دانلود کتاب Matrices in Engineering Problems

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Preface
Matrix Fundamentals
Definition of A Matrix
Notation
Elemetary Matrix Algebra
Addition (Including Subtraction)
Multiplication by A Scalar
Vector Multiplication
Matrix Multiplication
Transposition
Basic Types of Matrices
The Unit Matrix
The Diagonal Matrix
Orthogonal Matrices
Triangular Matrices
Symmetric and Skew-Symmetric Matrices
Complex Matrices
The Inverse Matrix
Transformation Matrices
Matrix Partitioning
Interesting Vector Products
An Interpretation of Ax = c
The (nX1X1Xn) Vector Product
Vector Cross Product
Examples
An Example Matrix Multiplication
An Example Matrix Triple Product
Multiplication of Complex Matrices
Exercises
Determinants
Introduction
General Definition of a Determinant
Permutations and Inversions of Indices
Inversions
An Example Determinant Expansion
Properties of Determinants
The Rank of a Determinant
Minors and Cofactors
Expansions by Minors—LaPlace Expansions
Expansion by Lower Order Minors
The Determinant of a Matrix Product
Geometry: Lines, Areas, and Volumes
The Adjoint and Inverse Matrices
Rank of the Adjoint Matrix
Determinant Evaluation
Pivotal Condensation
Gaussian Reduction
Rank of the Determinant Less Than n
Examples
Cramer\'s Rule
An Example Complex Determinant
The ``Characteristic Determinant\'\'
Exercises
Matrix Inversion
Introduction
Elementary Operations in Matrix Form
Diagonalization Using Elementary Matrices
Gauss-Jordan Reduction
Singular Matrices
The Gauss Reduction Method
Gauss Reduction in Detail
Example Gauss Reduction
LU Decomposition
LU Decomposition in Detail
Example LU Decomposition
Matrix Inversion By Partitioning
Additional Topics
Column Normalization
Improving the Inverse
Inverse of a Triangular Matrix
Inversion by Orthogonalization
Inversion of a Complex Matrix
Examples
Inversion Using Partitions
Exercises
Linear Simultaneous Equation Sets
Introduction
Vectors and Vector Sets
Linear Independence of a Vector Set
Rank of a Vector Set
Simultaneous Equation Sets
Square Equation Sets
Underdetermined Equation Sets
Overdetermined Equation Sets
Linear Regression
Example Regression Problem
Quadratic Curve Fit
Lagrange Interpolation Polynomials
Interpolation
The Lagrange Polynomials
Exercises
Orthogonal Transforms
Introduction
Orthogonal Matrices and Transforms
Righthanded Coordinates, and Positive Angle
Example Coordinate Transforms
Earth-Centered Coordinates
Rotation About a Vector (Not a Coordinate Axis)
Rotation About all Three Coordinate Axes
Solar Angles
Image Rotation in Computer Graphics
Congruent and Similarity Matrix Transforms
Differentiation of Matrices, Angular Velocity
Velocity of a Point on a Wheel
Dynamics of a Particle
Rigid Body Dynamics
Rotation of a Rigid Body
Moment of Momentum
The Inertia Matrix
The Torque Equation
Examples
Exercises
Matrix Eigenvalue Analysis
Introduction
The Eigenvalue Problem
The Characteristic Equation and Eigenvalues
Synthesis of A by its Eigenvalues and Eigenvectors
Example Analysis of a Nonsymmetric 3X3
Eigenvalue Analysis of Symmetric Matrices
Geometry of the Eigenvalue Problem
Non-Symmetric Matrices
Matrix with a Double Root
The Eigenvectors and Orthogonality
Inverse of the Characteristic Matrix
Vibrating String Problem
The Cayley-Hamilton Theorem
Functions of a Square Matrix
Sylvester\'s Theorem
Mechanics of the Eigenvalue Problem
Calculating the Characteristic Equation Coefficients
Factoring the Characteristic Equation
Calculation of the Eigenvectors
Example Eigenvalue Analysis
Example Eigenvalue Analysis; Complex Case
Eigenvalues by Matrix Iteration
The Eigenvalue Analysis of Similar Matrices; Danilevsky\'s Method
Danilevsky\'s Method
Example of Danilevsky\'s Method
Danilevsky\'s Method—Zero Pivot
Exercises
Matrix Analysis of Vibrating Systems
Introduction
Setting up Equations, Lagrange\'s Equations
Generalized Form of Lagrange\'s Equations
Mechanical / Electrical Analogies
Examples using the Lagrange Equations
Vibration of Conservative Systems
Conservative Systems – The Initial Value Problem
Interpretation of Equation (7.23)
Conservative Systems - Sinusoidal Response
Vibrations in a Continuous Medium
Nonconservative Systems. Viscous Damping
The Initial Value Problem
Sinusoidal Response
Determining the Vector Coefficients for the Driven System
Sinusoidal Response – NonZero Initial Conditions
Steady State Sinusoidal Response
Analysis of Ladder Networks; The Cumulant
Runge-Kutta Integration of Differential Equations
Exercises
Partial Differentiation of Bilinear and Quadratic Forms
Polynomials
Polynomial Basics
Polynomial Arithmetic
Evaluating a Polynomial at a Aiven Value
Evaluating Polynomial Roots
The Laguerre Method
The Newton Method
An Example
The Vibrating String
The Digitized – Matrix Solution
The Continuous Function Solution
Exercises
Solar Energy Geometry
Yearly Energy Output
An Example
Tracking the Sun
Answers to Selected Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Bibliography
Author\'s Biography
Index