### MA3351 Syllabus - Transforms And Partial Differential Equations - 2021 Regulation Anna University

## MA3351 Syllabus - Transforms And Partial Differential Equations - 2021 Regulation Anna University

MA3351 |
TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS | LTPC |
---|

**3104**

**COURSE OBJECTIVES:**

• To introduce the basic concepts of PDE for solving standard partial differential equations.

• 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 series techniques in solving heat flow problems used in various situations.

• To acquaint the student with Fourier, transform techniques used in wide variety of situations.

• To introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time systems.

• 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 series techniques in solving heat flow problems used in various situations.

• To acquaint the student with Fourier, transform techniques used in wide variety of situations.

• To introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time systems.

UNIT I |
PARTIAL DIFFERENTIAL EQUATIONS |
9+3 |
---|

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

UNIT II |
FOURIER SERIES |
9+3 |
---|

Dirichlet’s conditions – General Fourier series – Odd and even functions –
Half range sine series and cosine series – Root mean square value –
Parseval’s identity – Harmonic analysis.

UNIT III |
APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS | 9+3 |
---|

Classification of PDE – Method of separation of variables - Fourier series
solutions of one-dimensional wave equation – One dimensional equation of
heat conduction – Steady state solution of two- dimensional equation of
heat conduction (Cartesian coordinates only).

UNIT IV |
FOURIER TRANSFORMS |
9+3 |
---|

Statement of Fourier integral theorem– Fourier transform pair – Fourier
sine and cosine transforms – Properties – Transforms of simple functions –
Convolution theorem – Parseval’s identity.

UNIT V |
Z - TRANSFORMS AND DIFFERENCE EQUATIONS | 9+3 |
---|

Z-transforms - Elementary properties – Convergence of Z-transforms - –
Initial and final value theorems - Inverse Z-transform using partial
fraction and convolution theorem - Formation of difference equations –
Solution of difference equations using Z - transforms.

**TOTAL: 60 PERIODS**

**COURSE OUTCOMES: Upon successful completion of the course, students should be able to:**

1. Understand how to solve the given standard partial differential
equations.

2. Solve differential equations using Fourier series analysis which plays a vital role in engineering applications.

3. Appreciate the physical significance of Fourier series techniques in solving one- and two- dimensional heat flow problems and one-dimensional wave equations.

4. Understand the mathematical principles on transforms and partial differential equations would provide them the ability to formulate and solve some of the physical problems of engineering.

5. Use the effective mathematical tools for the solutions of partial differential equations by using Z transform techniques for discrete time systems

2. Solve differential equations using Fourier series analysis which plays a vital role in engineering applications.

3. Appreciate the physical significance of Fourier series techniques in solving one- and two- dimensional heat flow problems and one-dimensional wave equations.

4. Understand the mathematical principles on transforms and partial differential equations would provide them the ability to formulate and solve some of the physical problems of engineering.

5. Use the effective mathematical tools for the solutions of partial differential equations by using Z transform techniques for discrete time systems

**TEXT BOOKS:**

1. Grewal B.S., “Higher Engineering Mathematics", 44thEdition, Khanna
Publishers, New Delhi, 2018.

2. Kreyszig E, "Advanced Engineering Mathematics ", 10th Edition, John Wiley, New Delhi, India, 2018.

2. Kreyszig E, "Advanced Engineering Mathematics ", 10th Edition, John Wiley, New Delhi, India, 2018.

**REFERENCES:**

1. Andrews. L.C and Shivamoggi. B, "Integral Transforms for Engineers"
SPIE Press, 1999.

2. Bali. N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 10th Edition, Laxmi Publications Pvt. Ltd, 2021.

3. James. G., "Advanced Modern Engineering Mathematics", 4thEdition, Pearson Education, New Delhi, 2016.

4. Narayanan. S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for Engineering Students", Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

5. Ramana. B.V., "Higher Engineering Mathematics", McGraw Hill Education Pvt. Ltd, New Delhi, 2018.

6. Wylie. R.C. and Barrett. L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.

2. Bali. N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 10th Edition, Laxmi Publications Pvt. Ltd, 2021.

3. James. G., "Advanced Modern Engineering Mathematics", 4thEdition, Pearson Education, New Delhi, 2016.

4. Narayanan. S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for Engineering Students", Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

5. Ramana. B.V., "Higher Engineering Mathematics", McGraw Hill Education Pvt. Ltd, New Delhi, 2018.

6. Wylie. R.C. and Barrett. L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.

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