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8.5 Series Solutions Near a Regular Singular Point, Part I

8.5 Series Solutions Near a Regular Singular Point, Part I

8.5 Series Solutions Near a Regular Singular Point, Part I. We now consider the question of solving the general second order linear equation P ( x ) y'' + Q ( x ) y' + R ( x ) y = 0 (1)

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Ch 5.7: Series Solutions Near a Regular Singular Point, Part II

Ch 5.7: Series Solutions Near a Regular Singular Point, Part II

Ch 5.7: Series Solutions Near a Regular Singular Point, Part II. Recall from Section 5.6 (Part I): The point x 0 = 0 is a regular singular point of with and corresponding Euler Equation We assume solutions have the form . Substitute Derivatives into ODE. Taking derivatives, we have

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Ch 5.6: Series Solutions Near a Regular Singular Point, Part I

Ch 5.6: Series Solutions Near a Regular Singular Point, Part I

Ch 5.6: Series Solutions Near a Regular Singular Point, Part I. We now consider solving the general second order linear equation in the neighborhood of a regular singular point x 0 . For convenience, will will take x 0 = 0. Recall that the point x 0 = 0 is a regular singular point of

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Ch 5.5: Series Solutions Near a Regular Singular Point, Part I

Ch 5.5: Series Solutions Near a Regular Singular Point, Part I

Ch 5.5: Series Solutions Near a Regular Singular Point, Part I. We now consider solving the general second order linear equation in the neighborhood of a regular singular point x 0 . For convenience, will will take x 0 = 0. The point x 0 = 0 is a regular singular point of iff iff.

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Ch 5.4: Regular Singular Points

Ch 5.4: Regular Singular Points

Ch 5.4: Regular Singular Points. Recall that the point x 0 is an ordinary point of the equation if p ( x ) = Q ( x )/ P ( x ) and q ( x )= R ( x )/ P ( x ) are analytic at at x 0 . Otherwise x 0 is a singular point .

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1.63k views • 15 slides
N-th order linear DE

N-th order linear DE

Sec 6.2: Solutions About Singular Points. N-th order linear DE. Constant Coeff. variable Coeff. Cauchy-Euler 4.7. Ch 6 Series Point. Homog( find y p ) 4.3. NON-HOMOG (find y p ). Annihilator Approach 4.5. Variational of Parameters 4.6. Ordinary 6.1. Singular 6.2.

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