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数值分析双语教程檀结庆科学出版社 PDF电子教材 PDF电子书大学教材电子版电子课本网盘下载（价值119元）【高清非扫描版】（2023年9月）

工信部“十四五”规划教材《数值分析双语教程》檀结庆科学出版社 PDF电子教材 PDF电子书大学教材电子版电子课本网盘下载（价值119元）【高清非扫描版】（2023年9月）

图书简介：

《数值分析双语教程》系双语教材，主体部分用英语撰写，延伸阅读部分用汉语撰写. 主体部分主要内容包括：常见数学公式和数学表达式的英语读法、解线性方程组的直接法、矩阵代数迭代技术、一元方程求根、多项式插值、逼近论、数值微分与数值积分、常微分方程初值问题等. 延伸阅读部分内容包括：数学家传记、求解非线性方程组的*小二乘法、非线性方程组的不动点迭代法、牛顿迭代法及拟牛顿迭代法、有理函数插值、Thiele 型连分式插值、Padé 逼近、*佳一致逼近、高斯求积公式的收敛性、Radau 求积公式与Lobatto 求积公式、Euler-Maclaurin 展开、常微分方程边值问题等.

前言
Chapter 1 Mathematical Preliminaries (数学基础知识) 1
1.1 Mathematics English (数学英语) 1
1.2 Review of calculus (微积分回顾) 4
1.2.1 Limits and continuity (极限和连续性 ) 4
1.2.2 Differentiability (可微性) 6
1.2.3 Integration (积分) 6
1.2.4 Taylor polynomials and series (泰勒多项式和级数) 7
1.2.5 Examples (例题) 8
1.3 Errors and significant digits (误差和有效数字 ) 9
1.3.1 Source of errors (误差的来源) 9
1.3.2 Absolute error and relative error (绝对误差和相对误差) 11
1.3.3 Significant digit (or figure) (有效数字) 11
1.3.4 How to avoid the loss of accuracy (如何避免精度的丢失) 12
1.3.5 Examples (例题) 12
1.4本章要点 (Highlights) 14
1.5问题讨论 (Questions for discussion) 14
1.6关键术语 (Key terms) 14
1.7延伸阅读 (Extending reading) 15
1.7.1 背景知识 15
1.7.2 数学家传记：泰勒 (Taylor) 16
1.7.3 数学家传记：黎曼 (Riemann) 16
1.8习题 (Exercises) 18 Chapter 2 Direct Methods for Solving Linear Systems (解线性方程组的直接法) 21
2.1 Gauss elimination method (Gauss消元法 ) 21
2.1.1 Some preliminaries (预备知识) 21
2.1.2 Gauss elimination with backward-substitution process(可回代的 Gauss 消元法) 23
2.2 Pivoting strategies (选主元策略) 27
2.2.1 Partial pivoting (maximal column pivoting) (最大列主元) 28
2.2.2 Scaled partial pivoting (scaled-column pivoting) (按比例列主元) 29
2.3 Matrix factorization (矩阵分解法) 31
2.3.1 Doolittle factorization (Doolittle分解) 32
2.3.2 Crout factorization (Crout分解) 38
2.3.3 Permutation matrix (置换矩阵) 38
2.4 Special types of matrices (特殊形式矩阵的三角分解) 39
2.4.1 Strictly diagonally dominant matrix (严格对角占优矩阵 ) 39
2.4.2 Positive definite matrix (正定矩阵) 41
2.4.3 Strictly diagonally dominant tridiagonal matrix (严格对角占优三对角矩阵) 42
2.5本章算法程序及实例 (Algorithms and examples) 45
2.5.1 Gauss消元法 (Gauss elimination method) 45
2.5.2 选主元策略 (Pivoting strategies) 46
2.5.3 LU分解法 (LU decomposition) 48
2.6本章要点 (Hightlights) 49
2.7问题讨论 (Questions for discussion) 49
2.8 关键术语 (Key terms) 50
2.9 延伸阅读 (Extending reading) 51
2.10习题 (Exercises) 54 Chapter 3 Iterative Techniques in Matrix Algebra (矩阵代数迭代技术) 57
3.1 Norms of vectors and matrices (向量范数与矩阵范数) 58
3.1.1 Vector norm (向量范数 ) 58
3.1.2 Distance between vectors (向量之间的距离) 59
3.1.3 Matrix norm and distance (矩阵范数和距离) 60
3.1.4 Examples (例题) 61
3.2 Eigenvalues and eigenvectors (特征值和特征向量 ) 62
3.2.1 Eigenvalues and eigenvectors (特征值和特征向量) 63
3.2.2 Spectral radius (谱半径) 63
3.2.3 Convergent matrices (收敛矩阵 ) 64
3.2.4 Examples (例题) 64
3.3 Iterative techniques for solving linear systems (解线性方程组的迭代法 ) 66
3.3.1 Jacobi iterative method (Jacobi迭代法) 67
3.3.2 Gauss-Seidel iterative method (Gauss-Seidel迭代法) 68
3.3.3 General iteration method (一般迭代法) 69
3.3.4 Examples (例题) 70
3.4 Convergence analysis and SOR iterative method (收敛性分析与 SOR迭代法) 72
3.4.1 Convergence analysis (收敛性分析) 72
