
Anna Numerical Methods SemIII Unit 1 : Solutions of Equtions and Eigen Value Problems(Solution of algebraic and transcendental equations  Fixed point iteration method  Newton Raphson method Solution of linear system of equations  Gauss Elimination method  Pivoting  GaussJordan methods  Iterative methods of GaussJacobi and GaussSeidel  Matrix Inversion by GaussJordan method  Eigenvalues of a matrix by Power method and by Jacobi's method) 


1. LOAD FLOW STUDIES(Electrical ) 
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The numerical analysis involving the solution of algebraic simultaneous equations forms the basis for solution of the performance equations in computer aided electrical power system analyses, such as during linear graph analysis, load flow analysis (nonlinear equations), transient stability studies (differential equations), etc.
Title: Computer Techniques in Power System Analysis
Published on: 11/10/18
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2. Dynamic Analysis(Finite Element Method) 
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Introduction, Equation Of Motion, Orthogonality Of The Eigenvectors, Formulation Of Inertial Properties, Solution Techniques For Eigenproblems.
Title: Finite Element Method




3. Numerical Methods I(Mathematics) 
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In the process of analysing problems in engineering, the analysts come across systems of equations which belong to different categories like, linear algebraic, nonlinear, transcendental, differential and integral equations. School level mathematics and elementary engineering mathematics include, among other topics, solution aspects of certain simple classes of equations. But, in many contexts, it
......
Title: Engineering Mathematics  III




4. Mathematical Modeling(Physics) 
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Algorithms, modeling and simulation in physics, Errors in numerical calculations, Roots of an equation : NewtonRaphson method and Bisection method. Application using Bisection method for LCR transient circuit (to determine R for given values of L and C for a prespecified rate of dissipation of energy), program in C
Title: Concise Physics BSc VI Semester Volume 8 (603)




5. Numerical Methods  I(Mathematics III) 
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In this chapter we first present some numerical methods of solving algebraic and transcendental equations. Then we consider the GaussSeidel method and the Relaxation method of solving systems of linear equations. Lastly, we consider the power method of finding the largest eigenvalue of a square matrix.
Title: Engineering Mathematics Part  III





6. Introduction to Finite Element Method(Finite Element Method) 
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Introduction, General Description of the Finite Element Method, List of Steps Involved in the Finite Element Method, Engineering Applications of Finite Element Method, Advantages of the Finite Element Method.
Title: Finite Element Method




7. Matrix Algebra, Eigenproblem and Numerical Integration(Finite Element Method) 
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Introduction, Matrix Algebra, Methods of Solution of Linear Algebraic Equations, Methods of Solution of Linear Algebraic Equations, Numerical Integration.
Title: Finite Element Method




8. Computational Algorithms for the Configuration Design (Aerodynamics Airworthiness)(Aeronautical Engineering) 
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Introduction, Theoretical Algorithms, Computational Algorithms, Optimization of Computational Grids , Parallel Computational Computing.
Title: Aerodynamics Airworthiness




9. Computational Algorithms for the Configuration Design (Aerodynamics Airworthiness)(Aeronautical Engineering) 
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• Introduction
• Theoretical Algorithms
• Computational Algorithms, Optimization of Computational Grids
• Parallel Computational Computing
Title: Aerodynamics Airworthiness




10. Bisection Method and Iterative Methods of Transcendental Equations (Mathematics) 
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This unit deals with the definition of transcendental function and explains the Bisection Method, Secant and RegulaFalsi Methods and Newton Raphson Method. It also explains Muller method, Chebyshev method and describes the multipoint iteration methods to find roots of the equations.
Title: Math 2.4 Numerical Analysis




11. Linear Algebra(Engineering Mathematics  I
) 
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In this section we discuss the concepts of elementary transformations, rank of a matrix, system of linear equations, linear transformations and Eigen values and Eigen vectors of a matrix
Title: Engineering Mathematics  1




12. Matrices(Mathematics) 
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Elementary transformations of a matrix, Echelon form, Normal form, Rank of a matrix, Consistency of a System of Linear Equations, Homogeneous System of Linear Equations, Nonhomogeneous System of Linear Equations, Eigen values and Eigen vectors, CayleyHamilton Theorem
Title: Introductory Mathematics II




