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UNIT-1: Vector calculus

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: Laplace Transforms

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: Fourier series and Fourier Transforms

Non-homogeneous equations of higher order with constant coefficients “ with non-homogeneous term of the type eax, sin ax, cos ax, polynomials in xn , eaxV(x) and xnV(x) “ Method of Variation of parameters. Applications: LCR circuit, Simple Harmonic motion.

UNIT-4: PDE of first order

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: Second order PDE and Applications

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

Vector Calculus-Vector Differentiation -Definitions

Published on 2021-03-08

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