線性與非線性積分方程：方法及應用（簡體書）

《線性與非線性積分方程:方法及應用》是一本同時介紹線性和非線性積分方程的教材，分成兩部分，各部分自成體系。第一部分主要對第一類、第二類線性積分方程進行了系統、深入的分析并提供各種解法；第二部分主要講述非線性積分方程求解及其應用，針對不適定fredholm問題、分歧點和奇異點等問題進行了系統的分析，并提供易于理解的處理方法。
《線性與非線性積分方程:方法及應用》通過大量的例子講述線性與非線性積分方程最新發展起來的高效解法，無須要求讀者對抽象理論本身有很深的理解，同時也討論了某些經典方法一些有價值的改進。書中對這些方法都給出了很好的解釋，并通過對這些方法進行對比，使得讀者能夠快速地掌握并選擇可行且高效的方法。《線性與非線性積分方程:方法及應用》提供了大量的習題，并在書后附有答案。
《線性與非線性積分方程:方法及應用》可作為應用數學、工程學及其相關專業的高年級本科生和研究生教材，也可供相關領域的工程師參考。

作者：（美國）佤斯瓦茨（Abdul-Majid Wazwaz）

part i linear integral equations
1 preliminaries
1.1 taylor series
1.2 ordinary differential equations
1.3 leibnitz rule for differentiation of integrals
1.4 reducing multiple integrals to single integrals
1.5 laplace transform
1.6 infinite geometric series
references

2 introductory concepts of integral equations
2.1 classification of integral equations
2.2 classification of integro-differential equations
2.3 linearity and homogeneity
2.4 origins of integral equations
2.5 converting ivp to volterra integral equation
2.6 converting bvp to fredholm integral equation
2.7 solution of an integral equation
references

3　volterra integral equations
3.1 introduction
3.2 volterra integral equations of the second kind
3.3 volterra integral equations of the first kind references

4 fredholm integral equations
4.1 introduction
4.2 fredholm integral equations of the second kind
4.3 homogeneous fredholm integral equation
4.4 fredholm integral equations of the first kind
references

5　volterra integro-differential equations
5.1 introduction
5.2 volterra integro-differential equations of the second kind
5.3 volterra integro-differential equations of the first kind
references
6 fredholm integro-differential equations
6.1 introduction
6.2 fredholm integro-differential equations of the second kind
references

7　abels integral equation and singular integral equations
7.1 introduction
7.2 abels integral equation
7.3 the generalized abels integral equation
7.4 the weakly singular volterra equations
References

8　volterra-fredholm integral equations
8.1 introduction
8.2 the volterra-fredholm integral equations
8.3 the mixed volterra-fredholm integral equations
8.4 the mixed volterra-fredholm integral equations in two variables
references

9　volterra-fredholm integro-differential equations
9.1 introduction
9.2 the volterra-fredholm integro-differential equation
9.3 the mixed volterra-fredholm integro-differential equations
9.4 the mixed volterra-fredholm integro-differential equations in two variables
references

10 systems of volterra integral equations
10.1 introduction
10.2 systems of volterra integral equations of the second kind
10.3 systems of volterra integral equations of the first kind
10.4 systems of volterra integro-differential equations
references

11 systems of fredholm integral equations
11.1 introduction
11.2 systems of fredholm integral equations
11.3 systems of fredholm integro-differential equations
references

12 systems of singular integral equations
12.1 introduction
12.2 systems of generalized abel integral equations
12.3 systems of the weakly singular volterra integral equations
references
part ii nonlinear integral equations

13 nonlinear volterra integral equations
13.1 introduction
13.2 existence of the solution for nonlinear volterra integral equations
13.3 nonlinear volterra integral equations of the second kind
13.4 nonlinear volterra integral equations of the first kind
13.5 systems of nonlinear volterra integral equations
references

14 nonlinear volterra integro-differential equations
14.1 introduction
14.2 nonlinear volterra integro-differential equations of the second kind
14.3 nonlinear volterra integro-differential equations of the first kind
14.4 systems of nonlinear volterra integro-differential equations
references

15 nonlinear fredholm integral equations
15.1 introduction
15.2 existence of the solution for nonlinear fredholm integral equations
15.3 nonlinear fredholm integral equations of the second kind
15.4 homogeneous nonlinear fredholm integral equations
15.5 nonlinear fredholm integral equations of the first kind
15.6 systems of nonlinear fredholm integral equations
references

16 nonlinear fredholm integro-differential equations
16.1 introduction
16.2 nonlinear fredholm integro-differential equations.
16.3 homogeneous nonlinear fredholm integro-differential equations
16.4 systems of nonlinear fredholm integro-differential equations
references

17 nonlinear singular integral equations
17.1 introduction
17.2 nonlinear abels integral equation
17.3 the generalized nonlinear abel equation
17.4 the nonlinear weakly-singular volterra equations
17.5 systems of nonlinear weakly-singular volterra integral equations
references

18 applications of integral equations
18.1 introduction
18.2 volterras population model
18.3 integral equations with logarithmic kernels
18.4 the fresnel integrals
18.5 the thomas-fermi equation
18.6 heat transfer and heat radiation
references

appendix a table of indefinite integrals
a.1 basic forms
a.2 trigonometric forms
a.3 inverse trigonometric forms
a.4 exponential and logarithmic forms
a.5 hyperbolic forms
a.6 other forms
appendix b integrals involving irrational algebraic functions

b.1 integrals involving n is an integer, n ≥ 0
b.2 integrals involving n is an odd integer, n ≥ i
appendix c series representations
c.1 exponential functions series
c.2 trigonometric functions
c.3 inverse trigonometric functions
c.4 hyperbolic functions
c.5 inverse hyperbolic functions
c.6 logarithmic functions
appendix d the error and the complementary error
functions
d.1 the error function
d.2 the complementary error function
appendix e gamma function
appendix f infinite series
f.1 numerical series
f.2 trigonometric series
appendix g the fresnel integrals
g.1 the fresnel cosine integral
g.2 the fresnel sine integral
answers
index