13. Modeling Computational Aerodynamics for Speedup (Aerodynamics Airworthiness) (Aeronautical Engineering) 
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• Introduction
• Accelerating the Computational Algorithms
• Parallel Algorithms for Speedup, Parallel Computer Support
Title: Aerodynamics Airworthiness




14. MATLAB and Power System(Computer Science) 
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One of the major fields of electrical engineering for which the advent of computer techniques contributed a lot in research and development is Power Systems. Fortran was an effective programming language at one point of time in the past that suited the nature of computation required, before better languages replaced the same. MATLAB, undoubtedly, suits the computational challenges for power system
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Title: Fundamentals of MATLAB




15. General Iterative Methods(Mathematics) 
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This unit defines iteration function and explains high order Methods. It also explains acceleration of the convergence and efficiency of a method and helps in analyzing system of nonlinear equations.
Title: Math 2.4 Numerical Analysis




16. Rate of Convergence of Iterative Methods(Mathematics) 
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This unit defines rate of convergence of an iterative method and explains rate of convergence of Secant and RegulaFalsi Methods, and Newton
Raphson Method. It also explains rate of convergence of Muller method and Chebyshev method.
Title: Math 2.4 Numerical Analysis




17. Fundamental Aspects(Computer Science) 
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While the entry to a home is through a door, let us enter MATLAB through its windows !!! . After launching MATLAB, in order to plan, execute and obtain results for a specific analysis, there are dedicated display screens with associated task bars. These are called the windows.
Title: Fundamentals of MATLAB








18. Linear Programming  2, Simplex Method  1(Operations Research (computer Science and Information Science Engineering)) ) 
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Introduction, Basic Terms / Definitions, Standard Form of a LP Problem, (Characteristics of LPP), The Setting up and Algebra of Simplex Method, Steps of Simplex Method in Brief, Tie Breaking in Simplex Method (Degeneracy), Unbounded Solution, Multiple Optimal Solution.
Title: Introduction to operations Research




19. Operations Research(Computer Science) 
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Introduction, Linearprogramming1, LPâ€" 2, Simplex Method, Simplex Methodâ€" 2, Simplex Methodâ€" 2, Duality Theory, Duality Theory and Sensitivity Analysis, Other Algorithms for LP, Transportation and Assignment Problems, Game Theory, Decision Analysis, Metahuristics
Title: Operations Research




20. Solution of Linear Programming Problems(Operations Research
) 
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Graphical method used to solve a Linear Programming Problem is limited
to two decision variable problems. But most real life problems when formulated as LP model will have more than two decision variables.
Thus, we need a more efficient method to suggest an optimal solution of such problems. A more general method known as "Simplex Method" is suitable for solving Linear Programming Problems with
......
Title: Operations Research




21. Theory of Matrices  2(Mathematics I ) 
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In this chapter we continue the studies on Matrices. We first define the eigenvalues and eigenvectors of a square matrix and then prove some of their basic properties. The CayleyHamilton Theorem is stated and its applications illustrated. Thereafter, the reduction of a square matrix to a diagonal form is considered.
Title: Engineering Mathematics Volume  I




22. Complete Integrals of PDE(Mathematics) 
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In this unit, the reader studies various methods such as Charpit's method, Jacobi's method for finding the solution (Complete integral) of POE.
Title: Math 1.5 Differential Equations




23. Linear Programming Problem  Simplex Method(Operations Research (Mechanical and Allied Streams of VTU)) 
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Introduction, Standard Form of a LP Problem (Characteristics of LPP), Steps in Simplex Method, Artificial Variables, Dual Simplex Method, Degeneracy in LPP.
Title: Introduction to operations Research




24. Methods of Solving ODE 2(Mathematics) 
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In this unit the reader studies the zeros of solutions of ODE. Sturm's separation theorem. Sturm's comparison theorem , SturmLiouville problems. The reader also study the method of variation o f parameters. Eigenvalue problems.
Title: Math 1.5 Differential Equations




25. Flight Testing {Aerodynamics Airworthiness)(Aeronautical Engineering) 
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• Introduction
• Envelope Definition
• Flight Test Instrumentation and Telemetry Parameters
• Parametric Identification
• Atmospheric Disturbances Intensity
• Fault Tolerant FCS Testing
Title: Aerodynamics Airworthiness






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