### MA2161 MATHEMATICS – 2(II) Syllabus - Anna University Second semester | Common to All Branches B.E.

 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: rd 1. Bali  N.  P  and  Manish  Goyal,  “Text  book  of  Engineering Mathematics”,  3 Edition,  Laxmi Publications (p) Ltd., (2008). th 2. Grewal. B.S, “Higher Engineering Mathematics”, 40 Edition, Khanna Publications, Delhi, (2007).

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 REFERENCES: 1. Ramana   B.V,   “Higher   Engineering   Mathematics”,Tata McGraw   Hill   Publishing   Company, New Delhi, (2007). rd 2. Glyn James, “Advanced Engineering Mathematics”, 3 Edition, Pearson Education, (2007). th 3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7 Edition, Wiley India, (2007). rd 4. Jain   R.K   and   Iyengar   S.R.K,   “Advanced   Engineering Mathematics”,   3 Edition,   Narosa Publishing House Pvt. Ltd., (2007).
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