1 Mathematical Preliminaries and Error Analysis 2 Solutions of Equations in One Variable 3 Interpolation and Polynomial Approximation 4 Numerical Differentiation and Integration 5 Initial-Value Problems for Ordinary Differential Equations 6 Direct Methods for Solving Linear Systems 7 IterativeTechniques in Matrix Algebra 8 ApproximationTheory 9 Approximating Eigenvalues 10 Numerical Solutions of Nonlinear Systems of Equations 11 Boundary-Value Problems for Ordinary Differential Equations 12 Numerical Solutions to Partial Differential Equations

Section1 the Introduction of Practical Problem Section3 Newton—Cotes Quadrature Formula Section4 Compound Multiplicative Section2 Mechanical Quadrature Method and Algebraic Precision Section5 Romberg Quadrature Formula Section6 Gaussian Quadrature Formula Section7 Numerical Differentiation

§1 the introduction of practical problem §3 the triangular decomposition of matrixs §4 the chasing method §5 the norm of matrixs and vectors §6 the conditions and error analyses about system of linear equations §2 the gauss elimination method

第三章解线性方程组的直接法 Direct Method for Solving Linear Systems 求解A=万 1高斯消元法Gaussian Elimination*1 高斯消元法思首先将A化为上三角阵l*uper--triangular matrix*1路,再回代求解l* backward substitution*1

在电路网中每两点之间都有中继电路群需求,但并不是任两点都有物理传输链路。 根据两点间最短传输路径将该两点间的电路需求量加载到这条传输路径上去:设a25=10是节点2和5之间的电路需求,节点2和5之间的最短传输路径为2-1-3-5,则加载过程

例1研究函数F(y)=(2dx的连续性,其中(x)是[01]上连续且为正的函 0x+y 数。 yf(x) 解令g(x,y)=2 x2+y ,则g(x,y)在[0,×[c,d]连续,其中0∈[c,d]。从而F(y)在 y≠0连续

.下列函数的极大值点和极小值点: (1)f(x,y) (2)f(x,y)=3axy-x3-y2(a>0) (3)f(x,y) (a,b>0) (4)f(x,y)=e2(x+y2+2y)

1.求下列函数的高阶导数: (1)y=x3+2x2-x+1,求ym;(2)y=x4lnx,求y\; (3)y=x,求y; (4)y=2,求y\;

1.(1)证明√6不是有理数; (2)√3+√2是不是有理数? 证(1)反证法若√6是有理数,则可写成既约分数√6=m。由m2=6n2

1.设A是n阶矩阵,且经过 Gauss消去法一步消去后变为an (0A2 证明: (1)如果A是实对称矩阵,那么A2也是对称的; (2)如果ala(i=1,2,L,n),称A为(按行)严格对角占优矩阵,那么A2也是严格对角 占优