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Power Series are a very import­ant tool for solv­ing Dif­fer­en­tial Equations.

Return to Dif­fer­en­tial Equations

Video # Video Tutori­al Title Remarks
1 Clas­si­fic­a­tion of Dif­fer­en­tial Equations Dis­cuss­ing all the terms by which we clas­si­fy dif­fer­en­tial equations
2 What are Power Series Used For? I try to motiv­ate the prac­tic­al use of  P.S., in physics
3 Where Power Series Start Do they start at n=0, n=1, n=3 etc?
4 Shift­ing Power Series Indices A very import­ant skill; shift­ing from n=1 to n=0 (say)
5 Dif­fer­en­ti­at­ing Power Series As simple as it sounds but import­ant when we dis­cuss the meth­od of Frobenius
6 Mul­tiply­ing Power Series by Functions Dis­cuss­ing the impact on where the P.S., start
7 The Char­ac­ter­ist­ic Equa­tion 1/2 Deriv­ing the Char­ac­ter­ist­ic Equa­tion for solv­ing equa­tions with con­stant coefficients
8 Intro­duc­tion to P.S., Solutions How dif­fer­en­tial equa­tions are solved using the meth­od of power series solutions
9 Gen­er­al and Par­tic­u­lar Solutions Not yet recorded
10 The Gen­er­al Solution To 2nd order D.Es., with con­stant coef­fi­cients using power series
11 Example 1 y”- y’ = 0
12 Example 2 y” + 4y = 0
13 Example 3 y” — 9y = 0
14 a Proof of the Wronskian Find out if your solu­tions are lin­early depend­ent or not

 

dif­fer­en­tial equa­tions frobeni­us laplace’s equa­tion vari­ables sep­ar­a­tion com­plete­ness ortho­gon­al ortho­gon­al­ity dif­fer­en­tial equa­tions frobeni­us laplace’s equa­tion vari­ables sep­ar­a­tion com­plete­ness ortho­gon­al ortho­gon­al­ity dif­fer­en­tial equa­tions frobeni­us laplace’s equa­tion vari­ables sep­ar­a­tion com­plete­ness ortho­gon­al orthogonality

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