Home 2nd Semester MA6251 Mathematics 2 Syllabus for Anna University 2nd Semester REG 2013

MA6251 Mathematics 2 Syllabus for Anna University 2nd Semester REG 2013

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Anna University syllabus for Mathematics 2 which is common for all branches of 2nd semester exam of univ & affiliated colleges in Tamilnadu.

Type : Syllabus
Branch : Common to All
Subject : Mathematics 2
Exam     : April / May 2014

Download anna university syllabus for 2nd sem regulation 2013

Other subjects : Technical English 2 | All subjects

MA6251                                                 MATHEMATICS – II                                                

OBJECTIVES:

  • To make the student acquire sound knowledge of techniques in solving ordinary differential equations that model engineering problems.
  • To acquaint the student with the concepts of vector calculus, needed for problems in all engineering disciplines.
  • To develop an understanding of the standard techniques of complex variable theory so as to enable  the  student  to  apply  them  with  confidence,  in  application  areas  such  as  heat conduction, elasticity, fluid dynamics and flow the of electric current.
  • To make the student appreciate   the purpose of using transforms to create a new domain in which it is easier to handle the problem that is being investigated.

UNIT I             VECTOR CALCULUS                                                                                                9+3

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 parallelopipeds.

UNIT II            ORDINARY DIFFERENTIAL EQUATIONS                                                                9+3

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 III           LAPLACE TRANSFORM                                                                                           9+3

Laplace transform – Sufficient condition for existence – Transform of elementary functions – Basic properties – Transforms of derivatives and integrals of functions – Derivatives and integrals of transforms – Transforms of unit step function and impulse functions – Transform of periodic functions. Inverse Laplace transform -Statement of Convolution theorem   – Initial and final value theorems – Solution of  linear  ODE  of  second  order  with  constant  coefficients using  Laplace  transformation techniques.

UNIT IV          ANALYTIC FUNCTIONS                                                                                            9+3

Functions of a complex variable – Analytic functions: Necessary conditions – Cauchy-Riemann equations  and  sufficient  conditions  (excluding  proofs)  –  Harmonic  and  orthogonal  properties  of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping: w = z+k, kz, 1/z, z2, ez and bilinear transformation.

UNIT V           COMPLEX  INTEGRATION                                                                                       9+3

Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s integral formula – Taylor’s and Laurent’s series expansions – Singular points – Residues – Cauchy’s residue theorem – Evaluation of real definite integrals as contour integrals around unit circle and semi-circle (excluding poles on the real axis).

TEXT BOOKS:

TOTAL: 60 PERIODS

1.  Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd.,(2011)

2.  Grewal. B.S,  “Higher Engineering  Mathematics”,  41

(2011). Edition,  Khanna Publications,  Delhi,

REFERENCES:

1.  Dass,     H.K.,     and     Er.     Rajnish     Verma,”     Higher     Engineering     Mathematics”, S. Chand Private Ltd., (2011)

2.  Glyn James, “Advanced Modern Engineering Mathematics”, 3rd  Edition, Pearson Education, (2012).

3.  Peter V. O’Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, (2012).

4.  Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, (2008)

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