Book Details

MATHEMATICS-II

MATHEMATICS-II

Published by uLektz

Course Code:TMA201

Author:uLektz

University: Uttarakhand Technical University

Regulation:2010

Categories:Engineering Mathematics

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

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Topics
UNIT - I DIFFERENTIAL EQUATIONS

1.1 Ordinary differential equations of first order

1.2 Exact differential equations

1.3 Linear differential equations of first order

1.4 Linear differential equations of nth order with constant coefficients

1.5 Complementary functions and particular integrals

1.6 Simultaneous linear differential equations

1.7 Solutions of second order differential equations by changing the dependent and independent variables

1.8 Method of variation of parameters

UNIT - II LAPLACE TRANSFORM

2.1 Laplace transform

2.2 Existence theorem

2.3 Laplace transform of derivatives and integrals

2.4 Inverse Laplace transform

2.5 Laplace transform of periodic function, Unit step function

2.6 Convolution theorem

2.7 Applications to solve simple linear and simultaneous linear differential equations

UNIT - III INFINITE SERIES

3.1 Introduction, Sequences

3.2 Series: Convergence

3.3 Series of positive terms

3.4 Comparison tests

3.5 Integral tests

3.6 Comparison of ratio‘s

3.7 D‘Alembert ratio test

3.8 Raabe‘s test

3.9 Cauchy root test

3.10 Alternating series: Lebnitz rule

3.11 Power series

3.12 Uniform convergence

3.13 Weierstrass‘s M-test

3.14 Properties of uniformly convergent series

UNIT - IV FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS

4.1 Periodic functions

4.2 Trigonometric series

4.3 Fourier series of periodic function

4.4 Euler‘s formula

4.5 Functions having arbitrary period

4.6 Change of intervals

4.7 Even and odd functions

4.8 Half range sine and cosine series

4.9 Introduction to partial differential equations

4.10 Linear partial differential equations with constant coefficients of second order and their classifications: parabolic, hyperbolic and elliptic with illustrative examples

UNIT - V APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

5.1 Method of separation of variables for solving partial differential equations

5.2 One dimensional wave equation

5.3 Laplace equation in two dimensions

5.4 Heat conduction equations of one dimension and two dimension

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