
MSRIT Numerical and Mathematical Biology Sem 3 Unit 4 : Models for Blood Flows(Basic concepts of fluid dynamics, Hagen Poiseuille flow, Basic concepts about blood, Cardiovascular system and blood flows, Blood flow through artery with mild stenosis) 


1. 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




2. 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




3. Circulatory and Lymphatic System(Clinical Nutrition and Dietetics) 
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The Circulatory system is a system containing blood vessels, blood and heart which helps to transport lifegiving oxygen, nutrients and hormones to cells throughout the body and toxic waste products from the respective organ. An average adult contains 4.7 to 5.7 liters of blood, which consists of plasma, red blood cells, white blood cells and platelets.
Title: MSc.CND101 Human Physiology




4. 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




5. Blood Vessels and Heart: Cardio Circulatory System(Clinical Nutrition and Dietetics) 
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The main components of the human cardiovascular system are the heart, the veins, the blood vessels and blood and the blood circulates in the whole body. The circulation includes the pulmonary circulation, the loop through the lungs where blood is oxygenated and the systemic circulation, a "loop" through the rest of the body to provide oxygenated blood.
Title: MSc.CND101 Human Physiology




6. Probability, Random Variables, and Probability Distributions(Clinical Nutrition and Dietetics) 
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The foundation of all statistical methodology is probability theory, which progresses from elementary to the most advanced mathematics. Much of the misunderstanding and abuse of statistics comes from the lack of understanding of its probabilistic foundation. When assumptions of the underlying probabilistic (mathematical) model are grossly violated, derived inferential methods will lead to misleadi
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Title: MSc.CND103 Research Methods and Biostatistics




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. 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




11. 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




12. 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




13. 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




14. 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




15. 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




16. 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




17. 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




18. 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




19. Blood and Its Components(Clinical Nutrition and Dietetics) 
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You have learnt in the last unit that blood is a fluid connective tissue flowing allover the body As you know, red colored blood was associated with various emotions in olden days and continues to do so even now in certain situations. This unique fluid circulates in the body through heart, arteries, veins and capillaries.
Title: MSc.CND101 Human Physiology




20. 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




21. Chapter 1 * Basic Anatomy(Physics) 
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Chapter 1 deals with the basics of human anatomy and anatomical
terminology, various types of forces acts on the body, Physics of the
skeleton, hot and cold applications in medicines.
Title: Medical Physics
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22. 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




23. Cell and Its Membrane(Clinical Nutrition and Dietetics) 
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As you are aware all living organisms are made up of cells. You will be surprised to know that we have 50 trillion cells in our body carrying out various functions. The cells are responsible for all functions in a living organism. Cells join together to form tissues and these tissues associate to form organs.
Title: MSc.CND101 Human Physiology




24. Cell Models: Hadley Models(Geography) 
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At about the time that Coriolis published his studies on rotating bodies, scientists were beginning to realize that Hadley's single convection cell model was too simple. Atmospheric pressure and wind measurements taken at many locations around the planet did not fit the predictions made by the Hadley model. Some important modifications in the Hadley model were suggested in the 1850s, therefore, by
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Title: MSGE201 Climatology




25. Bisection Method and Iterative Methods of Transcendental Equations (Mathematics) 
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This unit deals with the definition of transcendental function and explains the Bisection Method, Secant and RegulaFalsi Methods and Newton Raphson Method. It also explains Muller method, Chebyshev method and describes the multipoint iteration methods to find roots of the equations.
Title: Math 2.4 Numerical Analysis






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