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Module 5 DOWNLOAD DOWNLOAD Module-5: Linear Algebra Elementary row transformation of a matrix, Rank of a matrix. Consistency and Solution of system oflinear equations; Gauss-elimination method, Gauss-Jordan method and Approximate solution byGauss-Seidel method. Eigenvalues and Eigenvectors-Rayleigh’s power method to find the dominantEigenvalue and Eigenvector.Self-Study: Solution of a system of equations by Gauss-Jacobi iterative method. The […]

Module 4 DOWNLOAD DOWNLOAD Module-4: Ordinary Differential Equations of higher order Higher-order linear ODE’s with constant coefficients – Inverse differential operator, method ofvariation of parameters, Cauchy’s and Legendre homogeneous differential equations. Problems.Self-Study: Applications to oscillations of a spring and L-C-R circuits.

Module 3 DOWNLOAD DOWNLOAD Module-3: Ordinary Differential Equations (ODE’s) of first order Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations.Applications of ODE’s-Orthogonal trajectories, Newton’s law of cooling.Nonlinear differential equations: Introduction to general and singular solutions; Solvable for p only;Clairaut’s equations, reducible to Clairaut’s equations. Problems.Self-Study: Applications of ODE’s: L-R circuits. Solvable

Module 2 DOWNLOAD DOWNLOAD Module-2: Differential Calculus – 2 Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems.Indeterminate forms-L’Hospital’s rule. Partial differentiation, total derivative-differentiation ofcomposite functions. Jacobian and problems. Maxima and minima for a function of two variables.Problems.Self-study: Euler’s Theorem and problems. Method of Lagrange undetermined multipliers withsingle constraint

Module 1 DOWNLOAD DOWNLOAD Module-1: Differential Calculus – 1 Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedalequations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and Pedal forms.Problems.Self-study: Center and circle of curvature, evolutes and involutes.