《NUMERICAL ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS》求取 ⇩
作者 | GEORGE E. FORSYTHE AND PAUL C. 编者 |
---|---|
出版 | 未查询到或未知 |
参考页数 | ✅ 真实服务 非骗流量 ❤️ |
出版时间 | 没有确切时间的资料 目录预览 |
ISBN号 | 无 — 违规投诉 / 求助条款 |
PDF编号 | 820349548(学习资料 勿作它用) |
求助格式 | 扫描PDF(若分多册发行,每次仅能受理1册) |
Chapter 1.Contemporary state of Numerical Analysis3
1WHAT IS NUMERICAL ANALYSIS?3
2 AREAS OF NUMERICAL ANALYSIS7
3 AN OLDER SOVIET VIEW OF NUMERICAL ANALYSIS8
4 A MORE PECENT SOVIET VIEW OF NUMERICAL ANALYSIS10
5 AUTOMATIC DIGITAL COMPUTERS IN THE WORLD11
6 TWO SOVIET COMPUTERS14
7 LITERATURE ON NUMERICAL ANALYSIS15
8 NUMERICAL INTEGRATION AND INTERPOLATION16
9 APPROXIMATIONS OF FUNCTIONS18
10 SOLVING LINEAR ALGEBRAIC EQUATIONS21
11 SOLVING MATRIX EIGENVALUE PROBLEMS27
12 DIFFERENCE METHODS FOR LAPLACE'S EQUATION31
Bibliography38
Introduction45
Chapter 1Partial Differential Equations in the Complex Domain46
The Cauchy Problem46
1TRANSFORMATION TO NORMAL FORM46
2 BASIC EXISTENCE THEOREMS48
The Leray-Fantappié Operational Calculus50
1PRELIMINARIES50
Equations oF Higher Order55
Chapter 2General Theory in the Real Domain59
Uniqueness and Domains of Dependence for the Cauchy Problem59
Preliminaries on Function Spaces62
1TESTING SPACES62
2 DUAL SPACES AND DISTRIBUTIONS64
3 BANACH AND HILBERT SPACES66
4 LINEAR OPERATORS67
5 APPLICATIONS TO DIFFERENTIAL EQUATIONS70
Fourier and Laplace Transforms.Other Operational Calculi75
1FOURIER TRANSFORMS75
2 LAPLACE TRANSFORMS77
3 SYSTEMS OF PARTIAL-DIFFERENTIAL EQUATIONS AND POTENTIALS79
4 GENERAL REMARKS ON OPERATIONAL CALCULI82
5 THEORY OF SEMIGROUPS85
Chapter 3General Theory of Equations with Constant Coefficients88
The Work of Ehrenpreis,Malgrange,and Hormander88
1GENERAL EXISTENCE THEOREMS88
2 GENERAL REGULARITY THEOREMS92
The Method of Gelfand and Silov97
Chapter 4Equations of Parabolic Type102
Equations with Constant Coefficients102
1THE CAUCHY PRQBLEM FOR HOMOGENEOUS EQUATIONS102
2 NONHOMOGENEOUS EQUATIONS105
Parabolic Equations with Variable Coefficents108
1PERTURBATION AMD PARAMETRIX METHODS108
2 APPLICATIONS OF SEMIGROUP THEORY113
3 BOUNDARY VALUE PROBLEMS115
4 THE METHOD OF VISIK117
5 VARIATIONAL PRINCIPLES119
6 REGULARITY PROPERTTES121
7 BARRAR'S a priori ESTIMATES124
Chapter 5Equations of Elliptic Type126
General Theory126
1CLASSIFICATION126
2 JOHN'S FUNDAMENTAL SOLUTION127
3 STRONGLY ELLIPTIC SYSTEMS132
4 REGULARITY SYSTEMS134
5 GARDING'S INEQUALITY136
6 THE DOUGLIS-NIRENBERG ESTIMATES138
7 THE ASSUMPTION OF BOUNDARY VALUES139
8 GREEN'S AND NEUMANN FUNCTIONS.THE BERGMAN RERNEL142
9 CONSTRUCTION OF SOLUTIONS145
Elliptic Equations of Second Order150
1MAXIMUM PRINCIPLE150
2 LAPLACE EQUATION IN A SPHERE152
3 LOCAL EXISTENCE THEOREMS154
4 PERRON'S METHOD159
5 CONCLUDING REMARKS161
Bibliography164
Index197
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