Textbooks
Other Sources
- B. LeMesurier, Elementary Numerical Analysis with Python.
- Scientific Python Lectures.
- Christian Hill, Learning Scientific Programming with Python.
- G. Okten, First Semester in Numerical Analysis with Julia.
- Y. Liu, G. Okten, First Semester in Numerical Analysis with Python
- E. Sullivan, Numerical Methods: An Inquiry-Based Approach With Python
- J.R. Chasnov, Numerical Analysis for Engineers
- Seongjai Kim, Numerical Analysis 1a
- Seongjai Kim, Numerical Analysis 1b
- A. Birkisson, T. A. Driscoll, L. N. Trefethen, Exploring ODEs.
- S. Linge, HP. Langtangen, Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python, Springer Open
- S. Linge, HP. Langtangen, Programming for Computations - MATLAB/Octave, Springer Open
- S. Linge, HP. Langtangen, Programming for Computations - Python, Springer Open
- T. A. Driscoll, N. Hale, L. N. Trefethen, Chebfun, an open-source package for computing with functions to about 15-digit accuracy.
- T. Driscoll, R. Braun, Fundamentals of Numerical Computation.
- Numerical Computing with MATLAB
- Tea Time Numerical Analysis, by Leon Q. Brin (Southern Connecticut State University)
- Use the annotated copy of the Lecture Notes, by B. Roman (U. of Cambridge), for Linear Algebra, pages 122-152.
- Holistic Numerical Methods, by A. Kaw (University of South Florida)
Videos
- Numerical Methods for Engineers, by Jeffrey Chesnov (Hong Kong University)
- Numerical Analysis, by Seongjai Kim (Mississippi State University)
- MIT 2016 Numerical Methods for PDE, by Qiqi Wang (MIT)
- Numerical Analysis by Joel Rosenfeld (U. of South Florida)
Outline
This class is an elementary introduction to the basic methods of the Numerical Analysis. At the same time, it also works as a basic introduction to scientific programming in Python with the goal of using this language throughout the semester to implement some of the algorithms and ideas covered in class. Because of this, we will be able to cover less theory than a normal Intro to Numerical Analysis class does but, in the end, you will be able to write effective code to study numerically mathematical problems rather than only knowing in theory how to do that.Topics to be covered (in bold the topics we already covered)
- Floating Point systems.
- Iterative methods to solve equations.
- Linear Systems of Equations.
- Eigenvalues and eigenvectors of a symmetric matrix.
- Optimization.
- Nonlinear Systems of Equations.
- Polynomial interpolation.
- Integration.
- Initial and boundary value problems for ODEs.
Grades policy
Grades will be evaluated on the following bases:- (Almost) weekly homework: 50%;
- Two take-home midterms: 2x15%;
- Final project: 20%.
Tentative Syllabus
- Week 1: Motivation and introduction to Scientific Computing. Floating point system. Truncation and algorithm errors.
- Week 2: Taylor series and approximations, Iterative methods, Octave/MATLAB elementary coding.
- Week 3 through 5: Iterative methods, Linear Systems.
- Week 6 & 7: Nonlinear Systems, Optimization.
- Week 8: Eigenvalues and eigenvectors
- Week 9 & 10: Interpolation and Integration.
- Week 11 & 12: ODEs.
- Week 13: Some example of PDEs.
- Week 14: Review.
Languages used
PythonCollaboration
Especially with online classes, teamwork is very important and will give you the occasion to interact with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. On the other side, you must write your solutions yourself, in your own words, and you must list all collaborators and outside sources of information.It is a serious violation of academic integrity to copy an answer without attribution.