**APPLICABLE TO CHENNAI,MADURAI,COIMBATORE,TRICHY,TRINELVELI AND ALL DISTRICT COLLEGES FIRST YEAR SECOND SEMESTER STUDENTS**

**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 semicircular 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”, 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”, 3 Rd 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”, 3**

**Rd Edition, Narosa Publishing House Pvt. Ltd., (2007).**