Module-4 ///1st year P-cycle/C-cycle:Advanced Calculus and Numerical Methods (18MAT21)

MODULE 4 NOTES:

CONTENTS OF MODULE 4:

MOD 4-INFINITE SERIES and POWER SERIES SOLUTIONS
1. Series of positive terms- convergence and divergence. Cauchy’s root test and D’Alembert’s ratio test(without proof)- Illustrative examples.

2.Solutions-Series solution of Bessel’s differential equation leading to Jn(x)- Bessel’s function of first kindorthogonality.

3. Series solution of Legendre’s differential equation leading to Pn(x)-Legendre polynomials. Rodrigue’s formula (without proof), problems (RBT Levels:L1 and L2)

M2- 18MAT21 handwritten notes below

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