Linear Algebra to Differential Equations

J. Vasundhara Devi, Sadashiv G. Deo, Ramakrishna Khandeparkar

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN: 9780815361466
• eBook ISBN: 9781351014939
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Linear Algebra to Differential Equations concentrates on the essential topics necessary for all engineering students in general and computer science branch students, in particular. Specifically, the topics dealt will help the reader in applying linear algebra as a tool.

The advent of high-speed computers has paved the way for studying large systems of linear equations as well as large systems of linear differential equations. Along with the standard numerical methods, methods that curb the progress of error are given for solving linear systems of equations.

The topics of linear algebra and differential equations are linked by Kronecker products and calculus of matrices. These topics are useful in dealing with linear systems of differential equations and matrix differential equations. Differential equations are treated in terms of vector and matrix differential systems, as they naturally arise while formulating practical problems. The essential concepts dealing with the solutions and their stability are briefly presented to motivate the reader towards further investigation.

This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics. Further, the book provides a quick and complete overview of linear algebra and introduces linear differential systems, serving the basic requirements of scientists and researchers in applied fields.

Features

• Provides complete basic knowledge of the subject
• Exposes the necessary topics lucidly
• Introduces the abstraction and at the same time is down to earth
• Highlights numerical methods and approaches that are more useful
• Essential techniques like SVD and PCA are given
• Applications (both classical and novel) bring out similarities in various disciplines:
• Illustrative examples for every concept: A brief overview of techniques that hopefully serves the present and future needs of students and scientists.

Chapter 1

Vectors and Matrices

DOI: 10.1201/9781351014953-1

1.1 Introduction

This is the foundation chapter for the book. The building blocks of all the topics covered in the book constitute this chapter. Section 1.2 begins with the definitions of a scalar and vector and proceeds with the study of their properties. These properties provide a base for the theory developed in later chapters. Matrices are introduced in terms of vectors in Section 1.3. This definition is useful as nearly in all applications a matrix consisting of linearly independent vectors or ortho-normal vectors is utilized ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• 1 Vectors and Matrices
• 2 Linear System of Equations
• 3 Vector Spaces
• 4 Numerical Methods in Linear Algebra
• 5 Applications
• 6 Kronecker Product
• 7 Calculus of Matrices
• 8 Linear Systems of Differential Equations
• 9 Linear Matrix Differential Equations
• Bibliography
• Answers
• Index