MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS MA 2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

MA2211   TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS          3  1  0  4

(Common to all branches)                                

                                                           

              

1.         Fourier Series                                                                                          9 + 3

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier Series – Parseval’s identify – Harmonic Analysis.

2.         Fourier TransformS                                                                               9 + 3

Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

3.         PARTIAL DIFFERENTIAL EQUATIONS                                                          9 +3

Formation of partial differential equations – Lagrange’s linear equation – Solutions of standard types of first order partial differential equations - Linear partial differential equations of second and higher order with constant coefficients.

4.         applications of partial differential equations                      9 + 3

Solutions of one dimensional wave equation – One dimensional equation of heat conduction  – Steady state solution of two-dimensional equation of heat conduction (Insulated edges excluded) – Fourier series solutions in cartesian coordinates.

5.         Z -TRANSFORMs AND DIFFERENCE Equations                                   9 + 3

Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z-transform.

                      

TEXT BOOKS

1.      Grewal, B.S, “Higher Engineering Mathematic”, 40^th Edition, Khanna publishers, Delhi, (2007)

 

 

REFERENCES

1.   Bali.N.P and Manish Goyal, “A Textbook of Engineering Mathematic”, 7^th Edition,       Laxmi Publications(P) Ltd. (2007)

2. Ramana.B.V., “Higher Engineering Mathematics”, Tata Mc-GrawHill Publishing Company limited, New Delhi (2007).

3.   Glyn James, “Advanced Modern Engineering Mathematics”, 3^rd Edition, Pearson Education (2007).

4.         Erwin Kreyszig, “Advanced Engineering Mathematics”, 8^th  edition, Wiley India