MA2161 MATHEMATICS II

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# 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).