Inverse of a Matrix-Linear Dependence and Independence of Vectors-Consistency and inconsistency
of a system of linear equations-Rank of a matrix. Eigen Values and Eigen Vectors- Properties-
Caylay-Hamilton Theories-Diagonalisation-Quadratic forms -Reduction to Canonical forms.
Differential Calculus:
Successive Differentiation-Leibnitz Theorem-Indeterminate forms-L' Hospital's Rule-Radius of
curvature-centre of curvature-Evolutes Partial Differentiation-Homogeneous functions Euler's
Theorem-Maxima and minima of functions of two variables.
Infinite Series:
Notions of Convergence and Divergence-Comparison test-Ratio test-Raabe's test-Cauchy's Root
test-Test for alternating series-absolute convergence.
Fourier Series:
Even functions, odd functions, periodic functions-Dirichelet's condition-Euler’s formula. Functions
with period 2 and 2L. Half range sine and cosine series. Laplace transforms -Properties-Inverse
Transforms.
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