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Chapter 1 Mathematical Renew and Introduction
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1£®1Mathematical Review
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1£®2Errors
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1£®3Avoiding the Loss of Accuracy
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Chapter 2 Solutions of Nonlinear Equations
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2£®1Bisection Method
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2£®2Fixed-Point Iteration
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2£®3Newton-Raphson Iteration
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2£®4 Secant Method
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2£®5Rate of Convergence
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Chapter 3 Solutions of Linear Systems of Equations
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3£®1Gaussian Elimination Method
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3£®1£®1Backward Substitution Method
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3£®1£®2Gaussian Elimination with Backward Substitution
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3£®1£®3Gaussian Elimination with Pivoting
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3£®1£®4Gaussian Elimination on Tridiagonal Linear System
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3£®2Matrix Factorization
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3£®3Iteration Methods
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3£®3£®1NOITflS of Vectors and Matrices
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3£®3£®2 Jacobi Iteration
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3£®3£®3Gauss-Seidel Iteration
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3£®3£®4Convergence of Iteration Methods
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Chapter 4 Interpolation and Polynomial Approximation
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4£®1Interpolation Problem
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4£®2Lagrange Interpolation
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4£®3Newton Interpolation
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4£®4Hermite Interpolation
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4£®5Piecewise-Polynomial Interpolation
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4£®6Cubic Spline Interpolation
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Chapter 5 Curve Fitting
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5£®1Least Squares Problem
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5£®2Polynomial Fitting
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5£®2£®1Least-Squares Line
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5£®2£®2Least-Squares Parabola
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5£®2£®3Polynomial Fitting
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5£®2£®4Polynomial Wiggle
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5£®3Data Linearization
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Chapter 6 Numerical Differentiation and Numerical Integration
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6£®1Numerical Differentiation
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6£®2Elements of Numerical Quadrature
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6£®3Newton-Cotes Integration
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6£®4Composite Numerical Integration
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6£®5Romberg Integration
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6£®6Gauss-Legendre Integration
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Chapter 7 Solutions of Ordinary Differential Equations
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7£®1Elementary Theory of Initial-Value Problems
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7£®2Euler's Method
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7£®3Modified Euler Method
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7£®4Runge-Kutta Methods
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References
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Appendix Math Expressions and Pronunciations
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