MA2161 Mathematics II - SUBJECT CATALOG

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SYLLABUS:

MA2161          MATHEMATICS – II                                                                                        L T P C

3 1 0 4

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 semi-circular 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:

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1.  Bali  N.  P  and  Manish  Goyal,  “Text  book  of  Engineering  Mathematics”,  3

Publications (p) Ltd., (2008).

Edition,  Laxmi

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2.  Grewal. B.S, “Higher Engineering Mathematics”, 40

Edition, Khanna Publications, Delhi, (2007).

REFERENCES:

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

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2.  Glyn James, “Advanced Engineering Mathematics”, 3

Edition, Pearson Education, (2007).

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

Edition, Wiley India, (2007).

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4.  Jain  R.K  and  Iyengar  S.R.K,  “Advanced  Engineering  Mathematics”,  3

Publishing House Pvt. Ltd., (2007).

Edition,  Narosa