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You are here:Open notes-->Anna-University-->MA2161-MATHEMATICS--II

**MA2161 MATHEMATICS – II**

# How to study this subject

**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 semicircular

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”, 3

rd

Edition, Laxmi

Publications (p) Ltd., (2008).

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. Glyn James, “Advanced Engineering Mathematics”, 3

rd

Edition, Pearson Education, (2007).

3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7

th

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).

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