Ordinary differential equations of the 1st order, exactness and integrating factors, variation of parameters, Picard's iteration method.

Ordinary linear differential equations of nth order, solution of homogeneous and non-homogeneous equations. Operator method. Methods of undetermined coefficients and variation of parameters.

Systems of differential equations, Phase plane. Critical points, stability.

Infinite sequences and series of real and complex numbers. Improper integrals. Cauchy criterion, tests of convergence, absolute and conditional convergence. Series of functions. Improper integrals depending on a parameter. Uniform convergence. Power series, radius of convergence. Power series methods for solutions of ordinary differential equations. Legendre equation and Legendre polynomials, Bessel equations and Bessel functions of first and second kind. Orthogonal sets of functions. Sturm-Liouville problems. Orthogonality of Bessel functions and Legendre polynomials.

Laplace transform. Inverse transform. Shifting properties, convolutions, Partial fractions.

Fourier series, half-range expansions. Approximation by trignometric polynomials. 

Fourier integrals. Transform techniques in differential equations


 E. Kreyszig, Advanced Engineering Mathematics, 8th ed., Wiley Eastern, 1999.

 W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd ed., Wiley, 1977.

 G. F. Simmons, Differential Equations with Applications and Historical Notes, Tata McGraw-Hill, 1972.

 E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice - Hall of India. Pvt, New Delhi 13th reprinting June, 2000.


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