1 edition of Complex Functions Examples c-7 Applications of the Calculus of Residues found in the catalog.
Published 2013 by Administrator in Bookboon.com
nodata
Statement | Bookboon.com |
Publishers | Bookboon.com |
Classifications | |
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LC Classifications | 2013 |
The Physical Object | |
Pagination | xvi, 51 p. : |
Number of Pages | 55 |
ID Numbers | |
ISBN 10 | nodata |
Series | |
1 | nodata |
2 | |
3 | |
Content 1. Some practical formulæ in the applications of the calculation of residues 1.1. Trigonometric integrals 1.2. Improper integrals in general 1.3. Improper integrals, where the integrand is a rational function 1.4. Improper integrals, where the integrand is a rational function time a trigonometric function 1.5. Cauchy’s principal value 1.6. Sum of some series 2. Trigonometric integrals 3. Improper integrals in general 4. Improper integral, where the integrand is a rational function 5. Improper integrals, where the integrand is a rational function times a trigonometric function 6. Improper integrals, where the integrand is a rational function times an exponential function 7. Cauchy’s principal value 8. Sum of special types of series |
nodata File Size: 5MB.
Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Which theorems of calculus remain true? It is my hope that the reader will show some understanding of my situation.
These are functions that have a complex derivative. Improper integrals, where the integrand is a rational function times a trigonometric function• For example, why does differentiability automatically imply infinite differentiability in this new form of calculus?
It revolves around complex analytic functions. In complex calculus, a once differentiable function is automatically infinitely many times differentiable.
The last third of the class will be devoted to a deeper look at applications. This is the seventh book containing examples from the Theory of Complex Functions. Improper integrals, where the integrand is a rational function time a trigonometric function• As part of the study of the complex plane, a good deal of topology will be covered; this is the study of continuous deformations of shape.
By itself and through some of these theories it also has a great many practical applications.
We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Now imagine that x and y are variables that take on COMPLEX number values, rather than simply real number values. For example, in real calculus, a function can be once differentiable while failing to be twice differentiable.
By itself and through some of these theories it also has a great many practical applications.
These are functions that have a complex derivative.
Among the applications will be harmonic functions, two dimensional fluid flow, easy methods for computing seemingly hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.