MA2161 MATHEMATICS – II SYLLABUS

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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
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 semi-circular 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.
TOTAL : 60 PERIODS
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”, 3rd 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”, 3rd Edition, Narosa Publishing House Pvt. Ltd., (2007).