Page 17 - REC :: B.E. BME Curriculum and Syllabus - R2019

Department of BME, REC

Semester II

MA19252 DIFFERENTIAL EQUATIONS AND COMPLEX VARIABLES L T P C

Common to B.E. - CSE, BME, ECE & EEE and B.Tech. – I.T 3 0 1 4

OBJECTIVES
• To handle practical problems arising in the field of engineering and technology using
differential equations.
• To solve problems using the concept of Vectors calculus, Complex analysis, Laplace
transforms.

UNIT I SECOND AND HIGHER ORDER DIFFERENTIAL EQUATIONS 12
Second and higher order Linear differential equations with constant coefficients - Method of
variation of parameters –Legendre’s linear equations - Formation of partial differential
equations - Solutions of standard types of first order partial differential equations -
Lagrange’s linear equation – Linear homogenous partial differential equations of second and
higher order with constant coefficients.

UNIT II VECTOR CALCULUS 12
Gradient, divergence and curl – Directional derivative – Irrotational and solenoidal vector
fields – Vector integration –Green’s theorem, Gauss divergence theorem and Stokes’
theorem (excluding proofs) – Simple applications involving cubes and rectangular
parallelopipeds.

UNIT III ANALYTIC FUNCTIONS 12
Analytic functions – Necessary and sufficient conditions for analyticity in Cartesian and polar
coordinates - Properties – Harmonic conjugates – Construction of analytic function -
1 2
Conformal mapping – Mapping by functions w = + , c cz , , z - Bilinear transformation.
z
z
UNIT IV COMPLEX INTEGRATION 12
Cauchy’s integral theorem – Cauchy’s integral formula (excluding proof) – Taylor’s and
Laurent’s series – Singularities – Residues – Residue theorem (excluding proof) –
Application of residue theorem for evaluation of real integrals - Evaluation of real definite
integrals as contour integrals around semi-circle (excluding poles on the real axis).

UNIT V LAPLACE TRANSFORM 12
Laplace transform – Sufficient condition for existence – Transform of elementary functions –
Basic properties – Transforms of derivatives and integrals of functions - Derivatives and
integrals of transforms - Transforms of unit step function and impulse functions, periodic
functions - Inverse Laplace transform – Problems using Convolution theorem – Initial and
final value theorems – Solution of linear ODE of second order with constant coefficients
using Laplace transformation techniques.
TOTAL: 60 PERIODS

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