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