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SYLLABUS

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, Problems and Applications on the Above Theorem

UNIT-2

Differential Equations 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 Homogeneous and Non-homogeneous Differential 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 xn V(x) - Method of Variation of Parameters, Cauchy and Legendre’s Linear Equations. 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 Maclaurin’s Series Expansion of Functions of Two Variables. Applications: Maxima and Minima of Functions of Two Variables without Constraints and Lagrange’s Method

UNIT-5

Multiple Integrals Double and Triple Integrals - Change of Order of Integration in Double Integrals - Change of Variables to Polar, Cylindrical and Spherical Coordinates. Applications: Finding Areas and Volumes.