MA4106 Applied Mathematics for Power Electronics Engineers Syllabus:

MA4106 Applied Mathematics for Power Electronics 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 Laplace transform associated with engineering applications.
 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 develop the ability among the students to solve problems using Fourier series associated with engineering applications.

UNIT I MATRIX THEORY

The Cholesky decomposition – Generalized Eigenvectors – Canonical basis – QR factorization – Singular value decomposition – Pseudo inverses – Least square approximation.

UNIT II CALCULUS OF VARIATIONS

Concept of variations and its properties – Euler’s theorem – Functional dependent on first and higher order of derivatives – Functionals dependent on functions of several independent variables – Variational problems with moving boundaries – Isoperimetric problems – Direct methods : Rayleigh Ritz method and Kantorovich problems .

UNIT III 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 IV Z – TRANSFORM TECNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

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

UNIT V 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.

TOTAL : 60 PERIODS

OUTCOMES :

 Able to apply the concepts of matrix theory in Electrical Engineering problems.
 Able to solve boundary value problems associated with engineering applications.
 Able to solve problems using Laplace transform associated with engineering applications.
 Use the effective mathematical tools for the solutions of partial differential equations by using Z transform techniques for discrete time systems.
 Able to solve problems using Fourier series associated with engineering applications.

REFERENCES:

1. Richard Bronson, MATRIX OPERATION , Schaum’s outline series, Second Edition, McGraw Hill, New Delhi , 2011.
2. Elsgolc. L.D., ” CALCULUS OF VARIATIONS ” , Dover Publications Inc., New York, 2007.
3. SankaraRao. K , INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS , Prentice Hall of India Pvt . Ltd, New Delhi , 1997.
4. Grewal.B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 44th Edition , 2018.
5. Andrews .L.C, and Phillips. R.L, MATHEMATICAL TECHNIQUES FOR ENGINEERS AND SCIENTISTS , Prentice Hall , New Delhi , 2005.