| Numerical Analysis - 13538 - CS 51400 - LE1 |
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Associated Term: Spring 2024
Levels: Undergraduate, Graduate, Professional West Lafayette Campus Lecture Schedule Type Learning Outcomes: This course is intended to be a first graduate course in Numerical Algorithms for graduate students in computer science, mathematics, statistics, computational science and engineering, engineering, and related fields. This is suitable as a foundational course for students from all these fields who use numerical algorithms in their work. The course will provide an introduction to the foundational algorithms in what is now called Scientific Computing. We will cover the topics traditionally included in such a course at the graduate level, with the exception of topics in numerical linear algebra (matrix computations), discussed in CS 515, and numerical optimization, discussed in CS 520. An undergraduate version of this course is available as CS314, and for students from disciplines other than CS and Mathematics, this might be more suitable depending on your previous knowledge of this material. Pre-requisites for this course would be knowledge of numerical algorithms (e.g., solution of linear and nonlinear equations, polynomial interpolation, least-squares data fitting) at the undergraduate level. You should be comfortable programming in one of Matlab, Python or Julia; I will use Matlab for teaching and for giving Homework problems. The topics discussed will include: \begin{itemize} \item Floating point arithmetic, the IEEE floating point standard \item Condition of problems, stability of algorithms \item Solution of nonlinear equations \item Algorithmic differentiation \item Polynomial interpolation \item Piecewise polynomial interpolation, splines \item Approximation of functions \item Numerical integration \item Numerical solution of ordinary differential equations (if time permits) \end{itemize} Students will be graded on regular homework problems including programming assignments (given weekly or fortnightly), quizzes, two evening midterm exams (dates to be chosen) and a final exam. Required Materials: Uri Ascher and Chen Greif, {\em A First Course in Numerical Methods\/}, Society for Industrial and Applied Mathematics, 2011. (ISBN 978-0-898719-97-0) {\bf Required.} Technical Requirements: Pre-requisites for this course would be knowledge of numerical algorithms (e.g., solution of linear and nonlinear equations, polynomial interpolation, least-squares data fitting) at the undergraduate level. You should be comfortable programming in one of Matlab, Python or Julia. Students from departments other than computer science would find it helpful to read the first chapters of the textbook to see if you have the pre-requisite background. If you have questions after that, please discuss with me. Students unfamiliar with Matlab might find an introductory book helpful, although on-line help is available within Matlab and at \verb|https://mathworks.com|. One such book is \newline Tobin Driscoll, {\em Learning Matlab\/}, SIAM, 2009. This book is NOT required. View Catalog Entry
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