By P.P.G. Dyke

ISBN-10: 144716394X

ISBN-13: 9781447163947

This complicated undergraduate/graduate textbook presents an easy-to-read account of Fourier sequence, wavelets and Laplace transforms. It positive factors many labored examples with all options supplied.

**Read or Download An Introduction to Laplace Transforms and Fourier Series PDF**

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**Additional info for An Introduction to Laplace Transforms and Fourier Series**

**Example text**

The definition of the delta function can be used to deduce that and that, provided Letting leads to a correct result. Another interesting result can be deduced almost at once and expresses mathematically the property of to pick out a particular function value, known to engineers as thefiltering property. Since with and we deduce that Mathematically, the impulse function has additional interest in that it enables insight to be gained into the properties of discontinuous functions. From a practical point of view too there are a number of real phenomena that are closely approximated by the delta function.

So Of course, this can succinctly be expressed using the Heaviside unit step function as We shall get more practice at this kind of inversion exercise, but you should try your hand at a few of the exercises at the end. 5 Limiting Theorems In many branches of mathematics there is a necessity to solve differential equations. Later chapters give details of how some of these equations can be solved by using Laplace transform techniques. Unfortunately, it is sometimes the case that it is not possible to invert to retrieve the desired solution to the original problem.

If determine the Laplace transform of in terms of and a finite integral. Prove the following change of scale result:- Hence evaluate the Laplace transforms of the two functions Phil DykeSpringer Undergraduate Mathematics SeriesAn Introduction to Laplace Transforms and Fourier Series2nd ed. uk Abstract Sometimes, a function represents a natural or engineering process that has no obvious starting value. Statisticians call this a time series. Although we shall not be considering as stochastic, it is nevertheless worth introducing a way of “switching on" a function.

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