Calculus: Partial differentiation, total derivative, differentiation of composite functions, Jacobian, Statement of Taylor’s and Maclaurin’s series expansion for two variables. Maxima and minima for the function of two variables.

Vector Calculus: Scalar and vector fields, Gradient, directional derivatives, divergence and curl – physical interpretation, solenoidal vector fields, irrotational vector fields and scalar potential. Introduction to polar coordinates and polar curves. Curvilinear coordinates: Scale factors, base vectors, Cylindrical polar coordinates, Spherical polar coordinates, transformation between cartesian and curvilinear systems, orthogonality.

System of Linear Equations, Eigenvalues and Eigenvectors: Elementary row transformation of a matrix, Echelon form, rank of a matrix. Consistency and solution of system of linear equations: Gauss elimination method, Gauss Jordan method. Applications: Traffic flow. Eigenvalues and Eigenvectors, diagonalization of the matrix, modal matrix.

Vector spaces: definition and examples, subspace: definition and examples. Linear Combinations, linear span, linearly independent and dependent sets, basis and dimension, row space and column space of a matrix, Coordinates vector, inner products and orthogonality.

Linear Transformation: Definition and examples, algebra of linear transformations, matrix of a linear transformation. Singular, non-singular linear transformations and invertible linear transformations. Rank and nullity of linear transformations, Rank-Nullity theorem.