3.4.2 SOR iterative method (SOR迭代法) 73
3.4.3 SOR iterative method in matrix form (矩阵形式的 SOR迭代法) 74
3.4.4 Examples (例题) 75
3.5 Condition number and iterative refinement (条件数和迭代优化 ) 77
3.5.1 Condition number (条件数) 77
3.5.2 Iterative refinement (迭代优化) 79
3.5.3 Examples (例题) 80
3.6本章算法程序及实例 (Algorithms and examples) 82
3.6.1 雅可比迭代法 (Jacobi iterative method) 82
3.6.2 高斯-赛德尔迭代法 (Gauss-Seidel iterative method) 83
3.6.3 SOR迭代法 (SOR iterative method) 84
3.7本章要点 (Highlights) 85
3.8问题讨论 (Questions for discussion) 86
3.9关键术语 (Key terms) 87
3.10延伸阅读 (Extending reading) 87
3.10.1 背景知识 87
3.10.2 数学家传记：高斯 (Gauss) 88
3.10.3 数学家传记：雅可比 (Jacobi) 89
3.11习题 (Exercises) 90 Chapter 4 Solutions of Equations in One Variable (一元方程求根) 98
4.1 Bisection method (二分法 ) 99
4.2 Fixed-point iteration and error analysis (不动点迭代及误差分析 ) 101
4.2.1 Fixed-point iteration (不动点迭代法) 101
4.2.2 Convergence analysis and error estimation (收敛性分析和误差估计) 101
4.2.3 The order of convergence (收敛阶) 104
4.3 Newton’s method (牛顿法) 105
4.3.1 Newton’s method and convergence analysis (牛顿法及其收敛性分析) 105
4.3.2 How to handle multiple roots using Newton’s method (如何采用牛顿法处理重根问题) 107
4.4 The secant method (弦截法 ) 111
4.5本章算法程序及实例 (Algorithms and examples) 113
4.5.1 二分法求方程的根 (Root finding by bisection method) 113
4.5.2 不动点迭代法求方程的根 (Root finding by fix point iteration) 113
4.5.3 牛顿法求方程的根 (Root finding by Newton’s method) 114
4.5.4 牛顿法求一元方程重根(未知重数) (Multiple root finding by Newton’s method) 115
4.5.5 割线法求方程的根 (Root finding by secant method) 116
4.6本章要点 (Highlights) 117
4.7问题讨论 (Questions for discussion) 118
4.8关键术语 (Key terms) 118
4.9延伸阅读 (Extending reading) 119
4.10习题 (Exercises) 127 Chapter 5 Interpolation by Polynomials (多项式插值) 129
5.1 Lagrange interpolation (Lagrange插值) 130
5.1.1 Linear interpolation (线性插值) 130
5.1.2 Quadratic interpolation(二次插值) 131
5.1.3 nth-order polynomial interpolation ( n次多项式插值) 132
5.1.4 Uniqueness of interpolation (插值的唯一性) 133
5.1.5 Lagrange error formula (Lagrange误差公式) 134
5.1.6 Examples (例题) 135
5.2 Neville interpolation (Neville 插值) 139
5.3 Newton interpolation (Newton插值) 143
5.3.1 Definition of divided differences (差商的定义) 144
5.3.2 Newton’s expansion of a function (函数的 Newton展开) 145
5.3.3 Properties of divided differences (差商的性质) 146
5.3.4 Computation of Newton’s interpolant (Newton插值的计算) 151
5.3.5 The relationship between divided differences and derivatives (差商与导数的关系) 153
5.3.6 Relations between Newton’s expansion and Taylor’s expansion (Newton展开与 Taylor展开之间的关系) 154
5.3.7 Comparisons among Lagrange, Neville and Newton interpolations (Lagrange插值、Neville插值与 Newton插值之间的比较) 154
5.3.8 Newton forward divided-difference formula (Newton向前差商公式) 156
5.3.9 Newton forward difference formula (Newton向前差分公式) 157
5.3.10 Newton backward divided-difference formula (Newton向后差商公式) 159
5.3.11 Newton backward-difference formula (Newton向后差分公式) 160
5.4 Hermite interpolation (Hermite插值) 164
5.4.1 Two-point Hermite interpolation (两点 Hermite插值) 164
5.4.2 General Hermit interpolation (一般 Hermite插值) 166
5.4.3 Examples (例题) 169
5.5 Cubic spline interpolation (三次样条插值) 172
5.5.1 Runge phenomenon (Runge现象) 172
5.5.2 Piecewise linear interpolation (分段线性插值) 172
