# tailieunhanh - Handbook of mathematics for engineers and scienteists part 122

## Handbook of mathematics for engineers and scienteists part 122. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Linear Integral Equations of the Second Kind with Variable Integration Limit 815 Let w w x be a solution of the simpler auxiliary equation with f x 1 and a 0 Aw x B J0 K x - t w t dt 1. In this case the solution of the original equation with an arbitrary right-hand side can be expressed via the solution of the auxiliary equation by the formula d fx fx y x J w x - t f t dt f a w x - a J w x - t f t dt. . Construction of Solutions of Integral Equations with Special Right-Hand Side in this section we describe some approaches to the construction of solutions of integral equations with special right-hand sides. These approaches are based on the application of auxiliary solutions that depend on a free parameter. . General scheme. Consider a linear equation which we shall write in the following brief form L y fg x A where L is a linear operator integral differential etc. that acts with respect to the variable x and is independent of the parameter A and fg x A is a given function that depends on the variable x and the parameter A. Suppose that the solution of equation is known y y x A . Let M be a linear operator integral differential etc. that acts with respect to the parameter A and is independent of the variable x. Consider the usual case in which M commutes with L. We apply the operator M to equation and find that the equation L w fM x fM x M fg x A has the solution w M y x A . By choosing the operator M in a different way we can obtain solutions for other righthand sides of equation . The original function fg x A is called the generating function for the operator L. . Generating function of exponential form. Consider a linear equation with exponential right-hand side L y eXx. Suppose that the solution is known and is given by formula . In Table we present solutions of the equation L y f x with various right-hand sides these .

TÀI LIỆU LIÊN QUAN
4    44    0
24    122    2
77    205    9
132    57    2
11    78    0
90    102    5
97    64    0
3    30    1
63    56    1
63    58    0
TÀI LIỆU XEM NHIỀU
8    322417    13
3    6988    92
14    6319    294
8    5784    1767
2    3408    28
9    3208    8
24    3165    60
35    3091    149
3    2919    38
21    2912    210
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
4    24    1    18-09-2021
5    75    0    18-09-2021
85    7    1    18-09-2021
8    23    1    18-09-2021
7    43    0    18-09-2021
94    44    0    18-09-2021
18    89    2    18-09-2021
62    15    3    18-09-2021
1    19    1    18-09-2021
167    5    2    18-09-2021
TÀI LIỆU HOT
8    5784    1767
112    1934    742
561    918    345
122    1869    343
14    6319    294
20    2418    263
35    1697    256
36    1977    228
21    2912    210
171    1326    203