ADVANCED MATHEMATICS Sub Code: EVS11 CIE:50 Hrs/ Week: 04 SEE:50 Total Hrs: 50 Credits: 4

Course Objectives: 1. Reduce the given matrix by applying different techniques of decomposition method. 2. Understand variation of functions and functionals to solve problems associated with calculus of variations. 3. Apply transform methods for wave equation and elliptic equations. 4. Analyze and solve Linear & Nonlinear programming problems with linear constraints to get optimum solution.

Course Content: Module-1 Matrix Theory: QR decomposition, shifted QR algorithm, generalized inverse and Singular-Value decomposition. 10 Hours

Module-2 The Calculus of Variations: Functional, Euler’s equation, Solutions of Euler’s Equation, Isoperimetric problems, Functional on several dependent variables and Functional involving higher order derivatives 10 Hours

Module-3 Transform Methods: Laplace transform methods for one dimensional wave equation, Displacements in a string and Fourier transform methods for one dimensional heat conduction problems in infinite and semi-infinite rod. 10 Hours

Module-4 Elliptic Equations: Laplace equation, Properties of Harmonic functions; Fourier transforms method for Laplace equation and Poisson equation. 10 Hours

Module-5 Linear & Nonlinear Programming: The Simplex method-Two Phase and Big M techniques, Dual Simplex method, Lagranges multiplier method and Karush-Kuhn-Tucker conditions and its solutions. 10 Hours

Course Outcomes: After completion of the course students are expected to 1. Understand the algorithmic approach to matrix operations. 2. Find the solution of problems in dynamics of rigid bodies, optimization of orbits, vibration problems and elliptic partial differential equations. 3. Approach a wide variety of engineering problems dealing with.

Text Books: 1. Richard Bronson, Schaum’s Outline of “Theory and Problems of Matrix Operations", McGraw-Hill, 1989. 2. B.S.Grewal, “Higher Engineering Mathematics”, Khanna Publishers, 39th Edition, 2005. 3. K. Sankara Rao, "Introduction to partial differential equations", Prentice–Hall of India, 3rd Edition, 2013. 4. Taha H. A., “Operations research - An introduction", McMilan Publishing co, 1982.

Reference Books: 1. David C. Lay, “Linear Algebra and its applications”, 3rd Edition, Pearson Education, 2002. 2. H. K. Dass, Er. Rajnish Verma, “Higher Engineering Mathematics”, S. Chand Publishers, 3rd Edition, 2014. 3. L. Elsgolts, “Differential equations and the calculus of variations, 3rd Print, 1977, MIR Publishers. 4. S. D. Sharma and Himanshu Sharma, “Operations Research: Theory, Methods and Applications”, KNRN Publisher, 15th Edition, 1972.