Tuesday, June 12, 2012
MA2161 MATHEMATICS – 2(II) Syllabus - Anna University Second semester | Common to All Branches B.E.
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:
|
rd
|
||||
1.
|
Bali
N. P and
Manish Goyal, “Text
book of Engineering
|
Mathematics”, 3
|
Edition, Laxmi
|
||
Publications (p) Ltd., (2008).
|
th
|
||||
2.
|
Grewal. B.S, “Higher Engineering
Mathematics”, 40
|
Edition, Khanna Publications, Delhi, (2007).
|
|||
9
REFERENCES:
|
||||||
1.
|
Ramana B.V,
“Higher Engineering Mathematics”,Tata
|
McGraw Hill Publishing Company,
|
||||
New Delhi, (2007).
|
rd
|
|||||
2.
|
Glyn James,
“Advanced Engineering Mathematics”, 3
|
Edition, Pearson Education, (2007).
|
||||
th
|
||||||
3.
|
Erwin Kreyszig, “Advanced
Engineering Mathematics”, 7
|
Edition, Wiley India, (2007).
|
||||
rd
|
||||||
4.
|
Jain R.K
and Iyengar S.R.K,
“Advanced Engineering
|
Mathematics”, 3
|
Edition, Narosa
|
|||
Publishing House Pvt. Ltd., (2007).
|
||||||
Subscribe to:
Post Comments (Atom)
0 Responses to “MA2161 MATHEMATICS – 2(II) Syllabus - Anna University Second semester | Common to All Branches B.E.”
Post a Comment