MAT207O ADVANCED CALCULUS & DIFFERENTIAL EQUATIONS

3 Hours/Week, 3 Credits

Advanced Calculus: Improper integrals; Gamma and Beta functions; their incompleteness and other properties; functions of several variables and limit and continuity; Taylorís expansion of such functions; maxima and minima of functions of more than one variable; Lagrangeís multipliers; multiple integrals; Jacobians of transformation; Dirichlet integral and its extension; Laplace transformation; concept of Fourier series. Differential Equations: Definition; solution of differential equations; basic theory of linear differential equations; basic theory of non-linear differential equations; equations of the first order and their solution; homogeneous differential equations; linear differential equations of the second and higher order and their solution.