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MA 201 |
MATHEMATICS - III |
3-1-0-8 |
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Prerequistes: Nil Syllabus: Complex analysis: Complex
numbers and elementary properties; Complex functions - limits, continuity and
differentiation, Cauchy-Riemann equations, analytic and harmonic functions,
elementary analytic functions, anti-derivatives and line (contour)
integrals, Cauchy-Goursat theorem, Cauchy's
integral formula, Morera's theorem, Liouville's theorem, Fundamental theorem of algebra and
maximum modulus principle; Power series, Taylor series, zeros of analytic functions, singularities and Laurent series, Rouche's theorem and argument principle, residues, Cauchy's Residue theorem and applications,
Mobius transformations and
applications. Partial differential equations: Fourier series,
half-range Fourier series, Fourier transforms, finite sine and cosine
transforms; First order
partial differential equations, solutions of linear and quasilinear first order
PDEs, method of characteristics; Classification of
second-order PDEs, canonical form; Initial and boundary value problems involving
wave equation and heat conduction equation, boundary value problems involving Laplace equation and solutions by method of separation of
variables; Initial-boundary value problems in non-rectangular coordinates. Laplace and
inverse Laplace transforms, properties,
convolutions; Solution of ODEs and PDEs by Laplace transform; Solution of
PDEs by Fourier transform. Textbooks: 1.
J. W. Brown
and R. V. Churchill, Complex Variables and Applications, 7th Ed., 2.
I. N. Sneddon, Elements of Partial Differential Equations,
McGraw Hill, 1957. 3.
E. Kreyszig,
Advanced Engineering Mathematics, 10th Ed., Wiley, 2015. References: 1.
J. H. Mathews
and R. W. Howell, Complex Analysis for Mathematics and Engineering, 3rd Ed.,
Narosa,1998. 2.
S. J. Farlow, Partial Differential Equations for Scientists and
Engineers, Dover Publications, 1993. 3.
K. Sankara Rao, Introduction to
Partial Differential Equations, 3rd Ed., Prentice Hall of India, 2011. |
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