Unit III : Partial Differentiation Introduction to functions of several variables, Partial Derivatives, Euler's Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables. (Chapter - 5) Unit IV : Applications of Partial Differentiation Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange's method of undetermined multipliers. (Chapter - 6) Unit V : Linear Algebra-Matrices, System of Linear Equations Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering. (Chapters - 7, 8) Unit VI : Linear Algebra-Eigen Values and Eigen Vectors, Diagonalization Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations. (Chapter - 9)
