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### YMA002 APPLIED MATHEMATICS - II SYLLABUS | ANNA UNIVERSITY BCA 2ND SEMESTER SYLLABUS | ANNA UNIVERSITY 2ND SEMESTER SYLLABUS

YMA002 APPLIED MATHEMATICS - II  SYLLABUS | ANNA UNIVERSITY BCA 2ND SEMESTER SYLLABUS | ANNA UNIVERSITY 2ND SEMESTER SYLLABUS

YMA002 APPLIED MATHEMATICS - II L T P C
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UNIT I MULTIPLE INTEGRALS 12
Double integration- Cartesian and polar co-ordinates- Change of order of integration- Area
as a double integral, Change of variables between Cartesian and polar co- ordinates-
Triple integration- Volume as a triple integral
UNIT II FOURIER SERIES 12
Dirichlet’s condition-General Fourier series-Odd and even functions-Half range
Fourier series-Parseval’s identity-Harmonic analysis
UNIT III COMPLEX DIFFERENTIATION 12
Functions of complex variable-analytic function-NecessaryCondition-CauchyRiemann
equation–Sufficient conditions (excluding proof) -Properties of analytic functions–
Harmonicconjugate-Construction of analytic functions – Conformal Mapping -
w=z+a,w=az,w=1/z.w=z2-Bilinear transformation.
UNIT IV COMPLEX INTEGRATION 12
Statement and applications of Cauchy’s Integral theorem andformula-Taylor’s and Laurent’s
expansions- Isolated singularities- Residues-Cauchy’s residue theorem- Contour
integration over unit circle and semi circular contour (excluding poles on boundaries)
UNIT V LAPLACE TRANSFORM 12
Laplace Transforms-Condition for existence-Transforms of Elementary functions- Basic
properties-Derivatives and integrals of transforms- Transforms of derivatives and integrals
– Initial and Final value theorem- Transform of unit step functions and impulse function–
Transformof Periodic function-InverseLaplace transform- Convolution theorem-
Solution of linear ODE of second order with constant co- efficient, using Laplace
transformation
LECTURE:45TUTORIALS:15 TOTAL: 60
REFERENCES AND TEXT BOOKS :
1 Kandasamy. P, Thilagavathy K and Gunavathy K, Engineering Mathematics for First
year B.E/B.Tech, S.Chand and company Ltd, New Delhi-110055, Seventh Revised
edition 2007
2 Veerarajan T , Engineering Mathematics (for First year) Tata Mc Graw Hill
Publishing co.New Delhi 110008 (2008)
3 Grewal B.S, Higher Engineering Mathematics 38th edition, Khanna Publishers
New Delhi (2004)