MA4107 Applied Mathematics for Power Systems Engineers Syllabus:

MA4107 Applied Mathematics for Power Systems Engineers Syllabus – Anna University PG Syllabus Regulation 2021

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.

UNIT I MATRIX THEORY

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

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

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 –Liouville systems – Generalized Fourier series.

UNIT IV LINEAR PROGRAMMING PROBLEMS

Formulation – Graphical solution – Simplex method – Big M method – Two phase method – Transportation and Assignment models.

UNIT V NON – LINEAR PROGRAMMING PROBLEMS

Lagrange multipliers – Equality constraints – Inequality constraints – Kuhn – Tucker Conditions – Quadratic programming.

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.

REFERENCES:

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