By P.P.G. Dyke
This complex undergraduate/graduate textbook presents an easy-to-read account of Fourier sequence, wavelets and Laplace transforms. It positive factors many labored examples with all suggestions supplied.
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This complex undergraduate/graduate textbook offers an easy-to-read account of Fourier sequence, wavelets and Laplace transforms. It gains many labored examples with all options supplied.
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Additional info for An Introduction to Laplace Transforms and Fourier Series
I suppose the main cause of this is the computer/video age in which we live, in which amazing eye-catching images are available at the touch of a button. However, another contributory factor must be the decrease in the time devoted to algebraic manipulation, manipulating fractions etc. in mathematics in the 11–16 age range. Fortunately, the impact of this on the teaching of Laplace transforms and Fourier series is perhaps less than its impact in other areas of mathematics. g. MAPLE©, MATHEMATICA©, DERIVE©, MACSYMA©) where appropriate.
In our view, this takes the engineer’s maxim “if it ain’t broke, don’t fix it” too far. This is primarily a mathematics textbook, therefore in this opening chapter we shall be more mathematically explicit than is customary in books on Laplace transforms. 4 there is some more pure mathematics when Fourier series are introduced. That is there for similar reasons. One mathematical question that ought to be asked concerns uniqueness. Given a function , its Laplace transform is surely unique from the well defined nature of the improper integral.
Let us now look at a more visual approach. 3, the top hat function if we let Of course there are many shapes that will behave like in some limit. The top hat function is one of the simplest to state and visualise. The crucial property is that the area under this top hat function is unity for all values of , so letting preserves this property. 4 where the length of the arrow is unity. 4) with we see that which is consistent with the area under being unity. Fig. 3The “top hat” function Fig. 4The Dirac- function We now ask ourselves what is the Laplace transform of ?
An Introduction to Laplace Transforms and Fourier Series by P.P.G. Dyke