MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS SYLLABUS
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 FOURIER TRANSFORM
Fourier integral theorem – Fourier transform pair-Sine and Cosine transforms –
Properties – Transform of elementary functions – Convolution theorem – Parseval’s
identity.
UNIT – III PARTIAL DIFFERENTIAL EQUATIONS
Formation – Solutions of first order equations – Standard 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 – IV APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Method of separation of Variables – Solutions of one dimensional wave equation and
one-dimensional heat equation – Steady state solution of two-dimensional heat equation
– Fourier series solutions in Cartesian coordinates.
UNIT – V Z – TRANSFORM AND DIFFERENCE EQUATIONS
Z-transform – Elementary properties – Inverse Z-transform – Convolution theorem –
Initial and Final value theorems – Formation of difference equation – Solution of
difference equation using Z-transform.
TEXT BOOK
Grewal, B.S. “Higher Engineering Mathematics”, Khanna Publications (2007)
REFERENCES:
1. Glyn James, “Advanced Modern Engineering Mathematics, Pearson Education(2007)
2. Ramana, B.V. “Higher Engineering Mathematics” Tata McGraw Hill (2007).
3. Bali, N.P. and Manish Goyal, “A Text Book of Engineering 7th Edition (2007)Lakshmi Publications (P) Limited, New Delhi
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 FOURIER TRANSFORM
Fourier integral theorem – Fourier transform pair-Sine and Cosine transforms –
Properties – Transform of elementary functions – Convolution theorem – Parseval’s
identity.
UNIT – III PARTIAL DIFFERENTIAL EQUATIONS
Formation – Solutions of first order equations – Standard 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 – IV APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Method of separation of Variables – Solutions of one dimensional wave equation and
one-dimensional heat equation – Steady state solution of two-dimensional heat equation
– Fourier series solutions in Cartesian coordinates.
UNIT – V Z – TRANSFORM AND DIFFERENCE EQUATIONS
Z-transform – Elementary properties – Inverse Z-transform – Convolution theorem –
Initial and Final value theorems – Formation of difference equation – Solution of
difference equation using Z-transform.
TEXT BOOK
Grewal, B.S. “Higher Engineering Mathematics”, Khanna Publications (2007)
REFERENCES:
1. Glyn James, “Advanced Modern Engineering Mathematics, Pearson Education(2007)
2. Ramana, B.V. “Higher Engineering Mathematics” Tata McGraw Hill (2007).
3. Bali, N.P. and Manish Goyal, “A Text Book of Engineering 7th Edition (2007)Lakshmi Publications (P) Limited, New Delhi