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Sequences and Series: Convergences and divergence – Ratio test – Comparison tests – Integral
test – Cauchy’s root test – Alternate series – Leibnitz’s rule.
Mean Value Theorems (without proofs): Rolle’s Theorem – Lagrange’s mean value theorem –
Cauchy’s mean value theorem – Taylor’s and Maclaurin’s theorems with remainders.
Linear differential equations – Bernoulli’s equations – Exact equations and equations reducible to
exact form.
Applications: Newton’s Law of cooling – Law of natural growth and decay – Orthogonal
trajectories – Electrical circuits.
Non-homogeneous equations of higher order with constant coefficients – with non-homogeneous term of
the type eax, sin ax, cos ax, polynomials in xn
, eax V(x) and xnV(x) – Method of Variation of parameters.
Applications: LCR circuit, Simple Harmonic motion
Introduction – Homogeneous function – Euler’s theorem – Total derivative – Chain rule –
Jacobian – Functional dependence – Taylor’s and Mc Laurent’s series expansion of functions of
two variables.
Applications: Maxima and Minima of functions of two variables without constraints and
Lagrange’s method (with constraints).
Double and Triple integrals – Change of order of integration – Change of variables.
Applications: Finding Areas and Volumes.