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You are here:Open notes-->Anna-University-->MA2211-TRANSFORMS-AND-PARTIAL-DIFFERENTIAL-EQUATIONS-

**MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS **

# How to study this subject

**OBJECTIVES**

The course objective is to develop the skills of the students in the areas of Transforms and

Partial Differtial Equations. This will be necessary for their effective studies in a large number of

engineering subjects like heat conduction, communication systems, electro-optics and

electromagnetic theory. The course will also serve as a prerequisite for post graduate and

specialized studies and research.

**UNIT I 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.

**UNIT II 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.

**UNIT III 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.

**UNIT IV 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.

**UNIT V 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.

TOTAL (L:45+T:15): 60 PERIODS

**TEXT BOOKS:**

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

(2007)

**REFERENCES:**

1. Bali.N.P and Manish Goyal, “A Textbook of Engineering Mathematic”, 7th 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”, 3rd Edition, Pearson Education

(2007).

4. Erwin Kreyszig, “Advanced Engineering Mathematics”, 8

th

edition, Wiley India (2007).

# Official Notes

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