Mathematics-III Syllabus in NIT Jalandhar
Limit and derivative of a complex function, analytic functions and Cauchy Riemann equations, line integral of elementary functions, Cauchy’s integral theorem, Cauchy’s integral formula and derivatives of analytic functions, Taylor and Laurent series, zeros and singularities, residues and residue theorem, evaluation of real improper integrals, conformal mappings, linear fractional transformations and mappings by elementary functions Series solution of differential equations, Bessel’s differential equation and Bessel functions and their properties, differential equations reducible to Bessel’s differential equation, Legendre’s differential equation, Legendre’s
polynomials and their properties, Fourier-Legendre expansion of a function.
Fundamental concepts of calculus of variations, functional involving several independent functions, one end fixed- other end free problems, both end free problems, constrained extrema.
1. Grewal, B S ,”Higher Engineering Mathematics”, Thirty-fifth edition, Khanna Publishers ,Delhi.
2. Elsgole L E,” Calculus of Variations ”, 1961Pergamon Press ,Addison-Wisley Publishing Company
3. Conway J B, “Functions of One Complex Variables”, Narosa Publishing House, 1980.