**Anna University**

**MA2161 MATHEMATICS – II Syllabus**

**Regulation 2008**

**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.

**UN****IT 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.

**UN****IT 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.

**UN****IT 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).

**UN****IT 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.

**T****EX****T BOOK:**

**T****O****T****A****L : 60 PERIODS**

1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3 Edition, Laxmi Publications (p) Ltd., (2008).

2. Grewal. B.S, “Higher Engineering Mathematics”, 40 Edition, Khanna Publications, Delhi, (2007).

**R****E****F****E****R****E****NC****ES****:**

1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company, New Delhi, (2007).

2. Glyn James, “Advanced Engineering Mathematics”, 3 Edition, Pearson Education, (2007).

3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7 Edition, Wiley India, (2007).

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