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.
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.
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
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.
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.
Unit VI Linear Algebra : Eigen Values and Eigen Vectors, Diagonalization Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonalization of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.
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.
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.
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
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.
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.
Unit VI Linear Algebra : Eigen Values and Eigen Vectors, Diagonalization Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonalization of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.