MA2161 MATHEMATICS – II anna university BE B.Tech second semester syllabus download

MA2161 MATHEMATICS – II  SYLLABUS


UNIT I ORDINARY DIFFERENTIAL EQUATIONS 
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 
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 
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 

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 

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.


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”, 3rd 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”, 3rd Edition, Narosa Publishing House Pvt. Ltd., (2007)
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