2. TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
SUBJECT CODE: MA6351

3. UNIT 1 PARTIAL DIFFERENTIAL EQUATIONS
FORMATION OF P.D.E
SINGULAR INTEGRALS
SOLUTION OF STANDARD TYPES OF 1ST ORDER P.D.E

4. LAGRANGE’S LINEAR EQUATION
LINEAR P.D.E OF 2ND AND HIGHER ORDER WITH CONSTANT COEFFICIENTS OF BOTH HOMOGENEOUS AND NON HOMOGENEOUS TYPES

5. applicationS MATHEMATICAL MODELING
ANY FIELD INVOLVING ATLEAST AN UNKNOWN FUNCTION

6. UNIT 2 FOURIER SERIES DRICHLET’S CONDITIONS GENERAL FOURIER SERIES
ODD AND EVEN FUNCTIONS

7. HALF RANGE SINE SERIES
HALF RANGE COSINE SERIES
COMPLEX FORM OF FOURIER SERIES
PARSEVAL’S IDENTITY
HARMONIC ANALYSIS

8. applicationS ANALYSIS OF CURRENT FLOW IN ELECTRICAL ENGINEERING
ANALYSIS OF SOUND WAVES
ELECTRONICALLY SYNTHESIZED MUSIC AND TAKING COMPUTER CLIPS

9. UNIT 3 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
CLASSIFICATION OF P.D.E
METHOD OF SEPARATION OF VARIABLES

10. SOLUTIONS OF ONE DIMENSIONAL WAVE EQUATION
ONE DIMENSIONAL EQUATION OF HEAT CONDUCTION
STEADY STATE SOLUTION OF TWO DIMENSIONAL EQUATION OF HEAT CONDUCTION

11. UNIT 4 FOURIER TRANSFORMS
STATEMENT OF FOURIER INTEGRAL THEOREM
FOURIER TRANSFORM PAIR

12. FOURIER SINE AND COSINE TRANSFORMS
PROPERTIES
TRANSFORMS OF SIMPLE FUNCTIONS
CONVOLUTION THEOREM
PARSEVAL’S IDENTITY

13. applicationS IN THE REPRESENTATION OF ELECTRICAL FIELD
DISCUSSION OF THE PHASE CHANGE ASSOCIATED WITH DIFFERENT PATHS
IT IS HIGHLY USEFUL IN SIGNAL PROCESSING

14. UNIT 5 Z-TRANSFORMS Z TRANSFORMS ELEMENTARY PROERTIES
INVERSE Z-TRANSFORM USING PARTIAL FRACTION AND RESIDUES

15. CONVOLUTION THEOREM
FORMATION OF DIFFERENTIAL EQUATIONS
SOLUTION OF DIFFERENTIAL EQUATIONS USING Z-TRANSFORMS

16. applicationS IN DIGITAL SIGNAL PROCESSING
ANALYSIS OF LINEAR DISCRETE SYSTEM
ANALYSIS OF DISCRETE SIGNALS
ANALYSIS OF DIGITAL FILTERS
SIMULATIONS OF CONTINUOUS SYSTEM

17. TEXT BOOKS
Veerarajan T., "Transforms and Partial Differential Equations", Tata McGraw Hill Education Pvt. Ltd., New Delhi, Second reprint, 2012.
Grewal B.S., "Higher Engineering Mathematics", 42nd Edition, Khanna Publishers, Delhi,

18. Narayanan S. , Manicavachagom Pillay. T. K and Ramanaiah
Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for Engineering Students" Vol. II & III, S.Viswanathan Publishers Pvt Ltd

19. references
Bali. N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 7th Edition, Laxmi Publications Pvt Ltd, 2007.
Ramana. B.V., "Higher Engineering Mathematics", Tata McGraw Hill Publishing Company Limited, New Delhi, 2008.

20. Glyn James, "Advanced Modern Engineering Mathematics", 3rd Edition, Pearson Education, 2007.
Erwin Kreyszig, "Advanced Engineering Mathematics", 8th Edition, Wiley India, 2007.

21. Ray Wylie C and Barrett. L
Ray Wylie C and Barrett.L.C, "Advanced Engineering Mathematics" Tata McGraw Hill Education Pvt Ltd, Sixth Edition, New Delhi, 2012.
Datta K.B., "Mathematical Methods of Science and Engineering", Cengage Learning India Pvt Ltd, Delhi, 2013.