Functions of Several Variables and Partial Differential Equations

<span>SYLLABUS- FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIAL EQUATIONS,</span><br><span>Functions of several variables: Limit, continuity and differentiability of functions of several variables.</span><br><span>Partial Derivatives: Partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, Jacobians, Chain rule, Euler’s theorem on homogeneous functions, harmonic functions, Taylor’s expansion of functions of several variables.</span><br><span>Maxima and Minima: Maxima and minima of functions of several variables – Lagrange’s method of multipliers.</span><br><span>Partial differential equations: Partial differential equations of first order, Charpit’s method, Linear partial differential equations with constant coefficients. First-order linear, quasi-linear PDE's using the method of characteristics.</span><br><span>Partial differential equations of 2nd-order: Classification of 2nd-order linear equations in two independent variables: hyperbolic, parabolic and elliptic types (with examples).</span></br></br></br></br></br>