### MA4107 - Applied Mathematics for Power Systems Engineers (Syllabus) 2021-regulation Anna University

## Title

MA4107 | APPLIED MATHEMATICS FOR POWER SYSTEMS ENGINEERS | LPTC |
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**3104**

**OBJECTIVES:**

• To develop the ability to apply the concepts of matrix theory in Electrical Engineering problems.

• To familiarize the students in the field of differential equations to solve boundary value problems associated with engineering applications.

• To develop the ability among the students to solve problems using Fourier series associated with engineering applications.

• To impart deep knowledge and concepts to solve complicated problems using linear programming.

• To develop the capability of solving problems using non - linear programming techniques.

• To familiarize the students in the field of differential equations to solve boundary value problems associated with engineering applications.

• To develop the ability among the students to solve problems using Fourier series associated with engineering applications.

• To impart deep knowledge and concepts to solve complicated problems using linear programming.

• To develop the capability of solving problems using non - linear programming techniques.

UNIT I | MATRIX THEORY | 9 |
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The Cholesky decomposition - Generalized Eigenvectors - Canonical basis - QR factorization - Singular value decomposition - Pseudo inverses - Least square approximation.

UNIT II | LAPLACE TRANSFORM TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS | 9 |
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Definitions - Properties - Transform error function - Bessel's function - Dirac Delta function - Unit step function - Convolution theorem - Inverse Laplace transform - Complex inversion formula - Solutions to partial differential equations : Heat and Wave equations.

UNIT III | FOURIER SERIES | 9 |
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Fourier Trigonometric series : Periodic function as power signals - Convergence of series - Even and odd functions : Cosine and sine series - Non periodic function - Extension to other intervals - Power signals : Exponential Fourier series - Parseval's theorem and power spectrum - Eigenvalue problems and orthogonal functions - Regular Sturm –Liouvillesystems - Generalized Fourier series.

UNIT IV | LINEAR PROGRAMMING PROBLEMS | 9 |
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Formulation - Graphical solution - Simplex method - Big M method - Two phase method - Transportation and Assignment models.

UNIT V | NON – LINEAR PROGRAMMING PROBLEMS | 9 |
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Lagrange multipliers – Equality constraints – Inequality constraints – Kuhn – Tucker Conditions – Quadratic programming.

**L - 45; T - 15; TOTAL – 60 PERIODS**

**OUTCOMES:**

• Student can able to apply the concepts of matrix theory in Electrical Engineering problems.

• Students can be easily understood to solve boundary value problems associated with engineering applications.

• Able to solve problems using Fourier series associated with engineering applications.

• Able to understood the basic concepts and also to solve complicated problems using linear programming.

• Student have capability of solving problems using non - linear programming techniques.

• Students can be easily understood to solve boundary value problems associated with engineering applications.

• Able to solve problems using Fourier series associated with engineering applications.

• Able to understood the basic concepts and also to solve complicated problems using linear programming.

• Student have capability of solving problems using non - linear programming techniques.

**REFERENCES:**

1. Richard Bronson , MATRIX OPERATION , Schaum's outline series, Second Edition, McGraw Hill, New Delhi , 2011.

2. Sankara Rao . K, INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS , Prentice Hall of India Pvt . Ltd, New Delhi , 1997.

3. Andrews .L.C, and Phillips. R.L, MATHEMATICAL TECHNIQUES FOR ENGINEERS AND SCIENTISTS , Prentice Hall , New Delhi , 2005.

4. Taha .H.A , OPERATIONS RESEARCH - AN INTRODUCTION , Tenth Edition, Pearson Education, New Delhi , 2010.

2. Sankara Rao . K, INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS , Prentice Hall of India Pvt . Ltd, New Delhi , 1997.

3. Andrews .L.C, and Phillips. R.L, MATHEMATICAL TECHNIQUES FOR ENGINEERS AND SCIENTISTS , Prentice Hall , New Delhi , 2005.

4. Taha .H.A , OPERATIONS RESEARCH - AN INTRODUCTION , Tenth Edition, Pearson Education, New Delhi , 2010.

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