An Introduction to Numerical Computation

by Wen Shen

This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.

The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.

The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.

The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.

Contents: Computer Arithmetic Polynomial Interpolation Piecewise Polynomial Interpolation: Splines Numerical Integration Numerical Solutions of Non-linear Equations Direct Methods for Systems of Linear Equations Fixed Point Iterative Solvers for Linear and Non-linear Systems The Method of Least Squares Numerical Solutions of ODEs Numerical Methods for Two-Point Boundary Value Problems Finite Difference Methods for Some Partial Differential Equations A Few Other Important Algorithms

Readership: Junior or senior undergraduate students interested in numerical computation and analysis, majoring in mathematics, computer science, physics, engineering, etc.

340 pages, Kindle Edition

Published August 28, 2019

Reviews

[Forlife Maths]

I'm a math professor in Albania. I'm teaching at University. So, I need to read this book. Thanks.

[Ahmed]

I'm a master student and need so much to read your book, Prof. in order to solve an Euler equation thanks

[Tom Schulte · Rating 4 out of 5]

"Drawing on ten years’ teaching, the author presents complete lecture notes and assignments for a semester’s introductory numerical methods course for senior undergraduates. Videos at the author's YouTube channel from live lectures with short tutorials augment the text making it self-contained for self-study. Multivariable calculus, matrix basics, and some basic computer programming skills are the prerequisites here. The programming examples are in MATLAB. For a compact volume, the homework—homework, not exercises—is ample and well-conceived. Homework problems concluding each chapter include applications, programming tasks, and a list of items to turn in. A complete set of solutions is available for instructors upon request..."

[Look for my entire review at MAA Reviews]