Linear Algebra for Computational Sciences and Engineering

Beschreibung

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.
It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who needa theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.
It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who needa theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.

Second Edition contains over 150 pages of new material, including theory, illustrations, pseudocodes and examples throughout. Includes new information on matrices, vector spaces and linear mapping. Covers all aspects of linear algebra from the perspective of computational science and engineering Provides both a technical approach and an informal interpretation of mathematics Includes examples with definitions and theorems, as well as end-of-chapter exercises with solutions Presents a chapter where the study of an electrical network is shown as an algebraic exercise

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Themen in »Linear Algebra for Computational Sciences and Engineering«

Boolean algebra Linear mappings Set theory Matrices Systems of linear equations Vectors Complex numbers Polynomials Geometry Conics Vector spaces Graph theory Electrical networks Electrical circuits matrix theory

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“The book is well written, structured, and very intuitive. Every concept is thoroughly introduced and theorems are rigorously proved. Definitions and proofs are explained in a clear and friendly way.” (Ctirad Matonoha, zbMATH 1442.15001, 2020)

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