科學計算引論：基于MATLAB的數(shù)值分析

第1章MATLAB入門                  
 1.1 計算前的準備                  
 1.2怎樣進行計算                  
 1.3分支結構                  
 1.4循環(huán)結構for/end和while/end                  
 1.5讀與寫                  
 1.6數(shù)組變量                  
 1.7MATLAB特有的數(shù)字特征                    
 1.8MATLAB的數(shù)學函數(shù)                  
 1.9功能函數(shù)                  
 1.10用M文件開發(fā)程序                  
 1.11如何編寫函數(shù)                  
 1.12保存和載入數(shù)據(jù)                  
 1.13硬拷貝                  
 習題                  
 第2章MATLAB繪圖.                   
 2.1簡單繪圖                  
 2.2圖形的交互式編輯                  
 2.3打印和記錄圖形                  
 2.4繪制二維函數(shù)的圖形                  
 2.5三角網(wǎng)格和等高線                  
 2.6曲線網(wǎng)格和等高線                  
 2.7繪制曲面                  
 2.8MATLAB制圖板                  
 2  9交互式圖形功能                  
 2.10M文件                  
 習題                  
 第3章線性代數(shù)                  
 3.1矩陣和向量                  
 3.2MATLAB里的矩陣和向量運算                  
 3.3逆矩陣                  
 3.4線性方程組                  
 3.5不可解問題                  
 3.6行列式                  
 3.7病態(tài)問題                  
 3.8高斯消去法                  
 3.9GaussJordan 消去法和矩陣求逆                  
 3.10LU分解                  
 3.11迭代法                  
 3.12矩陣的特征值                  
 習題                  
 第4章多項式與插值                  
 4.1關于多項式的MATLAB命令                  
 4.2線性插值                  
 4.3用冪級數(shù)做多項式插值                  
 4.4Lagrange 插值多項式                  
 4.5插值多項式的誤差                  
 4.6Lagrange 插值公式的微分與積分                  
 4.7Chebyshev 點的插值                  
 4.8三次Hermite插值                  
 4.9二維插值                  
 4.10超限插值                  
 4.11M文件                  
 習題                  
 第5章數(shù)值積分                  
 5.1梯形法                  
 5.2辛普森法                  
 5.3其他求積公式                  
 5.4關于積分限無界以及被積函數(shù)有奇點的數(shù)值積分法                  
 5.4.1復合梯形求積公式的使用                  
 5.4.2指數(shù)變換                  
 5.4.3二重指數(shù)變換                  
 5.5MATLAB中的積分命令                  
 5.6二維區(qū)域上的數(shù)值積分                  
 5.7M文件                  
 習題                  
 第6章數(shù)值微分                  
 6.1插值多項式的導數(shù)                  
 6.2差分近似                  
 6.3Taylor 展開方法                  
 6.4自動求導算法                  
 6.4.1算法1                  
 6.4.2算法2                  
 6.5偏導數(shù)的差分近似                  
 6.6高階導數(shù)的數(shù)值計算                  
 6.7〖KG*9M文件                  
 習題                  
 第7章非線性方程求根                  
 7.1圖解法                  
 7.2二分法                  
 7.3牛頓迭代法                  
 7.4割線法                  
 7.5逐次代換法                  
 7.6非線性方程組                  
 7.7M文件                  
 習題                  
 第8章數(shù)據(jù)的曲線擬合                  
 8.1直線擬合                  
 8.2非線性曲線擬合：冪函數(shù)擬合                  
 8.3高次多項式曲線擬合                  
 8.4函數(shù)線性組合曲線擬合法                  
 習題                  
 第9章樣條函數(shù)與非線性插值                  
 9.1c樣條插值                  
 9.2三次b樣條插值                  
 9.3非線性函數(shù)插值                  
 9.4M文件                  
 習題                  
 第10章常微分方程的初值問題                  
 10.1一階ODE問題                  
 10.2Euler方法                  
 10.2.1向前Euler法                  
 10.2.2改進的Euler法                  
 10.2.3向后Euler法                  
 10.2.4Euler法的精度                  
 10.2.5二階ODE問題                  
 10.2.6高階ODE問題                  
 10.3龍格-庫塔方法                  
 10.3.1二階龍格-庫塔方法                  
 10.3.2二階龍格-庫塔方法的精度                  
 10.3.3高階ODE問題                  
 10.3.4三階龍格-庫塔方法                  
 10.3.5四階龍格-庫塔方法                  
 10.3.6誤差. 穩(wěn)定分析及時間步長的優(yōu)化                  
 10.4打靶法                  
 10.5直線法                  
 習題                  
 第11章常微分方程的邊值問題                  
 11.1引言                  
 11.2桿狀物和板狀物的邊值問題                  
 11.3三對角方程的解法                   
 11.4變系數(shù)及非均勻網(wǎng)格情形                  
 11.5柱體和球體                  
 11.6非線性常微分方程                  
 11.6.1逐次代換法                  
 11.6.2牛頓迭代法                   
 習題                  
 附錄A色彩                  
 附錄B繪制三維對象                  
 附錄C動畫                  
 附錄D圖像處理                  
 附錄E圖形用戶界面                  
 附錄F習題答案                  
 序言/前言