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INTEGRAL EQUATIONS【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

INTEGRAL EQUATIONS
  • F.G. TRICOMI 著
  • 出版社： INC.
  • ISBN：
  • 出版时间：1957
  • 标注页数：238页
  • 文件大小：34MB
  • 文件页数：243页
  • 主题词：

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图书目录

Ⅰ．Volterra Equations1

1．1．A Mechanical Problem Leading to an Integral Equation1

1．2．Integral Equations and Algebraic Systems of Linear Equations3

1．3．Volterra Equations5

1．4．L2-Kernels and Functions8

1．5．Solution of Volterra Integral Equations of the Second Kind10

1．6．Volterra Equations of the First Kind15

1．7．An Example17

1．8．Volterra Integral Equations and Linear Differential Equations18

1．9．Equations of the Faltung Type(Closed Cycle Type)22

1．10．Transverse Oscillations of a Bar26

1．11．Application to the Bessol Functions32

1．12．Some Generalizations of the Theory of Volterra Equations38

1．13．Non-Linear Volterra Equations42

Ⅱ．Fredholm Equations49

2．1．Solution by the Method of Successive Approximations:Neumann＇s Series49

2．2．An Example53

2．3．Fredholm＇s Equations with Pincherle-Goursat Kernels55

2．4．The Fredholm Theorem for General Kernels64

2．5．The Formulae of Fredholm66

2．6．Numerical Solution of Integral Equations75

2．7．The Fredholm Solution of the Dirichlet Problem76

Ⅲ．Symmetric Kernels and Orthogonal Systems of Functions81

3．1．Introductory Remarks and a Process of Orthogonalization81

3．2．Approximation and Convergence in the Mean83

3．3．The Riesz-Fischer Theorem88

3．4．Completeness and Closure90

3．5．Completeness of the Trigonometric System and of the Polynomials95

3．6．Approximation of a General L2-Kernel by Means of PG-Kernels98

3．7．Enskog＇s Method100

3．8．The Spectrum of a Symmetric Kernel102

3．9．The Bilinear Formula106

3．10．The Hilbert-Schmidt Theorem and Its Applications110

3．11．Extremal Properties and Bounds for Eigenvalues118

3．12．Positive Kernels—Mercer＇s Theorem124

3．13．Connection with the Theory of Linear Differential Equations127

3．14．Critical Velocities of a Rotating Shaft and Transverse Oscillations of a Beam136

3．15．Symmetric Fredholm Equations of the First Kind143

3．16．Reduction of a Fredholm Equation to a Similar One with a Symmetric Kernel145

3．17．Some Generalizations150

3．18．Vibrations of a Membrane154

Ⅳ．Some Types of Singular or Non-Linear Integral Equations161

4．1．Orientation and Examples161

4．2．Equations with Cauchy＇s Principal Value of an Integral and Hilbert＇s Transformation166

4．3．The Finite Hilbert Transformation and the Airfoil Equation173

4．4．Singular Equations of the Carleman Type185

4．5．General Remarks About Non-Linear Integral Equations197

4．6．Non-Linear Equations of the Hammerstein Type202

4．7．Forced Oscillations of Finite Amplitude213

Appendix Ⅰ．Algebraic Systems of Linear Equations219

Appendix Ⅱ．Hadamard＇s Theorem223

Exercises227

References231

Index235

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