# 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    68    0
24    189    2
77    318    10
132    101    3
11    125    0
90    156    9
97    140    1
3    64    2
63    83    1
63    119    1
TÀI LIỆU XEM NHIỀU
8    460197    47
14    12417    36
13    9230    483
3    8201    102
14    7983    416
8    6782    2142
16    6755    397
249    5891    980
7    4677    3
17    4525    195
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
15    102    1    02-02-2023
40    94    0    02-02-2023
2    102    0    02-02-2023
117    111    0    02-02-2023
6    130    0    02-02-2023
21    117    0    02-02-2023
9    119    0    02-02-2023
5    100    0    02-02-2023
126    99    1    02-02-2023
12    131    3    02-02-2023
TÀI LIỆU HOT
8    6782    2142
112    2541    1120
249    5891    980
561    1871    574
152    2111    519
122    2639    491
62    1966    483
13    9230    483
35    2738    436
14    7983    416
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