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Electrical Transients in Power Systems, 2ed
by Allan Greenwood
To develop the ability to apply the concepts of Matrix theory and Linear programming in Electrical Engineering problems.
To achieve an understanding of the basic concepts of one dimensional random variables and apply in electrical engineering problems.
To familiarize the students in calculus of variations and solve problems using Fourier transforms associated with engineering applications.
UNIT I MATRIX THEORY
- The Cholesky decomposition – Generalized Eigen vectors, Canonical basis – QR factorization – Least squares method – Singular value decomposition.
UNIT II CALCULUS OF VARIATIONS
- Concept of variation and its properties – Euler‟s equation – Functional dependant on first and higher order derivatives – Functionals dependant on functions of several independent variables – Variational problems with moving boundaries – problems with constraints – Direct methods: Ritz and Kantorovich methods.
UNIT III ONE DIMENSIONAL RANDOM VARIABLES
- Random variables – Probability function – moments – moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a Random Variable.
UNIT IV LINEAR PROGRAMMING
- Formulation – Graphical solution – Simplex method – Two phase method – Transportation and Assignment Models
UNIT V FOURIER SERIES
- Fourier Trigonometric series: Periodic function as power signals – Convergence of series – Even and odd function: cosine and sine series – Non-periodic function: Extension to other intervals – Power signals: Exponential Fourier series – Parseval‟s theorem and power spectrum – Eigen value problems and orthogonal functions – Regular Sturm-Liouville systems – Generalized Fourier series.