
MSRIT Numerical and Mathematical Biology Sem 3 Unit 3 : Numerical Differentiation and Numerical Integration(Derivatives using Newton Gregory forward and backward interpolation formulae, NewtonCote s quadrature formula, Trapezoidal Rule, Simpson s (1/3)rd rule, Simpson s(3/8)th rule) 


1. 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




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. Differentiation of an Integral(Mathematics) 
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In this unit, we introduce the concept of the differentiation of an integral.
Title: Math 3.2 Measure Theory




4. Absolute Continuity(Mathematics) 
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In this unit, students are introduced to the concept of Absolute continuity of functions.
Title: Math 3.2 Measure Theory




5. 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




6. 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




7. 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




8. Differentiation of Monotone Functions,Vitali Lemma(Mathematics) 
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In this unit, we introduce the concept of differentiation of monotone
functions.
Title: Math 3.2 Measure Theory




9. Ordinary Differential Equations and Finite Difference Methods(Mathematics) 
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This unit explains Initial Value Problem and linear second order differential equations. It also explains nonlinear second order differential equations. and describes finite difference methods.
Title: Math 2.4 Numerical Analysis




10. 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




11. Role of Biostatistics in Scientific Research(Clinical Nutrition and Dietetics) 
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Biostatistics has been demanded increasingly in biomedical research since the 1960s for support in experimental design, mathematical and statistical modelling as well as computational statistics. This resulted in the establishment of biostatistical units in universities, research institutes and larger pharmaceutical companies; a development not without disturbances and regularly rethinking the ro
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Title: MSc.CND103 Research Methods and Biostatistics




12. 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




13. 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




14. 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




15. 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




16. 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




17. 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




18. 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




19. 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




20. 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




21. The Derivative of a Function, Mean Value Theorems, Taylor Theorem, Maxima and Minima(Mathematics) 
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The derivative of a function y = f(x) at a point x = c represents the instantaneous rate of change of the function f(x) with respect to the independent variable x at the point c. It is equal to the slope of the tangent to the function at point x = c In other words, dy/dx. = tan theta where theta is the angle between the tangent to the function at x = c and the x axis. The derivative finds applicat
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Title: Math 2.2 Real Analysis II




22. 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




23. Limit of a Function, Continuity and Uniform Continuity(Mathematics) 
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The concept of a limit is fundamental to calculus. In this unit we will introduce important notions of limit of a function, continuity and uniform continuity. The idea of the function f having the limit A at a point c is that the values f(x) are close to A when x is close to c (but different from c). The term 'close to' is explained technically by delta definition.
Continuous functions are very i
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Title: Math 2.2 Real Analysis II




24. 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




25. 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






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