5.5.3 Piecewise cubic interpolation (分段三次插值) 174
5.5.4 Definition of cubic splines (三次样条的定义) 176
5.5.5 Derivation of cubic splines (三次样条的推导) 177
5.5.6 Examples (例题) 179
5.6 本章算法程序及实例 (Algorithms and examples) 187
5.6.1 拉格朗日插值 (Lagrange interpolation) 187
5.6.2 Neville 插值 (Neville interpolation) 189
5.6.3 牛顿插值 (Newton interpolation) 190
5.6.4 牛顿向前差商插值 (Interpolation by Newton forward divided differences) 192
5.6.5 牛顿向后差商插值 (Interpolation by Newton backward divided differences) 194
5.6.6 埃尔米特插值 (Hermite interpolation) 196
5.6.7 分段线性插值 (Piecewise linear interpolation) 197
5.6.8 分段三次插值 (Piecewise cubic interpolation) 198
5.6.9 三次样条插值 1 (边界条件：固支边界) (Cubic spline interpolation with clamped boundary) 200
5.6.10 三次样条插值 2 (边界条件为自然边界) (Cubic spline interpolation with natural boundary ) 202
5.7 本章要点 (Hightlights) 204
5.8 问题讨论 (Questions for discussion) 205
5.9 关键术语 (Key terms) 205
5.10 延伸阅读 (Extending reading) 207
5.10.1 有理函数插值 (Interpolation by rational functions) 207
5.10.2 Thiele型连分式插值 (Interpolation by Thiele type continued fractions) 209
5.10.3 Padé逼近 (Padé approximation) 212
5.10.4 数学家简介: 牛顿 (Newton) 212
5.10.5 数学家简介: 拉格朗日 (Lagrange) 213
5.10.6 数学家简介: 埃尔米特 (Hermite) 214
5.11习题 (Exercises) 215 Chapter 6 Approximation Theory (逼近论) 223
6.1 Discrete least squares approximation (离散昀小二乘逼近) 223
6.1.1 Linear regression (线性回归) 224
6.1.2 Criteria for the “best” fit (最佳拟合准则) 224
6.1.3 Least squares fit of a straight line (最小二乘直线拟合) 225
6.1.4 Polynomial fitting (polynomial regression) (多项式拟合(多项式回归)) 226
6.1.5 Exponential fitting (指数拟合) 227
6.2 Orthogonal polynomials and least squares approximation (正交多项式和昀小平方逼近 ) 228
6.2.1 Basic ideas (基本思想) 228
6.2.2 Linearly independent functions (线性无关函数) 230
6.2.3 Orthogonal functions (正交函数) 233
6.2.4 Gram-Schmidt process (Gram-Schmidt 正交化) 233
6.3 Chebyshev polynomials and economization of power series (Chebyshev多项式与幂级数约化 ) 235
6.3.1 Definition of Chebyshev polynomial Tn(x)(Chebyshev多项式Tn(x)的定义) 236
6.3.2 Orthogonality of the Chebyshev polynomials (Chebyshev多项式的正交性) 236
6.3.3 The zeros and extreme points of Tn(x)(Tn(x)的零点与极值点) 237
6.3.4 Minimization property (极小性质) 238
6.3.5 Application of minimization property in polynomial interpolation (极小性质在多项式插值中的应用) 239
6.3.6 Economization of power series (幂级数的约化) 240
6.4本章算法程序及实例 (Algorithms and examples) 241
6.4.1 最小二乘法 (Discrete least squares approximation) 241
6.4.2 指数拟合 (Exponential fitting) 243
6.4.3 Gram-Schmidt正交化 (Gram-Schmidt process) 245
6.4.4 勒让德正交多项式 (Legendre orthogonal polynomials) 245
6.4.5 切比雪夫正交多项式 (Chebyshev orthogonal polynomials) 246
6.4.6 最佳平方逼近 (Least squares approximation) 247
6.5本章要点 (Hightlights) 248
6.6问题讨论 (Questions for discussion) 249
6.7 关键术语 (Key terms) 250
6.8 延伸阅读 (Extending reading) 251
6.9习题 (Exercises) 259 Chapter 7 Numerical Differentiation and Integration (数值微分与数值积分) 263
7.1 Numerical differentiation (数值微分) 264
7.1.1 Forward-difference formula (向前差分公式) 264
7.1.2 Backward-difference formula (向后差分公式) 265
7.1.3 Three-point formula (三点公式) 265
7.1.4 Five-point formula (五点公式) 266
7.1.5 Approximation to higher derivatives (高阶导数逼近) 269
