Also see these resources listed by my colleague David Bindell. In particular, some coding advice that may be useful in general.
Matlab Resources
There are many free online materials that can be consulted as
additional reading, depending on your background and interests. Here
are some suggestions (more may be added as the course progresses)
that you have special access to through the NYU/Courant library:
- Numerical Computing with MATLAB, by Cleve Moler, available for free in PDF form at the MATLAB site.
- The Cambridge Engineering guide to MATLAB has lots of useful information.
- An Introduction to Programming and Numerical Methods in MATLAB, Stephen R. Otto & James P. Denier, Springer, 2005, available in PDF format through the library. This book provides an elementary introduction to Matlab with less focus on actual scientific computing.
Also see these resources listed by my colleague David Bindell.
Lastly, for a quick tutorial see the MATLAB Onramp. This is a 2-hour self-paced interactive course on the basics of using MATLAB. The other self-paced courses on that page are freely available to NYU and students can share completion certificates on LinkedIn.
Do not use sym in Matlab, i.e., do not use symbolic algebra in this class. This class is about computing with floating-point numbers, not symbolic computing, which is an important but distinct tool. If you want to use symbolic algebra, I strongly suggest using Mathematica (e.g. via Wolfram alpha) or Maple (the symbolic algebra in Matlab is just an interface to Maple’s core) or Sage.