Introduction to Numerical Methods and Analysis, Julia Edition (Under Construction)

Brenton LeMesurier

College of Charleston, Charleston, South Carolina, lemesurierb@cofc.edu

Last Revised on September 14, 2022

Under Construction from its older sibling “… Python Edition”, which is in turn derived from Elementary Numerical Analysis with Python, which is my notes for the course Elementary Numerical Analysis at the University of Northern Colorado in Spring 2021.)

For now, sections from that edition that have not yet been converted are here, with “- Python version” appended to their titles and “-python” to their file names.

Some recent updates (most recent first):

• Continued conversion to Julia: now up to the section Polynomial Collocation (Interpolation/Extrapolation) and Approximation

• Introduced the use of Julia modules (but in a clumbsy way, not yet using packages), and started collecting functions from the text in a module NumericalMethodsAndAnalysis

Note that some subsequent sections are “language neutral”, and so are also ready:

• Approximating Derivatives by the Method of Undetermined Coefficients

• Richardson Extrapolation

• Global Error Bounds for One Step Methods — Preliminary

• Initial Value Problems for Ordinary Differential Equations, Part 4: Systems of ODEs and Higher Order ODEs

• Initial Value Problems for Ordinary Differential Equations, Part 5: Error Control and Variable Step Sizes — Preview

The material is based in part on Jupyter notebooks and other materials for the courses MATH 245, MATH 246, MATH 445 and MATH 545 at the College of Charleston, South Carolina, and MATH 375 at the University of Northern Colorado.

Some References for Further Reading

(As in the section References)

• [Sauer] Numerical Analysis by Timothy Sauer, 2nd or 3rd edition.

• [Burden&Faires] Numerical Analysis by Richard L. Burden and J. Douglas Faires, 9th edition.

• [Chenney&Kincaid] Numerical Mathematics and Computing by Ward Chenney and David Kincaid.

These will often be cited by [nickname in brackets].

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