Engineering Mathematics by Example Vol I Algebra and Linear Algebra 2nd Edition by Robert Sobot ISBN ‎ 3031411994 ‎ 978-3031411991

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ISBN 10:‎ 3031411994
ISBN 13:  ‎ 978-3031411991
Author:  Robert Sobot

This textbook is a complete, self-sufficient, self-study/tutorial-type source of mathematical problems. It serves as a primary source for practicing and developing mathematical skills and techniques that will be essential in future studies and engineering practice. Rigor and mathematical formalism is drastically reduced, while the main focus is on developing practical skills and techniques for solving mathematical problems, given in forms typically found in engineering and science. These practical techniques cover the subjects of algebra, complex algebra, linear algebra, and calculus of single and multiple argument functions. In addition, the second part of the book covers problems on Convolution and Fourier integrals/sums of typical functions used in signal processing.

 

• Offers a large collection of progressively more sophisticated mathematical problems on main mathematical topics required for engineers/scientists;
• Provides, at the beginning of each topic, a brief review of definitions and formulas that are about to be used and practiced in the following problems;
• Includes tutorial-style, complete solutions, to all problems.

Engineering Mathematics by Example Vol. I: Algebra and Linear Algebra 2nd Table of contents:

Preface

• About This Book
• How to Use This Book
• Acknowledgments

Chapter 1: Basic Algebra

• 1.1 Introduction to Algebraic Expressions
• 1.2 Simplification of Algebraic Expressions
• 1.3 Solving Linear Equations
• 1.4 Solving Quadratic Equations
• 1.5 Factorization Techniques
• 1.6 Polynomial Functions
• 1.7 Rational Expressions and Equations
• 1.8 Radical Expressions
• 1.9 Applications of Algebra in Engineering

Chapter 2: Systems of Linear Equations

• 2.1 Introduction to Systems of Equations
• 2.2 Solving Systems of Linear Equations by Substitution
• 2.3 Solving Systems of Linear Equations by Elimination
• 2.4 Solving Systems of Linear Equations Using Matrices
• 2.5 Gaussian Elimination Method
• 2.6 Cramer’s Rule
• 2.7 Application of Linear Systems in Engineering

Chapter 3: Matrices and Determinants

• 3.1 Introduction to Matrices
• 3.2 Types of Matrices
• 3.3 Matrix Operations: Addition, Subtraction, and Scalar Multiplication
• 3.4 Matrix Multiplication
• 3.5 The Determinant of a Matrix
• 3.6 Properties of Determinants
• 3.7 The Inverse of a Matrix
• 3.8 Solving Systems of Linear Equations Using the Inverse Matrix
• 3.9 Applications of Matrices in Engineering

Chapter 4: Vector Spaces

• 4.1 Introduction to Vectors
• 4.2 Vector Operations: Addition, Scalar Multiplication
• 4.3 Linear Independence and Dependence
• 4.4 Basis and Dimension of a Vector Space
• 4.5 Subspaces and Their Properties
• 4.6 Applications of Vectors in Engineering

Chapter 5: Eigenvalues and Eigenvectors

• 5.1 Introduction to Eigenvalues and Eigenvectors
• 5.2 Finding Eigenvalues and Eigenvectors of Matrices
• 5.3 Diagonalization of Matrices
• 5.4 Properties of Eigenvalues and Eigenvectors
• 5.5 Applications of Eigenvalues and Eigenvectors in Engineering

Chapter 6: Linear Transformations

• 6.1 Introduction to Linear Transformations
• 6.2 Matrix Representation of Linear Transformations
• 6.3 Properties of Linear Transformations
• 6.4 Kernel and Image of a Linear Transformation
• 6.5 Applications of Linear Transformations in Engineering

Chapter 7: Inner Product Spaces

• 7.1 Introduction to Inner Product Spaces
• 7.2 The Dot Product
• 7.3 Norms and Distances in Inner Product Spaces
• 7.4 Orthogonality and Orthonormality
• 7.5 Gram-Schmidt Orthogonalization Process
• 7.6 Applications of Inner Product Spaces in Engineering

Chapter 8: Applications of Algebra and Linear Algebra in Engineering

• 8.1 Engineering Problems Involving Linear Systems
• 8.2 Structural Analysis and Matrix Methods
• 8.3 Control Systems and Stability Analysis
• 8.4 Electrical Circuit Analysis Using Matrices
• 8.5 Signal Processing and Eigenvalues
• 8.6 Optimization Problems in Engineering

Chapter 9: Advanced Topics (Optional)

• 9.1 Jordan Canonical Form
• 9.2 Singular Value Decomposition
• 9.3 Advanced Applications in Engineering

Appendices

• A. Mathematical Tables
• B. Solutions to Selected Problems
• C. Further Reading and Resources
• D. Index

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Robert Sobot,Engineering Mathematics,Linear Algebra