Preface
Contents
Preface#
Brenton LeMesurier
College of Charleston, Charleston, South Carolina
lemesurierb@cofc.edu,
with contributions by Stephen Roberts (Australian National University).
Last revised December 20, 2022
This Jupyter book is a sibling of “… with Python”, both of which are based in part on Jupyter notebooks and other materials for the courses MATH 245, Numerical Methods and Mathematical Computing and MATH 445 and MATH 545, Numerical Analysis at the College of Charleston, South Carolina, and MATH 375, Elementary Numerical Analysis at the University of Northern Colorado.
Several sections are based on notes by Stephen Roberts of the Australian National University, for the course Mathematics B15, Numerical Analysis there.
Recent changes:
Gathering exercises at the end of each section, with links to them from relevant locations.
Improved formating of definitions, theorems, proofs, examples, remarks, etc.
Created a small bibliography using a BiBTeX file: see https://jupyterbook.org/en/stable/tutorials/references.html
Added a draft section Piecewise Polynomial Approximating Functions: Splines and Hermite Cubics, based on notes by Stephen Roberts.
Added a draft section Choosing the collocation points: the Chebyshev method, based on notes by Stephen Roberts.
Added notes on the stiff limit \(K = D \gg 1\) of the damped mass-spring system (use this for future stiff-stability examples.)
Expanded the notes on Adams-Bashforth methods, and revised somewhat the notes on leapfrog.
Added first drafts of some sections on multi-step methods: leapfrog, Adams-Bashforth methods and Adams-Moulton methods.
To do:
Add the basics of boundary value problems for ODEs, with both finite difference and (finite) element methods.
Positive definite matrices and the Cholesky factorization.
More on minimization; in particular, for functions of several variables.
Predictor-corrector methods for ODE IVP’s.
Stability analysis for multi-step methods.
More exercises.
Expand the notes on “Julia for people who know Matlab or Python”, Notes on the Julia Language
This is published at http://lemesurierb.people.cofc.edu/introduction-to-numerical-methods-and-analysis-julia/ and as PDF at http://lemesurierb.people.cofc.edu/introduction-to-numerical-methods-and-analysis-julia.pdf, and its Python sibling at http://lemesurierb.people.cofc.edu/introduction-to-numerical-methods-and-analysis-python/
About Julia#
On the topic of programming, this book tries to address two audiences: people who already know Julia (only a basic familiarity is needed), and people who are familiar with either Matlab or “Python Scientific” (Python + NumPy + Matplotlib) and are Julia-curious.
Julia is designed with a fair degree of backward compatability with Matlab, and NumPy and Matplotlib often mimic Matlab syntax too, so the jump is not so big.
To help, there are two appendices
Some Further Reading on Numerical Methods and Analysis#
[Sauer, 2019] Numerical Analysis by Timothy Sauer, 2nd or 3rd edition.
[Burden et al., 2016] Numerical Analysis by Richard L. Burden and J. Douglas Faires, 9th edition.
[Chenney and Kincaid, 2012] Numerical Mathematics and Computing by Ward Chenney and David Kincaid.
[Kincaid and Chenney, 1990] Numerical Analysis by David Kincaid and Ward Chenney.
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