MATHEMATICS – II

2.         MA22                          MATHEMATICS – II                                     3  1  0  100

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).