MA2161 MATHEMATICS – II Syllabus [Regulation: 2008]

MA2161                                         MATHEMATICS – II                                        L T  P C

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”, 3rd Edition, Laxmi Publications (p) Ltd., (2008).

2.  Grewal. B.S, “Higher Engineering Mathematics”, 40th 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”,  7th Edition,  Wiley  India, (2007).

4.   Jain  R.K  and  Iyengar  S.R.K,  “Advanced  Engineering  Mathematics”,  3rd Edition, Narosa Publishing House Pvt. Ltd., (2007).