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Partial Differentiation and its applications, Curve Tracing,  Multiple Integrals, Vector Differentiation and Integration, Matrices

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Partial Differentiation : Function of two or more variables; Homogeneous function; Euler’s theorem; Composite functions; Implicit functions; Total derivatives; Jacobians.
Application of Partial Differentiation : Taylor’s and Maclaurin’s series for a function of two variables; Maxima and Minima of functions of several variables; Lagrange’s method of undetermined multipliers; Error and approximation.
Curve Tracing : Asymptotes, Curve Tracing of standard curves for polar and Cartesian coordinates. Curvature. Radius of Curvature in polar, Cartesian co-ordinates and parametric coordinates.
Introduction to Multiple Integrals : Double and Triple integral, change of order of integration change of variables. Application of double integration to find areas, application of triple integration to find volume.
Vector Differentiation : Scalar and vector fields; differentiation of vectors ; vector differential operators: del, gradient, divergence, curl and their physical interpretations.
Vector Integration : Line integrals; surface integrals and volume integrals, flux ; solenoidal and irrotational vectors; Gauss divergence theorem; Green’s theorem in plane; Stoke’s theorem (without proofs) and their applications.
Matrices : Vector Algebra, Matrix as a set of Vectors, Properties of Matrix, Rank of matrix; elementary operations; reduction to normal form; consistency and solution of homogenous and non homogeneous simultaneous equations; Linear dependence and independence of vectors; Eigen values and Eigen vectors Cayley Hamilton theorem(without proof) and problems, Reduction to diagonal form.

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