
Anna Numerical Methods SemIII Unit 5 : Boundary Value problem in Ordinary andPartial Differential Equations(Finite difference methods for solving twopoint linear boundary value problems, Finite difference techniques for the solution of two dimensional Laplace's and Poisson's equations on rectangular domain  One dimensional heatflow equation by explicit and implicit (Crank Nicholson) methods  One dimensional wave equation by explicit method) 


1. 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




2. 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




3. 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




4. Existence of Solutions of ODE(Mathematics) 
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In this unit, the reader will learn some basic definitions of ordinary differential equations. Also the reader will study the existence and uniqueness of solutions of initial value problem and a system of differential equations. In order to fully understand the proofs of these theorems, the reader must be familiar with certain concepts of real function theory.
Title: Math 1.5 Differential Equations




5. Numerical Differentiation(Physics) 
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The method of finding derivatives analytically are well established when the functional relation between the dependent variable y and the independent variable x is known. However, in many practical situations like that of experimental data generated, the explicit relation between the dependent and independent variables is unknown
Title: Concise Physics BSc VI Semester Volume 8 (603)




6. Heat Transfer(Finite Element Method) 
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Introduction, Heat Transfer, Basic Equations of Heat Transfer, Governing Differential Equation for Heat Transfer in ThreeDimensional Bodies, Finite Element Formulation for Heat Transfer Problems, OneDimensional Heat Conduction with Convection.
Title: Finite Element Method








7. Fundamentals of Finite Element Method(Finite Element Method) 
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Introduction, Governing Differential Equation Formulation, Finite Element Formulation for Static Problems, Mathematical Model, Discretization, Elements, Nodal Degree of Freedom, Coordinate Systems, Generalized Coordinate Finite Element Models, Shape Function, Assemblage Of Element Matrices And Vectors, Structural Symmetry And AntiSymmetry.
Title: Finite Element Method




8. 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




9. Recent Advancements in Aerodynamics (Aerodynamics Airworthiness) (Aeronautical Engineering) 
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• Introduction
• High AnglesofAttack Computations
• Laminar and Unsteady Flows
• Numerical Optimisation
• Aeroelasticity
• Stealth Aerodynamics
Title: Aerodynamics Airworthiness




10. THEORY OF IC ENGINES(THEORY OF IC ENGINES ) 
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Title: THEORY OF IC ENGINES
Published on: 02/08/18
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Pages:
71








11. Numerical Methods  III(Mathematics III) 
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In Chapter 3, we obtained Fourier series solutions to onedimensional heat
equation, onedimensional wave equation and twodimensional Laplace equation. In this chapter we present some Numerical solutions to these equations.
Title: Engineering Mathematics Part  III




12. Difference Equations and Generating Functions(Mathematics) 
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After going through this unit we can define and construct generating functions for sequences arising in various types of combination problems. Also we use generating functions to find the number of integer solution to linear equations. We solve recurrence relation using generating functions.
Title: Math 1.4 Discrete Mathematics




13. Cauchy Problem(Mathematics) 
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In this unit, the reader studies about the Cauchy problem, principle of superposition. They also study the method of characteristics to solve semilinear, quasilinear and nonlinear PDEs.
Title: Math 1.5 Differential Equations




14. Introduction to PDE(Mathematics) 
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In this unit, the reader studies about introduction and formation of partial differential equation (PDE). They also study the classification of first order PDE and some basic definition pertaining to POE.
Title: Math 1.5 Differential Equations




15. Aerodynamic Strategic Design Software Development and Application (Aerodynamics Airworthiness)(Aeronautical Engineering) 
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• Introduction
• Computer Codes
• Geometry Discretization
• Numerical Viscosity
Title: Aerodynamics Airworthiness




16. 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





18. Numerical Methods for Ordinary Differential Equations(Engineering Mathematics  IV
) 
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Introduction, Preliminaries, TaylorSeries Method, Modified Euler's Method, RungeKutta Methods, MultiStep Predictor  Corrector Methods
Title: Engineering Mathematics  IV




19. Contents(Mathematics II) 
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This comprehensive and assimilable text introduces to the students the Mathematical concepts such as Matrices, Vector Calculus, Analytic Functions, Complex Integration and Laplace Transforms. The simple and systematic presentation will enable the students to grasp the concepts easily.
Title: Engineering Mathematics II
Published on: 09/02/19
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Pages:
10








20. 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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Pages:
34








21. 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




22. Solutions to NonLinear System of ODE(Mathematics) 
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The objective of this unit is the study of Nonlinear Autonomous system of ordinary differential equations, critical points, path and their nature. The reader also studies the method to find the nature of critical points. stability and paths by Liapunov direct method.
Title: Math 1.5 Differential Equations




23. Differential Equations(Physics) 
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Euler method, Runge  Kutta II and IV order methods. Applications: Freely falling body in a resistive medium with resistance proportional to velocity, Projectile motion, LCR transient circuit, solution to Schrodinger wave equation for Harmonic potential (plotting wave function only)
Title: Concise Physics BSc VI Semester Volume 8 (603)




24. Microwave Transmission Lines(Microwave Engineering) 
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Compare the solution of (8.4) with that of (8.6). It is found that the general solution of the former equation contains an exponentially increasing function and an exponentially decreasing function. Depending on the boundary conditions available, we can determine which of the two components will be the real solution. In a similar fashion, it is found that the general solution of (8.6) contains two
......
Title: Microwave Engineering









25. MATLAB and Electric Circuits(Computer Science) 
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The beauty of Electric Circuit is that it is the backbone of analysis for all types of electrical and electronic devices. Every electrical device, be it a generator, motor, an electronic amplifier, oscillator...and so on is characterised by a corresponding electric circuit. Depending upon the type of analysis like a frequency domain or time domain, the circuit is investigated for the required vari
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Title: Fundamentals of MATLAB






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