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Table of Contents
1. Roots of algebraic and transcendental equations
1.1 Equations
1.2 Polynomials
1.3 Descartes' rule
1.4 Synthetic division
1.5 Incremental search method
1.6 Refined incremental search method
1.7 Bisection method
1.8 Method of false position or linear interpolation
1.9 Secant method
1.10 Newton-Raphson method or Newton's tangent
1.11 Newton's second order method
1.12 Graeffe's root squaring method
1.13 Bairstow's method
References
2. Solutions of simultaneous linear algebraic equations using matrix algebra
2.1 Simultaneous equations
2.2 Matrices
2.3 Matrix operations
2.4 Cramer's rule
2.5 Method of adjoints or cofactor method
2.6 Gaussian elimination method
2.7 Gauss-Jordan elimination method
2.8 Improved Gauss-Jordan elimination method
2.9 Cholesky decomposition method
2.10 Error equations
2.11 Matrix inversion method
2.12 Gauss-Seidel iteration method
2.13 Eigenvalues by Cramer's rule
2.14 Faddeev-Leverrier method
2.15 Power method or iteration method
References
3. Numerical integration and differentiation
3.1 Trapezoidal rule
3.2 Romberg integration
3.3 Simpson's rule
3.4 Gaussian quadrature
3.5 Double integration by Simpson's one-third rule
3.6 Double integration by Gaussian quadrature
3.7 Taylor series polynomial expansion
3.8 Difference operators by Taylor series expansion
3.9 Numeric modeling with difference operators
3.10 Partial differential equation difference operators
3.11 Numeric modeling with partial difference operators
References
4. Matrix structural stiffness
4.1 Matrix transformations and coordinate systems
4.2 Rotation matrix
4.3 Transmission matrix
4.4 Area moment method
4.5 Conjugate beam method
4.6 Virtual work
4.7 Castigliano's theorems
4.8 Slope-deflection method
4.9 Moment-distribution method
4.10 Elastic member stiffness, X-Z system
4.11 Elastic member stiffness, X-Y system
4.12 Elastic member stiffness, 3-D system
4.13 Global joint stiffness
References
5. Advanced structural stiffness
5.1 Member end releases, X-Z system
5.2 Member end releases, X-Y system
5.3 Member end releases, 3-D system
5.4 Non-prismatic members
5.5 Shear stiffness, X-Z system
5.6 Shear stiffness, X-Y system
5.7 Shear stiffness, 3-D system
5.8 Geometric stiffness, X-Y system
5.9 Geometric stiffness, X-Z system
5.10 Geometric stiffness, 3-D system
5.11 Geometric and shear stiffness
5.12 Torsion
5.13 Sub-structuring
References
About the authors
Index.
1.1 Equations
1.2 Polynomials
1.3 Descartes' rule
1.4 Synthetic division
1.5 Incremental search method
1.6 Refined incremental search method
1.7 Bisection method
1.8 Method of false position or linear interpolation
1.9 Secant method
1.10 Newton-Raphson method or Newton's tangent
1.11 Newton's second order method
1.12 Graeffe's root squaring method
1.13 Bairstow's method
References
2. Solutions of simultaneous linear algebraic equations using matrix algebra
2.1 Simultaneous equations
2.2 Matrices
2.3 Matrix operations
2.4 Cramer's rule
2.5 Method of adjoints or cofactor method
2.6 Gaussian elimination method
2.7 Gauss-Jordan elimination method
2.8 Improved Gauss-Jordan elimination method
2.9 Cholesky decomposition method
2.10 Error equations
2.11 Matrix inversion method
2.12 Gauss-Seidel iteration method
2.13 Eigenvalues by Cramer's rule
2.14 Faddeev-Leverrier method
2.15 Power method or iteration method
References
3. Numerical integration and differentiation
3.1 Trapezoidal rule
3.2 Romberg integration
3.3 Simpson's rule
3.4 Gaussian quadrature
3.5 Double integration by Simpson's one-third rule
3.6 Double integration by Gaussian quadrature
3.7 Taylor series polynomial expansion
3.8 Difference operators by Taylor series expansion
3.9 Numeric modeling with difference operators
3.10 Partial differential equation difference operators
3.11 Numeric modeling with partial difference operators
References
4. Matrix structural stiffness
4.1 Matrix transformations and coordinate systems
4.2 Rotation matrix
4.3 Transmission matrix
4.4 Area moment method
4.5 Conjugate beam method
4.6 Virtual work
4.7 Castigliano's theorems
4.8 Slope-deflection method
4.9 Moment-distribution method
4.10 Elastic member stiffness, X-Z system
4.11 Elastic member stiffness, X-Y system
4.12 Elastic member stiffness, 3-D system
4.13 Global joint stiffness
References
5. Advanced structural stiffness
5.1 Member end releases, X-Z system
5.2 Member end releases, X-Y system
5.3 Member end releases, 3-D system
5.4 Non-prismatic members
5.5 Shear stiffness, X-Z system
5.6 Shear stiffness, X-Y system
5.7 Shear stiffness, 3-D system
5.8 Geometric stiffness, X-Y system
5.9 Geometric stiffness, X-Z system
5.10 Geometric stiffness, 3-D system
5.11 Geometric and shear stiffness
5.12 Torsion
5.13 Sub-structuring
References
About the authors
Index.