
MSRIT Numerical and Mathematical Biology Sem 3 Unit 3 : Finite Differences and Interpolation(Forward and backward differences, Interpolation,
NewtonGregory forward and backward Interpolation formulae, Lagrange s interpolation formula, Newton s divided difference interpolation formula (no proof)) 


1. Hermite Interpolation, Piecewise and Spline Interpolation and Bivariate Interpolation(Mathematics) 
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The Hermite interpolating polynomial interpolates not only the function f(x) but also its (certain order) derivatives at a given set of tabular points.
Title: Math 2.4 Numerical Analysis




2. Numerical Differentiation(Mathematics) 
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There are several methods available to find the derivative of a function f(x) in closed form. However, when f(x) is a complicated function or when it is given in a tabular form, we use numerical methods.
Title: Math 2.4 Numerical Analysis




3. Lagrange and Newton Interpolations and Finite Difference Operators(Mathematics) 
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There are two main uses of .interpolation or 'interpolating polynomials. The first use is in reconstructing the function f(x) when it is not given explicitly and only the value of f(x) and / or its certain order derivatives at it set of points, called nodes; tabular points or arguments are known. The second use is to replace the function f(x) by and interpolating polynomial P(x) so that many commo
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Title: Math 2.4 Numerical Analysis




4. Numerical MethodsII(Mathematics III) 
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This chapter is a continuation of Chapter 6. Here, we consider the topic of
Finite Differences with applications to Interpolation and Integration.
Title: Engineering Mathematics Part  III




5. 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




6. Introduction to Wildlife Biology(Environmental Science and Technology) 
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Wildlife means all living things that are found outside direct human control. It includes plants, animals and microbes that are not cultivated or reared by man. Some people use the term wildlife only to large organisms that are living in the forests. In fact wildlife includes all
organisms right from bacteria, many microscopic organisms like protozoa, fungi, worms, insects, frogs, birds, mammals,
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Title: MSc Tech 203 Biodiversity and Conservation




7. Fundamental Numerical Computations(Mathematics) 
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In this unit, students will be able to study the Logic, algorithm, program and sample output of sum of first 10 terms of sine series, the entered number is prime number or not, sum of two matrices, A+ B, and product of two matrices A *B and finally, the factorial of a number.
Title: Math 3.5 Computer Programming




8. Mathematical Modeling of Some Fundamental Problems(Mathematics) 
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Mathematical Modeling in terms of differential equations arises when the situation modeled involves some continuous variables varying with respect to other continuous variables and we have reasonable hypothesis about the rate of change of dependent variables with respect to independent variables. Mathematical models in terms of ordinary differential equations will be studied in this unit and the u
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Title: Math 3.4 Mathematical Modeling




9. Numerical Differentiation and Integration(Mathematics) 
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In this unit deals with Trapezoidal rule, Simpson's 1/3rd and 3/8 rule,
Weddle's rule and RungeKutta 2nd and 4th order. The evaluation of expressions involving these integrals can become daunting, if not indeterminate. For this reason, a wide variety of numerical methods has been developed to simplify the integral.
Title: Math 3.5 Computer Programming




10. Mathematical Modelling through System of Differential Equations(Mathematics) 
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In mathematics, an ordinary differential equation (ODE) is an equation in which there is only one independent variable and one or more derivatives of a dependent variable with respect to the independent variable, so that all the derivatives occurring in the equation are ordinary derivatives.
Title: Math 3.4 Mathematical Modeling




11. Introduction to mathematical Modeling(Mathematics) 
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A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences such as physics, biology, earth science, meteorology and engineering disciplines like computer science, artificial intelligence, but also in the social sciences Physi
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Title: Math 3.4 Mathematical Modeling




12. 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




13. 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




14. Numerical Methods II(Mathematics) 
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Interpolation is the `art of reading between the lines in a table'. To explain this briey, suppose that a data consisting of (n + 1) ordered pairs of values of the form (xi; yi); i = 0; 1; 2; _ _ _ ; n; is available. Let yi be the value of an unknown function of x at x = xi. A question of practical importance here is, what is the value of y at x = ~x where ~x is none of xi; i = 0; 1; 2; _ _ _ ; n,
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Title: Engineering Mathematics  III




15. 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




16. Mathematical Logic Part II(Information Technology) 
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In this unit concepts like equivalence of WFFs, tautological implication, duality of WFF, two important normal forms namely disjunctive and conjunctive forms and finally inference process given some set of premises are discussed in various sections, in detail with several examples.
Title: MSIT101 Essential Mathematics




17. Mathematical Modelling for Suspended Particulate Matter(Mathematics) 
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Suspended Particulate Matter (SPM) is solid and liquid particle suspended in
ambient air of which particle size is not more than 10 microm. In this unit, we have considered the effects of SPM on human body and climate etc.
Title: Math 3.4 Mathematical Modeling




18. Mathematical Modelling through Second Order Differential Equations(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 price of commodities, the flow of fluids, the concentration of chemicals, etc., often lead to differential equation. Such equations may depend on one or more independent variables.
Title: Math 3.4 Mathematical Modeling




19. Mathematical Principles of Air Pollution(Mathematics) 
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After studying this unit, students will be able to construct and analyse mathematical principle of air pollution using gradient diffusion model. They will also be able to explain conservation of mass, conservation of momentum and conservation of species/turbulent flow in the atmosphere.
Title: Math 3.4 Mathematical Modeling




20. 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
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Title: Math 3.4 Mathematical Modeling




21. Limitations of Mathematical Modeling(Mathematics) 
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A crucial part of the modeling process is the evaluation of whether or not a given mathematical model describes a system accurately. This question can be difficult to answer as it involves several different types of evaluation. In this regard we have discussed the limitations of modeling in following sections.
Title: Math 3.4 Mathematical Modeling




22. Mathematical Logic Part I(Information Technology) 
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Logic is the discipline that deals with the methods of reasoning. On an elementary level, logic provides rules and techniques to determine whether a given statement (argumep') is valid. Logical reasoning is used in mathematics to prove theorems, and in computer science to verify the covertness of programs. Logic has its applications in various other fields such as natural science, social science a
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Title: MSIT101 Essential Mathematics




23. Finite Automata and Conversion from NFA to DFA(Computer Science) 
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The extension to NFA  a "feature" called epsilon transitions, denoted by E, the empty string. The E transition lets us spontaneously take a transition, without receiving an input symbol. This is another mechanism that allows NFA to be in multiple states at once.
Title: MSCS516C Theory of Computation




24. Numerical Solution of System of Linear Equations(Mathematics) 
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This unit deals with the various direct methods of solving linear system of
simultaneous equations, the prominent methods being the Gauss elimination and the iterative procedures of GaussSeidels are explored.
Title: Math 3.5 Computer Programming




25. PredictorCorrector Methods and Stiff System(Mathematics) 
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We shall discuss the application of the explicit and implicit multistep methods for the solution of the initial value problems in this unit.
Title: Math 2.4 Numerical Analysis






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