7.1.6 Effect of round-off error (舍入误差影响) 271
7.1.7 Examples (例题) 272
7.2 Richardson’s extrapolation (Richardson外推) 273
7.2.1 Basic idea (基本思想) 273
7.2.2 Examples (例题) 276
7.3 Elements of numerical integration (数值积分) 281
7.3.1 Basic idea (基本思想) 282
7.3.2 Midpoint rule (中点公式) 283
7.3.3 Trapezoidal rule (梯形公式) 283
7.3.4 Simpson’s rule (Simpson公式) 284
7.3.5 Newton-Cotes formulas (Newton-Cotes公式) 286
7.3.6 Degree of accuracy (代数精度) 287
7.3.7 Examples (例题) 287
7.4 Composite numerical integration (复化数值积分 ) 289
7.4.1 Composite midpoint rule (复化中点公式) 290
7.4.2 Composite trapezoidal rule (复化梯形公式) 290
7.4.3 Composite Simpson’s rule (复化 Simpson公式) 291
7.4.4 Stability (稳定性) 292
7.5 Romberg integration (Romberg积分) 293
7.6 Gaussian quadrature (Gauss求积) 296
7.6.1 Basic idea (基本思想) 297
7.6.2 Two-point Gaussian quadrature (两点 Gauss求积公式) 298
7.6.3 Gaussian nodes (Gauss结点) 299
7.6.4 The error estimation for the Gaussian quadrature (Gauss求积的误差估计) 300
7.6.5 Method to get Gaussian quadrature (Gauss求积的方法 ) 301
7.6.6 Examples (例题) 302
7.7 本章算法程序及实例 (Algorithms and examples) 304
7.7.1 数值微分 (Numerical differentiation) 304
7.7.2 数值积分 (Numerical integration) 308
7.8 本章要点 (Highlights) 312
7.9 问题讨论 (Questions for discussion) 313
7.10 关键术语 (Key terms) 316
7.11 延伸阅读 (Extending reading) 317
7.11.1 Gauss求积公式的收敛性 (The Convergence of Gauss quadrature) 317
7.11.2 Radau求积公式与 Lobatto求积公式 (Radau quadrature and Lobatto quadrature) 320
7.11.3 Euler-Maclaurin 展开 (Euler-Maclaurin expansion) 330
7.12 习题 (Exercises) 338 Chapter 8 Initial-Value Problems for Ordinary Differential Equations (常微分方程初值问题) 345
8.1 The elementary theory of initial- value problem (初值问题基本理论 ) 345
8.1.1 Convex set (凸集) 346
8.1.2 Lipschitz condition (李普希茨条件) 346
8.1.3 Picard’s theorem (Picard定理) 347
8.1.4 Well-posed problem (适定问题) 351
8.2 Euler’s method (Euler方法) 354
8.2.1 Basic ideas of Euler’s method (Euler方法的基本思想) 354
8.2.2 Order of a method (方法的阶) 355
8.2.3 Implicit Euler’s scheme (隐式 Euler格式) 356
8.2.4 Two-step Euler’s scheme (两步 Euler格式) 356
8.2.5 Trapezoidal scheme (梯形格式) 357
8.2.6 Modified Euler scheme (改进的 Euler格式) 359
8.2.7 Error bounds for the Euler’s scheme (Euler格式的误差界) 360
8.3 Runge-Kutta method (Runge-Kutta方法) 363
8.3.1 Taylor polynomials in two variables (二元 Taylor多项式) 363
8.3.2 Basic ideas of Runge-Kutta method (Runge-Kutta方法的基本思想) 364
8.3.3 Runge-Kutta method of order two (二阶 Runge-Kutta方法) 365
8.3.4 Runge-Kutta method of order three (三阶 Runge-Kutta方法) 366
8.3.5 Runge-Kutta method of order four (四阶 Runge-Kutta方法) 366
8.4 Multistep methods (多步方法 ) 367
8.4.1 Adams explicit schemes (Adams显式格式) 367
8.4.2 Adams implicit schemes (Adams隐式格式) 370
8.5本章算法程序及实例 (Algorithms and examples) 371
8.5.1 Euler方法 (Euler’s scheme) 371
8.5.2 隐式 Euler方法 (Euler implicit scheme) 373
8.5.3 梯形方法 (Trapezoidal scheme) 374
8.5.4 改进的 Euler公式 (Modified Euler’s scheme) 375
8.5.5 二阶龙格-库塔方法 (Runge-Kutta order two) 377
8.5.6 三阶龙格-库塔方法 (Runge-Kutta order three) 379
8.5.7 四阶龙格-库塔方法 (Runge-Kutta order four) 380
8.6本章要点 (Hightlights) 382
8.7问题讨论 (Questions for discussion) 383
8.8关键术语 (Key terms) 384
8.9延伸阅读 (Extending reading) 385
8.10习题 (Exercises) 391
References (参考文献) 396