JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Mathematics

Course Objectives

to prepare the students to

• understand the relevance of mathematical methods to solve engineering problems.
• understand how to apply these methods for a given engineering problem.

Course Outcomes

Students will be able to

• understand vector spaces, linear transformation, eigenvalues and eigenvectors of linear operators
• learn about linear programming problems and understand the simplex method for solving linear programming problems in various fields of science and technology
• acquire knowledge about nonlinear programming and various techniques used for solving constrained and unconstrained nonlinear programming problems
• understand the concept of random variables, functions of random variable and their probability distribution
• understand stochastic processes and their classification

UNIT - I

Vector spaces, Linear transformations, Matrix representation of linear transformation, Eigen values and Eigen vectors of linear operator

UNIT - II

Linear Programming Problems, Simplex Method, Duality, Non Linear Programming problems

UNIT - III

Unconstrained Problems, Search methods, Constrained Problems

UNIT - IV

Lagrange method, Kuhn-Tucker conditions, Random Variables, Marginal and Conditional distributions, Elements of stochastic processes

UNIT - V

Mathematical methods applied to Power Engineering, examples – economic load dispatch, optimal power flow, unit commitment

TEXT BOOKS:

• 1. Kenneth Hoffman and Ray Kunze, “Linear Algebra”, 2nd Edition, PHI, 1992
• 2. Erwin Kreyszig, “Introductory Functional Analysis with Applications”, John Wiley & Sons, 2004

REFERENCES:

• 1. Irwin Miller and Marylees Miller, John E. Freund’s “Mathematical Statistics”, 6th Edn, PHI, 2002
• 2. J. Medhi, “Stochastic Processes”, New Age International, New Delhi., 1994
• 3. A Papoulis, “Probability, Random Variables and Stochastic Processes”, 3rd Edition, McGraw Hill, 2002
• 4. John B Thomas, “An Introduction to Applied Probability and Random Processes”, John Wiley, 2000 R19 M. TECH. EPE/EPS
• 5. Hillier F S and Liebermann G J, “Introduction to Operations Research”, 7th Edition, McGraw Hill, 2001
• 6. Simmons D M, “Non Linear Programming for Operations Research”, PHI, 1975
• 7. MIT online course, Prof. Gilbert Strang, Linear Algebra, https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D
• 8. Matpower, Free open-source tools for electric power system simulation and optimization, https://matpower.org/ R19 M. TECH. EPE/EPS M. TECH. I Year I Sem. (EPE/EPS)