An Introduction to Numerical Computation

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 ArithmeticPolynomial InterpolationPiecewise Polynomial Interpolation: SplinesNumerical IntegrationNumerical Solutions of Non-linear EquationsDirect Methods for Systems of Linear EquationsFixed Point Iterative Solvers for Linear and Non-linear SystemsThe Method of Least SquaresNumerical Solutions of ODEsNumerical Methods for Two-Point Boundary Value ProblemsFinite Difference Methods for Some Partial Differential EquationsA Few Other Important Algorithms
Readership: Junior or senior undergraduate students interested in numerical computation and analysis, majoring in mathematics, computer science, physics, engineering, etc.Numerical Computation;Numerical Method;Numerical Analysis;Numerical Algorithm0Key Features:The book is written in an informal style, which eases the preparation of the instructorThere is a complete set of YouTube videos accompanying the book, great for self-learning as wellNew additional sections and chapters are added for the second edition, for selected more advanced topics, leading to pathways of further study