MA9211 Anna university syllabus common to all branches B.E/B.TECH

**A**

**I**

**M**

**:**

To facilitate the understanding of the principles and to cultivate the art of formulating
physical
problems in the language of mathematics.

**O**

**B**

**JE**

**C**

**T**

**I**

**V**

**E**

**S**

**:**

· To introduce
Fourier
series analysis
which
is central to
many applications
in engineering apart from
its use in solving boundary value problems

· To acquaint the student with Fourier transform techniques used in wide variety of
situations in which the functions used are not periodic

· To introduce the effective mathematical tools for the solutions of partial differential
equations that model physical processes

· To develop Z-
transform techniques which will perform
the same task for
discrete time systems as Laplace Transform, a valuable aid in analysis of continuous time systems

**UN**

**I**

**T I FOURIER SERIES 9+3**

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.

**UN**

**I**

**T II FOURIER TRANSFORM 9+3**

Fourier integral theorem – Fourier transform pair-Sine and Cosine transforms –
Properties – Transform of elementary functions – Convolution theorem
– Parseval’s
identity.

**UN**

**I**

**T III PARTIAL DIFFERENTIAL EQUATIONS 9+3**

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.

**UN**

**I**

**T IV APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 9+3**

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.

**UN**

**I**

**T V Z – TRANSFORM AND DIFFERENCE EQUATIONS 9+3**

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.

**T**

**EX**

**T BOOK:**

**L**

**: 45, T: 15, TOTAL = 60 PERIODS**

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

**R**

**E**

**FERENCES:**

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.

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