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MSRIT Numerical and Mathematical Biology Sem 3
Unit 3 : Numerical Differentiation and Numerical Integration(Derivatives using Newton- Gregory forward and backward interpolation formulae, Newton-Cote s quadrature formula, Trapezoidal Rule, Simpson s (1/3)rd rule, Simpson s(3/8)th rule)
1. Numerical Differentiation and Integration(Mathematics) Total View (985)

In this unit deals with Trapezoidal rule, Simpson's 1/3rd and 3/8 rule, Weddle's rule and Runge-Kutta 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.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 16
 Price: Rs 12

2. Numerical Differentiation(Mathematics) Total View (340)

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.
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 Published on: 01/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 13
 Price: Rs 9.75

3. Differentiation of an Integral(Mathematics) Total View (279)

In this unit, we introduce the concept of the differentiation of an integral.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 4
 Price: Rs 3

4. Absolute Continuity(Mathematics) Total View (283)

In this unit, students are introduced to the concept of Absolute continuity of functions.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 4
 Price: Rs 3

5. Lagrange and Newton Interpolations and Finite Difference Operators(Mathematics) Total View (679)

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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 Published on: 01/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 14
 Price: Rs 10.5

6. Hermite Interpolation, Piecewise and Spline Interpolation and Bivariate Interpolation(Mathematics) Total View (340)

The Hermite interpolating polynomial interpolates not only the function f(x) but also its (certain order) derivatives at a given set of tabular points.
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 Published on: 01/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 13
 Price: Rs 9.75

7. Predictor-Corrector Methods and Stiff System(Mathematics) Total View (359)

We shall discuss the application of the explicit and implicit multi-step methods for the solution of the initial value problems in this unit.
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 Published on: 01/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 17
 Price: Rs 12.75

8. Differentiation of Monotone Functions,Vitali Lemma(Mathematics) Total View (278)

In this unit, we introduce the concept of differentiation of monotone functions.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 3
 Price: Rs 2.25

9. Ordinary Differential Equations and Finite Difference Methods(Mathematics) Total View (384)

This unit explains Initial Value Problem and linear second order differential equations. It also explains non-linear second order differential equations. and describes finite difference methods.
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 Published on: 01/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 13
 Price: Rs 9.75

10. Introduction to Wildlife Biology(Environmental Science and Technology) Total View (418)

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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 Published on: 23/09/13 Author: KSOU Publisher: Karnataka State Open University Pages: 11
 Price: Rs 8.25

11. Role of Biostatistics in Scientific Research(Clinical Nutrition and Dietetics) Total View (461)

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 re-thinking the ro ......
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 Published on: 02/12/13 Author: KSOU Publisher: Karnataka State Open University Pages: 14
 Price: Rs 10.5

12. Fundamental Numerical Computations(Mathematics) Total View (972)

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.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 12
 Price: Rs 9

13. Mathematical Modeling of Some Fundamental Problems(Mathematics) Total View (910)

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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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 16
 Price: Rs 12

14. Mathematical Modelling through System of Differential Equations(Mathematics) Total View (989)

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.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 19
 Price: Rs 14.25

15. Introduction to mathematical Modeling(Mathematics) Total View (913)

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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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 17
 Price: Rs 0

16. Mathematical Modelling for Convection Diffusion and Reaction Processes(Mathematics) Total View (971)

After studying this unit, students will be able to analyse about convection diffusion processes-Burger's equation which will cover Burger's equation and the plane wave solution, Cole-Hopf 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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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 32
 Price: Rs 24

17. Mathematical Logic -Part II(Information Technology) Total View (212)

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.
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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 14
 Price: Rs 10.5

18. Mathematical Modelling for Suspended Particulate Matter(Mathematics) Total View (978)

Suspended Particulate Matter (SPM) is solid and liquid particle suspended in ambient air of which particle size is not more than 10 micro-m. In this unit, we have considered the effects of SPM on human body and climate etc.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 23
 Price: Rs 17.25

19. Mathematical Modelling through Second Order Differential Equations(Mathematics) Total View (981)

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.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 11
 Price: Rs 8.25

20. Mathematical Principles of Air Pollution(Mathematics) Total View (1000)

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.
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 Published on: 21/10/13 Author: KSOU Publisher: Karnataka State Open University Pages: 11
 Price: Rs 8.25

21. The Derivative of a Function, Mean Value Theorems, Taylor Theorem, Maxima and Minima(Mathematics) Total View (884)

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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 Published on: 29/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 21
 Price: Rs 15.75

22. Setting up of First Order Differential Equations and their Solutions(Mathematics) Total View (927)

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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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 21
 Price: Rs 15.75

23. Limit of a Function, Continuity and Uniform Continuity(Mathematics) Total View (874)

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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 Published on: 29/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 20
 Price: Rs 0

24. Limitations of Mathematical Modeling(Mathematics) Total View (906)

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.
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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 3
 Price: Rs 2.25

25. Mathematical Logic -Part I(Information Technology) Total View (213)

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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 Published on: 30/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 12
 Price: Rs 0