MA 9211 MATHEMATICS III

MA 9211 MATHEMATICS III

(Common to all branches of BE / B.Tech)

UNIT I FOURIER SERIES

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half-range Sine and Cosine series – Complex form of Fourier Series – Parseval’s identity – Harmonic Analysis.

UNIT II PARTIAL DIFFERENTIAL EQUATIONS

Formation – Solutions of first order equations – Sandard types and Equations reducible to standard types – Singular solutions - Lagrange’s Linear equation – Integral surface passing through a given curve – Solution of linear equations of higher order with constant coefficients.

UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

Method of separation of Variables – Solutions of one dimensional wave equation, - One-dimensional heat equation – Steady state solution of two-dimensional heat equation – Fourier series solutions in Cartesian coordinates. 

UNIT IV FOURIER TRANSFORM 

Fourier integral theorem – Fourier transform pair-Sine and Consine transforms – Properties – Transform of simple function – Convolution theorem - Parseval’s identity.

UNIT V Z – TRANSFORM AND DIFFERENCE EQUATION

Z-transform-Elementary properties-Inverse z transform – Convolution theorem- Formation of difference equation-Solution of difference equation using z transform.

TEXT BOOK

1. B.S.Grewal, “Higher Engineering Mathematics”, Khanna Publications (2007)

REFERENCES

1. Glyn James, “Advanced Modern Engineering Mathematics, Pearson

Education (2007)

2. B.V.Ramana, “Higher Engineering Mathematics” Tata McGraw Hill 2007.

3. N.P.Bali, and Manish Goyal, “A Text Book of Engineering 7th Edition (2007)

Lakshmi Publications (P) Limited, New Delhi.