MATHEMATICS II anna university syllabus

MATHEMATICS II                                     L  T  P  C

 (Common to all B.E/B.Tech programmes)                  3   1  0   4

UNIT I           ORDINARY DIFFERENTIAL EQUATIONS                                9+3

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             PARTIAL DIFFERENTIAL EQUATIONS                                    9+3

Formation of partial differential equations – Lagrange’s linear equation – Solutions of standard types of first order partial differential equations - Linear partial differential equations of second and higher order with constant coefficients.

UNIT III        VECTOR CALCULUS                                                                       9+3

Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector fields – Line and Surface integrals – Green’s theorem in a plane, Gauss divergence theorem and stokes’ theorem (only statements) – Verification of Green’s theorem – Applications of Gauss divergence and Stoke’s theorems involving spheres, parallelepipeds and cylinders.

UNIT IV        ANALYTIC FUNCTIONS                          9+3

Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy – Riemann equation and Sufficient conditions (only statements) – Harmonic and orthogonal properties of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping : and bilinear transformation.

UNIT V          COMPLEX INTEGRATION                                                             9+3

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).

L = 45     T =15                                          TOTAL = 60 PERIODS

TEXT BOOKS

1. Narayanan, S., Manicavachagom Pillay, T.K. and Ramanaiah, G, “Advanced Mathematics for     Engineering Students, Vol I and Vol II”,  Viswanathan (Printers and Publishers) Pvt. Ltd.     Chennai (2002).
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. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, Third edition, Laxmi Publications (P) Ltd.,(2008).
3. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3^rd Edition, Narosa Publishing House Pvt. Ltd., (2007).
4. Greenberg, M.D., Advanced Engineering Mathematics, 2^nd Edition, Pearson Education, Delhi (2009).
5. Ravish R. Singh and Mukul Bhutt, Engineering Mathematics, Tata McGraw Hill Pvt. Ltd., New Delhi (2010).
6. Jafferey, A. Advanced Engineering Mathematics, Academic Press, Elsevier India (2003).
7. Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th edition, Wiley India (2007).