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MATHEMATICS - I
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Lemma Yimer
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UNIT I
Ordinary differential equations-Introduction
Linear and Bernoulli’s equations
Exact equations
equations reducible to exact equations
Orthogonal trajectories
Linear Differential equations:
Definition
Theorem
Operator D
Rules for finding the complementary function
Inverse operator
Rules for finding the particular integral
Working procedure to solve the equation
Newton’s law of cooling
Heat flow
Rate of Decay of Radio-Active Materials
UNIT II
Linear dependence of solutions
Method of variation of parameters
Equations reducible to linear equations
Cauchy’s homogeneous linear equation
Legendre’s linear equation Simultaneous linear equations with constant coefficients
Statistics
Method of least squares
Correlation
co-efficient of correlation
lines of regression
UNIT III
Laplace Transforms
Introduction
Transforms of elementary functions
Properties of Laplace Transforms
existence conditions
Transforms of derivatives
Integrals
multiplication by tn
division by t
Evaluation of integrals by Laplace Transforms
Inverse transforms
convolution theorem
Application to Differential equations with constant coefficients
transforms of unit step function
unit impulse function
periodic function
Convolution Theorem
Application to ordinary differential equations
UNIT IV
Introduction and Euler’s formulae
Conditions for a Fourier expansion
Functions having points of discontinuity
Change of interval
Even and Odd functions
Half range series Typical wave forms and Parseval’s formulae,
Complex form of the Fourier series Practical harmonic analysis
2nd
Acharya Nagarjuna University
Bapatla Engineering College
Engineering
General
1st
Yearbook
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