| Lectures: 3 Periods/Week | Sessional Marks: 30 |
| University Exam: 3 Hours | University Examination Marks: 70 |
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 (direct method only),
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
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