Circuits Matrices and Linear Vector Spaces 1st edition by Lawrence Huelsman ISBN ‎ 048648534X 978-0486485348

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ISBN 10: ‎ 048648534X
ISBN 13: 978-0486485348
Author: Lawrence Huelsman 

This high-level undergraduate text explains the mathematics behind basic circuit theory. Its self-contained treatment covers matrix algebra, which provides a general means of formulating the details of a linear system. In addition, the author presents the basic theory of n-dimensional spaces and demonstrates its application to linear systems.
A development of the mathematics of matrix algebra and determinants is followed by the application of matrix techniques to a general discussion of circuits. Subsequent topics include the properties of active and passive two-port devices, the basic theory of linear vector spaces, and the natural frequencies of a network. Appendixes cover the indefinite-transfer matrix, gyrators with complex gyration admittance, and network transformations. A wealth of equations and calculation problems appear throughout the text.

Circuits, Matrices and Linear Vector Spaces 1st Table of contents:

• Introduction to Electrical Circuits

  • 1.1. Basic Components of Electrical Circuits
  • 1.2. Ohm’s Law and Kirchhoff’s Laws
  • 1.3. Circuit Analysis: Techniques and Methods
  • 1.4. Power and Energy in Circuits
  • 1.5. AC and DC Circuits: A Comparison

• Chapter 1: Matrices and Their Properties

  • 2.1. Definition and Types of Matrices
  • 2.2. Matrix Operations: Addition, Subtraction, and Multiplication
  • 2.3. Inverse Matrices and Determinants
  • 2.4. Special Matrices: Symmetric, Diagonal, Identity
  • 2.5. Matrix Rank and Its Importance

• Chapter 2: Linear Systems and Vector Spaces

  • 3.1. Introduction to Linear Systems
  • 3.2. Vector Spaces: Definition and Properties
  • 3.3. Linear Independence and Basis
  • 3.4. Subspaces and Spanning Sets
  • 3.5. Linear Transformations and Matrices

• Chapter 3: Circuit Analysis using Matrices

  • 4.1. Matrix Representation of Circuits
  • 4.2. Solving Circuits Using Linear Algebra
  • 4.3. Node-Voltage Method and Mesh Current Method
  • 4.4. The Role of Matrices in Solving Linear Circuit Systems
  • 4.5. Matrix Decomposition in Circuit Analysis

• Chapter 4: Eigenvalues and Eigenvectors

  • 5.1. Introduction to Eigenvalues and Eigenvectors
  • 5.2. Solving for Eigenvalues and Eigenvectors
  • 5.3. Applications of Eigenvalues in Circuit Theory
  • 5.4. Diagonalization of Matrices
  • 5.5. Stability Analysis in Electrical Circuits

• Chapter 5: Linear Transformations in Electrical Engineering

  • 6.1. What are Linear Transformations?
  • 6.2. Matrix Representation of Linear Transformations
  • 6.3. Transformations in Circuit Analysis
  • 6.4. System of Equations and Circuit Behavior
  • 6.5. Applications in Signal Processing and Control Systems

• Chapter 6: Advanced Circuit Analysis

  • 7.1. Frequency Response and Impedance
  • 7.2. The Laplace Transform in Circuit Analysis
  • 7.3. State-Space Representation of Circuits
  • 7.4. Stability and Control of Circuit Systems
  • 7.5. Feedback Systems and Linear Control

• Chapter 7: Fourier Analysis and Circuit Behavior

  • 8.1. Introduction to Fourier Series
  • 8.2. Fourier Transforms in Circuit Analysis
  • 8.3. Circuit Behavior in the Frequency Domain
  • 8.4. Applications in Communication and Signal Processing
  • 8.5. The Role of Linear Vector Spaces in Fourier Analysis

• Chapter 8: Numerical Methods in Circuit Simulation

  • 9.1. Overview of Numerical Methods
  • 9.2. Numerical Techniques for Solving Linear Systems
  • 9.3. Simulation of Circuits Using MATLAB and Python
  • 9.4. Time Domain and Frequency Domain Simulations
  • 9.5. Solving Nonlinear Circuits Using Numerical Methods

• Appendices

  • A.1. Mathematical Review: Linear Algebra Concepts
  • A.2. Circuit Analysis Tools and Software
  • A.3. Sample Problems and Solutions
  • A.4. Glossary of Terms

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