MA 2161 MATHEMATICS – II MA2161 MATHEMATICS – II

MA2161 MATHEMATICS – II 3 1 0 4
UNIT I ORDINARY DIFFERENTIAL EQUATIONS 12
Higher order linear differential equations with constant coefficients – Method of
variation of parameters – Cauchy’s and Legendre’s linear equations – Simultaneous
first order linear equations with constant coefficients.
UNIT II VECTOR CALCULUS 12
Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal
vector fields – Vector integration – Green’s theorem in a plane, Gauss divergence
theorem and stokes’ theorem (excluding proofs) – Simple applications involving
cubes and rectangular parallelpipeds.
UNIT III ANALYTIC FUNCTIONS 12
Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy
– Riemann equation and Sufficient conditions (excluding proofs) – Harmonic and
orthogonal properties of analytic function – Harmonic conjugate – Construction of
analytic functions – Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.
UNIT IV COMPLEX INTEGRATION 12
Complex integration – Statement and applications of Cauchy’s integral theorem and
Cauchy’s integral formula – Taylor and Laurent expansions – Singular points –
Residues – Residue theorem – Application of residue theorem to evaluate real
integrals – Unit circle and semi-circular contour(excluding poles on boundaries).
UNIT V LAPLACE TRANSFORM 12
Laplace transform – Conditions for existence – Transform of elementary functions –
Basic properties – Transform of derivatives and integrals – Transform of unit step
function and impulse functions – Transform of periodic functions.
Definition of Inverse Laplace transform as contour integral – Convolution theorem
(excluding proof) – Initial and Final value theorems – Solution of linear ODE of
second order with constant coefficients using Laplace transformation techniques.
TOTAL : 60 PERIODS
TEXT BOOK:
1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3
rd
Edition, Laxmi Publications (p) Ltd., (2008).
2. Grewal. B.S, “Higher Engineering Mathematics”, 40
th
Edition, Khanna
Publications, Delhi, (2007).
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing
Company, New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 3
rd
Edition, Pearson
Education, (2007).
3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7
th
Edition, Wiley
India, (2007).
4. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3
rd
Edition, Narosa Publishing House Pvt. Ltd., (2007).