MA 9161 Mathematics II syllabus download

 MA 9161 MATHEMATICS - II L T P C
(Common to all branches of B.E. / B.Tech Programmes) 3 1 0 4


AIM:

To introduce the effective mathematical tools needed for solving engineering problems
and to emphasize the underlying mathematical principles in specific situations
confronting practicing engineers.
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 DIFFERENTIAL EQUATIONS 9+3
Method of variation of parameters – Method of undetermined coefficients – Homogenous
equation of Euler’s and Legendre’s type – System of Simultaneous linear differential
equations with constant coefficients.

UNIT II VECTOR CALCULUS 9+3
Gradient and directional derivative – Divergence and Curl – Irrotational and Solenoidal
vector fields – Line integral over a plane curve – Surface Integral and Volume Integral -
Green’s, Gauss divergence and Stoke’s theorems – Verification and Application in
evaluating line, surface and volume integrals.

UNIT III ANALYTIC FUNCTION 9+3
Analytic functions – Necessary and sufficient conditions for analyticity - Properties –
Harmonic conjugates – Construction of analytic function - Conformal Mapping – Mapping
by functions
2 1
, , , w z c az z
z
  - Bilinear transformation.

UNIT IV COMPLEX INTEGRATION 9+3
Line Integral - Cauchy’s theorem and integral formula – Taylor’s and Laurent’s Series –
Singularities – Residues – Residue theorem – Application of Residue theorem for
evaluation of real integrals – Use of circular contour and semicircular contour with no
pole on real axis.

UNIT V LAPLACE TRANSFORMS 9+3
Existence conditions – Transforms of elementary functions – Basic properties –
Transforms of derivatives and integrals – Initial and Final value theorems – Inverse 18
transforms – Convolution theorem – Transform of periodic functions – Application to
solution of linear ordinary differential equations with constant coefficients.

L: 45, T: 15, TOTAL : 60 PERIODS

TEXT BOOKS
1. Grewal, B.S. “Higher Engineering Mathematics”, Khanna Publications (2007)
2. Ramana, B.V. “Higher Engineering Mathematics” Tata McGraw Hill (2007).

REFERENCES
1. Glyn James, “Advanced Modern Engineering Mathematics, Pearson Education
(2007)
2. Jain R.K. and Iyengar S.R.K., Advanced Engineering Mathematics (3
rd
Edition)
Narosa Publications, Delhi (2007).
For more information contact us via Studentstrainer@gmail.com.

Tweet