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UNIT-1: Sequences, Series and Mean value theorems

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.

UNIT-2: Diff. eqs of first order and first degree

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.

UNIT-3: Linear differential equations of higher order

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

UNIT-4: Partial differentiation

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). 

UNIT-5: Multiple integrals

Double and Triple integrals – Change of order of integration – Change of variables. Applications: Finding Areas and Volumes.

Sequences And Series Convergence And Divergence Comparison Test

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Published on 2021-03-08

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