
MSRIT Numerical and Mathematical Biology Sem 3 Unit 2 : Partial Differential EquationsII(Derivation of one dimensional heat and wave equations, Numerical solution of one dimensional heat and wave equations, Two dimensional Laplace equation, Poisson equation) 


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. 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




3. Situations giving rise to Partial Differential Equations(Mathematics) 
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A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown or difficult to measure without this technique.
Title: Math 3.4 Mathematical Modeling




4. 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




5. 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




6. 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




7. 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





8. Mathematical Modelling for Convection Diffusion and Reaction Processes(Mathematics) 
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After studying this unit, students will be able to analyse about convection diffusion processesBurger's equation which will cover Burger's equation and the plane wave solution, ColeHopf transformation and the exact solution of Burger's equation. They will also be able to explain asymptotic behavior of the exact solution of Burger's equation and Burger's initial and boundary value problem and exp
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Title: Math 3.4 Mathematical Modeling




9. Partial Differential Equations(Mathematics III) 
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This chapter is a continuation of Chapter 4 of Part II. Here, we consider
the method of solving onedimensional wave equation, onedimensional heat equation and twodimensional Laplace equation by separation of variables. The D'Alembert's solution for onedimensional wave equation is also included.
Title: Engineering Mathematics Part  III





10. 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. Application of Partial Differential Equations(Mathematics) 
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We now study three linear homogeneous second order PDEs which are important in physical applications, the wave equation, the heat equation and Laplace's equation.
Title: Engineering Mathematics  III




13. 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




14. 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




15. 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




16. Variational Principles Probability Generating Function and Model For Traffic Flow(Mathematics) 
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A variational principle is a scientific principle used within the calculus of
variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions.
Title: Math 3.4 Mathematical Modeling




17. Classification of Second Order PDE(Mathematics) 
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In this unit the reader studies classification of second order partial differential equation. They also study the method of characteristics and classify the given second order POE to its respective canonical form.
Title: Math 1.5 Differential Equations




18. RandomProcesses(Applied Mathematics) 
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Now we are going to study about a family of random variables. A family of random variables indexed by a parameter (like time,) is known as a stochastic process or a random process. We know that the r.v. X, is by definition, a function of the possible outcomes S, of an experiment. Now a random process is a function of both time and S. When time t is fixed, the random process represents the random v
......
Title: Statistics Random Processes and Queuing Theory





20. 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




21. 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)




22. Poisson Distribution(Quantitative Techniques) 
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Poisson distribution is considered as a limiting case of binomial distribution. Poisson distribution derived by 'French mathematician Simon D. Poisson' in 1837. This distribution is a discrete probability function. Interestingly herewith the large number of experiments conducted, the probability of success would be very small.
Title: MB105 Quantitative Techniques




23. 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








24. Quantum Mechanics(Engineering Physics
) 
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All bodies absorb and emit radiation to different extents. The radiation spectrum of a black body is of important concern. This study is to understand the mechanism of absorption and emission of radiation.
Title: ENGINEERING PHYSICS
Published on: 11/04/19
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Pages:
8











25. Setting up of First Order Differential Equations and their Solutions(Mathematics) 
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Differential equations occur quite frequently in our daily life. The motion of an object can always be associated with a differential equation. The change in prices of commodities, the flow of fluids, the concentration of chemicals etc., often lead to differential equations. Such equations may depend on one or more independent variables. Further, it may include the derivatives of the first or high
......
Title: Math 3.4 Mathematical Modeling






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