Esempio: funzioni di Kelvin

Funzioni > Funzioni speciali > Funzioni di Bessel > Esempio: funzioni di Kelvin

Mostrare la relazione tra le funzioni ber e bei. Per tali funzioni non sono disponibili versioni scalate.

1. Tracciare il grafico delle funzioni di ordine zero ber e bei:

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Le due funzioni appaiono simmetriche.

2. Reimpostare i valori delle tacche per ingrandire l'asse x per mostrare il modo in cui i due picchi delle funzioni ber e bei cambiano all'aumentare dell'ordine:

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3. Utilizzare la valutazione simbolica per mostrare le relazioni tra le funzioni ber e bei con la funzione Jn e quindi creare grafici per indicare visivamente i risultati.

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Questo esempio è incentrato sulla funzione ber, ma le stesse osservazioni si applicano alla funzione bei.

4. Definire il vettore Z1 utilizzando la funzione ber:

Le funzioni localmin e localmax richiedono una matrice di input di due colonne. Passare il vettore Z alla funzione augment per creare tale matrice.

5. Trovare i valori minimi locali della funzione ber:

La funzione ber ha 8 valori minimi quando m=0. La funzione è simmetrica. Funzioni di ordine superiore hanno un numero diverso di valori minimi con posizioni e ampiezze diverse.

6. Trovare i valori massimi locali della funzione ber:

La funzione ber ha 7 picchi quando m=0. La funzione è simmetrica. Le funzioni di ordine superiore hanno un numero diverso di valori massimi con posizioni e ampiezze diverse.

7. Trovare le coordinate verticali dei quattro valori minimi di destra.

8. Utilizzare la funzione match per trovare l'indice di ogni valore minimo corrispondente e quindi trovare le coordinate orizzontali equivalenti.

9. Trovare le coordinate verticali dei quattro valori massimi di destra.

10. Utilizzare la funzione match per trovare l'indice di ogni valore massimo corrispondente e quindi trovare le coordinate orizzontali equivalenti.

L'intervallo di ampiezze di valori minimi e massimi varia notevolmente e rende difficile osservarli tutti in un solo grafico.

11. Utilizzare indicatori per mostrare il primo valore minimo (D0) e il primo valore massimo (P0):

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Come previsto, il grafico mostra un secondo valore minimo a sinistra dell'asse y.

12. Utilizzare indicatori per mostrare il successivo valore minimo (D1) e il successivo valore massimo (P1):

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Come previsto, il grafico mostra un secondo valore minimo e un secondo valore massimo a sinistra dell'asse y.

13. Utilizzare indicatori per mostrare il successivo valore minimo (D2) e il successivo valore massimo (P2):

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Come previsto, il grafico mostra un secondo valore minimo e un secondo valore massimo a sinistra dell'asse y.

14. Utilizzare indicatori per mostrare il successivo valore minimo (D3) e il successivo valore massimo (P3):

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Come previsto, il grafico mostra un secondo valore massimo a sinistra dell'asse y.

Poiché il valore minimo (D3) e il suo valore equivalente di sinistra corrispondono esattamente ai limiti dell'intervallo, è consigliabile ignorarli.

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Funzioni di Bessel Kelvin

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