chapter 1 solution of nonlinear equations f (x)= 0 非线方程f (x) = 0的解法 1.1 iteration for solving x = g(x) 求解x = g(x)的迭代法 1.2 bracketing methods for locating a root 定位一个根的分类方法 1.3 newton-raphson and secant methods 牛顿-拉夫森法和割线法 chapter 2 solution of linear systems ax = b 线方程组ax = b的数值解法 2.1 upper-triangular linear systems 上三角线方程组 2.2 gaussian elimination and pivoting 高斯消去法和选主元 2.3 triangular factorization 三角分解法 2.4 iterative methods for linear systems 求解线方程组的迭代法 2.5 iteration for nonlinear systems (optional) 非线方程组的迭代法(选读) chapter 3 interpolation and polynomial appromation 插值与多项式逼近 3.1 taylor series and calculation of functions 泰勒级数和函数计算 3.2 introduction to interpolation 插值简介 3.3 lagrange appromation 拉格朗逼近 3.4 newton polynomials 牛顿多项式 3.5 chebyshev polynomials (optional) 切比雪夫多项式(选读) 3.6 padé appromations 帕德逼近 chapter 4 curve fitting 曲线拟合 4.1 least-squares line 小二乘拟合曲线 4.2 methods of curve fitting 曲线拟合 4.3 interpolation by spline functions 样条函数插值 4.4 bézier curves 贝塞尔曲线 chapter 5 numerical integration 数值积分 5.1 introduction to quadrature 积分简介 5.2 ite trapezoidal and simon’s rule 组合梯形公式和辛普森公式 5.3 recursive rules and romberg integration 递归公式与龙贝格积分 5.4 gauss-legendre integration (optional) 高斯-勒让德积分(选读) chapter 6 solution of differential equations 微分方程求解 6.1 introduction to differential equations 微分方程简介 6.2 euler’s method 欧拉方法 6.3 heun’s method 休恩方法 appendix a introduction to matlab matlab简介 appendix b some math expressions and pronunciations 一些数学表达式及其读法 appendix c 1000 english-chinese math key words 1000英汉数学词汇
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