UNIT I
Matrices: Rank of a Matrix, Elementary transformations, Inverse of a Matrix (Gauss
Jordan Method), Consistency of Linear System of Equations, Linear Transformations,
Vectors, Eigen values, Properties of Eigen values, Finding Inverse and Powers of a
Matrix by Cayley-Hamilton Theorem. Reduction to Diagonal form, Reduction of
Quadratic form to Canonical form, Nature of a Quadratic form, Complex matrices.
UNIT II
Differential Calculus: Rolle’s Theorem, Lagrange’s Mean Value Theorem, Cauchy’s
Mean Value Theorem, Taylor’s Theorem, Maclaurin’s Series.
Application: Curvature, Radius of Curvature.
Functions of two or more Variables: Partial Derivatives, Change of Variables,
Jacobians, Taylor’s Theorem for Function of two Variables, Maxima and Minima of
Functions of two Variables, Lagrange’s Method of Undetermined Multipliers.
UNIT III
Differential Equations of First Order: Formation of a Differential Equation, Solution
of a Differential Equation, Linear Equations, Bernoulli’s Equation, Exact Differential
Equations, Equations Reducible to Exact Equations.
Applications: Orthogonal Trajectories, Newton’s Law of Cooling.
Linear Differential Equations of Higher Order: Definitions, Operator D, Rules for
Finding the Complementary Function, Inverse Operator, Rules for finding Particular
Integral, Working Procedure to Solve the Equation.
UNIT IV
Linear Dependence of Solutions, Method of Variation of Parameters, Method of
Undetermined Coefficients, Equations Reducible to Linear Equations with Constant
Coefficients: Cauchy’s Homogeneous Linear Equation, Legendre’s Linear Equation,
Simultaneous Linear Differential Equations with Constant Coefficients.
Applications: L-C-R Circuits.
2014.