Page 15 - REC :: B.E. EEE Curriculum and Syllabus - R2019

Reference Books / Web links:
1 Sharma, Brij Kishore, “ Introduction to the Constitution of India:, Prentice Hall of India, New Delhi.
2 U.R.Gahai, “Indian Political System “, New Academic Publishing House, Jalaendhar..

SEMESTER II

Subject Code Subject Name Category L T P C
MA19252 DIFFERENTIAL EQUATIONS AND COMPLEX VARIABLES BS 3 1 0 4
Common to II sem. B.E.- Computer Science and Engineering,
Biomedical Engineering, Electronics and Communication
Engineering & Electrical and Electronics Engineering and B.Tech. –
Information Technology

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 - Conformal mapping – Mapping by functions
1
w  z  , c cz , , z - Bilinear transformation.
2
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 Contact Hours : 60

Course Outcomes:
On completion of the course, students will be able to
 Apply various techniques in solving ordinary differential equations and partial differential equations
 Use the concept of Gradient, divergence and curl to evaluate line, surface and volume integrals.
 Use the concept of Analytic functions, conformal mapping and bilinear transformation.