Functions of Several Variables and Partial Differential Equations

SYLLABUS- FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIAL EQUATIONS,
Functions of several variables: Limit, continuity and differentiability of functions of several variables.
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.
Maxima and Minima: Maxima and minima of functions of several variables – Lagrange’s method of multipliers.
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.
Partial differential equations of 2nd-order: Classification of 2nd-order linear equations in two independent variables: hyperbolic, parabolic and elliptic types (with examples).
SYLLABUS- FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIAL EQUATIONS,
Functions of several variables: Limit, continuity and differentiability of functions of several variables.
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.
Maxima and Minima: Maxima and minima of functions of several variables – Lagrange’s method of multipliers.
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.
Partial differential equations of 2nd-order: Classification of 2nd-order linear equations in two independent variables: hyperbolic, parabolic and elliptic types (with examples).