Unit I : Differential Calculus Rolle’s Theorem, Mean Value Theorems, Taylor's Series and Maclaurin's Series, Expansion of functions using standard expansions, Indeterminate Forms, L' Hospital's Rule, Evaluation of Limits and Applications. (Chapters - 1, 2, 3) Unit II : Fourier Series Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval’s identity and Applications to problems in Engineering. (Chapter - 4) 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)
