Book Details

MATHEMATICS – I

MATHEMATICS – I

Published by uLektz

Course Code:15A54101

Author:uLektz

University: Jawaharlal Nehru Technological University, Anantapur (JNTUA)

Regulation:2015

Categories:Engineering Mathematics

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

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Topics
UNIT – I DIFFERENTIAL EQUATION

1.1 Exact, linear and Bernoulli equations

1.2 Applications to first order equations: Orthogonal trajectories

1.3 Simple electric circuits

1.4 Non-homogeneous linear differential equations of second and higher order with constant coefficients with RHS term of the type eax, sin ax, cos ax, polynomials in x, eax V(x), xV(x)

UNIT - II LINEAR DIFFERENTIAL EQUATIONS

2.1 Method of variation of parameters, Linear equations with variable coefficients: Euler-Cauchy Equations, Legendre’s linear equation

2.2 Applications of linear differential equations - Mechanical and Electrical oscillatory circuits and Deflection of Beams

UNIT - III PARTIAL DIFFERENTIATION

3.1 Taylor’s and Maclaurin’s Series

3.2 Functions of several variables

3.3 Jacobian

3.4 Maxima and Minima of functions of two variables

3.5 Lagrange's method of undetermined Multipliers with three variables only

3.6 Radius of curvature

UNIT – IV MULTIPLE INTEGRAL

4.1 Multiple integral – Double and triple integrals – Change of Variables – Change of order of integration.

4.2 Applications to areas and volumes in Cartesian and polar coordinates using double and triple integral.

UNIT – V VECTOR CALCULUS

5.1 Vector Calculus: Gradient – Divergence – Curl and their properties

5.2 Vector integration – Line integral - Potential function – Area – Surface and volume integrals

5.3 Vector integral theorems: Green's theorem

5.4 Stoke’s theorem

5.5 Gauss's Divergence Theorem (Without proof) - Application of Green's, Stoke’s and Gauss's Theorem

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