M. Krasnov | A. Kiselev | G. Makarenko | Category: Mathematics
Binding Type: Paperback Binding
Book DetailsISBN: 9789386677044
YOP: 2018
Pages: 224Order also on
As the name suggests the book is about integral equations and methods of solving them under different conditions. The book has three chapters. Chapter 1 covers Volterra Integral Equations in details. Chapter 2 covers Fredholm integral equations. Finally, in Chapter 3, Approximate Methods for solving integral equations are discussed. There are plenty of solved examples in the text to illustrate the methods, along with problems to solve. This will be a useful resource book for those studying integral equations.
CHAPTER I. VOLTERRA INTEGRAL EQUATIONS
1.Basic Concepts
2. Relationship Between Linear Diflerential Equations and Volterra Integral Equations
3. Resolvent Kernel oi Volterra Integral Equation. Solution of Integral Equation by Resolvent Kernel
4. The Method of Successive Approximations
5. Convolution-Type Equations
6. Solution Set Integro-Difierential Equations with the Aid at the Laplace Transformation
7. Volterra Integral Equations with Limits (x.+00)
8. Volterra Integral Equations of the First Kind
9.Euler Integrals
1O. Abel’s Problem. Abel’s Integral Equation and Its Generalizations
11. Volterra Integral Equations of the First Kind of the Convolution Type
CHAPTER II- FREDHOLM INTEGRAL EQUATIONS
12. Fredholm Equations of the Second Kind. Fundamentals
13. The Method of Fredholm Determinants
14- Iterated Kernels Constructing the Resolvent Kernel with the Aid of Iterated Kernels
I5. Integral Equations with Degenerate Kernels. Hammer-Stein Type Equation
16. Characteristic Numbers and Eigenfunctions
17. Solution of Homogeneous Integral Equations with Degenerate Kernel
l8. Nonhomogeneous Symmetric Equations
19. Fredholm Alternative
20. Construction of Green’s Function for Ordinary Differential Equations
21. Using Green’s Function in the Solution of Boundary- Value Problems.
22- Boundary-Value Problems Containing a Parameter; Reducing Them to Integral Equations
23. Singular Integral Equations
CHAPTER III- APPROXIMATE METHODS
24. Approximate Methods of Solving Integral Equations
l. Replacing the kernel by a degenerate kernel
2. The method of successive approximations
3. The Bubnov-Galerkin method
25. Approximate Methods for Finding Characteristic Num-bers
1-Ritz method
2-The method of traces
As the name suggests the book is about integral equations and methods of solving them under different conditions. The book has three chapters. Chapter 1 covers Volterra Integral Equations in details. Chapter 2 covers Fredholm integral equations. Finally, in Chapter 3, Approximate Methods for solving integral equations are discussed. There are plenty of solved examples in the text to illustrate the methods, along with problems to solve. This will be a useful resource book for those studying integral equations.
CHAPTER I. VOLTERRA INTEGRAL EQUATIONS
1.Basic Concepts
2. Relationship Between Linear Diflerential Equations and Volterra Integral Equations
3. Resolvent Kernel oi Volterra Integral Equation. Solution of Integral Equation by Resolvent Kernel
4. The Method of Successive Approximations
5. Convolution-Type Equations
6. Solution Set Integro-Difierential Equations with the Aid at the Laplace Transformation
7. Volterra Integral Equations with Limits (x.+00)
8. Volterra Integral Equations of the First Kind
9.Euler Integrals
1O. Abel’s Problem. Abel’s Integral Equation and Its Generalizations
11. Volterra Integral Equations of the First Kind of the Convolution Type
CHAPTER II- FREDHOLM INTEGRAL EQUATIONS
12. Fredholm Equations of the Second Kind. Fundamentals
13. The Method of Fredholm Determinants
14- Iterated Kernels Constructing the Resolvent Kernel with the Aid of Iterated Kernels
I5. Integral Equations with Degenerate Kernels. Hammer-Stein Type Equation
16. Characteristic Numbers and Eigenfunctions
17. Solution of Homogeneous Integral Equations with Degenerate Kernel
l8. Nonhomogeneous Symmetric Equations
19. Fredholm Alternative
20. Construction of Green’s Function for Ordinary Differential Equations
21. Using Green’s Function in the Solution of Boundary- Value Problems.
22- Boundary-Value Problems Containing a Parameter; Reducing Them to Integral Equations
23. Singular Integral Equations
CHAPTER III- APPROXIMATE METHODS
24. Approximate Methods of Solving Integral Equations
l. Replacing the kernel by a degenerate kernel
2. The method of successive approximations
3. The Bubnov-Galerkin method
25. Approximate Methods for Finding Characteristic Num-bers
1-Ritz method
2-The method of traces
