Book Details

MATHEMATICS I

MATHEMATICS I

Published by uLektz

Course Code:R16102

Author:uLektz

University: JNTU Kakinada

Regulation:2016

Categories:Engineering Mathematics

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

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Description :R16102 MATHEMATICS I

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

Topics
Unit I: Differential equations of first order and first degree

1.1 Linear equation

1.2 Bernoulli equation

1.3 Exact-Reducible to exact.

1.4 Applications : Newton’s Law of cooling-Law of natural growth and decay orthogonal trajectories.

1.5 Electrical circuits- Chemical reactions

Unit II: Linear differential equations of higher order

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

2.2 Method of Variation of parameters

2.3 Applications: LCR circuit, Simple Harmonic motion

Unit III: Laplace transforms

3.1 Laplace transforms of standard functions-Shifting theorems

3.2 Transforms of derivatives and integrals

3.3 Unit step function –Dirac’s delta function

3.4 Inverse Laplace transforms– Convolution theorem (with out proof)

3.5 Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms

Unit IV: Partial differentiation

4.1 Introduction- Homogeneous function-Euler’s theorem

4.2 Total derivative-Chain rule

4.3 Generalized Mean value theorem for single variable (without proof)

4.4 Taylor’s and Mc Laurent’s series expansion of functions of two variables- Functional dependence

4.5 Jacobian

4.6 Applications: Maxima and Minima of functions of two variables without constraints and Lagrange’s method (with constraints)

Unit V: First order Partial differential equations

5.1 Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions

5.2 Solutions of first order linear (Lagrange) equation and nonlinear (standard types) equations

Unit VI: Higher order Partial differential equations

6.1 Solutions of Linear Partial differential equations with constant coefficients.

6.2 RHS term of the type eax + by, sin(ax + by), cos(ax + by), xm yn - Classification of second order partial differential equations

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