
MSRIT Numerical and Mathematical Biology Sem 3 Unit 1 : Partial Differential Equations I(Formation of PDE S by elimination of arbitrary constants and arbitrary functions, Solution of PDE  Lagrange s linear form, Method of separation of variables) 


1. 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




2. 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




3. 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




4. 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




5. 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




6. 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




7. 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




8. 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




9. 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




10. 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




11. 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




12. 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




13. 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




14. 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




15. 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




16. General Iterative Methods(Mathematics) 
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This unit defines iteration function and explains high order Methods. It also explains acceleration of the convergence and efficiency of a method and helps in analyzing system of nonlinear equations.
Title: Math 2.4 Numerical Analysis




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. Rate of Convergence of Iterative Methods(Mathematics) 
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This unit defines rate of convergence of an iterative method and explains rate of convergence of Secant and RegulaFalsi Methods, and Newton
Raphson Method. It also explains rate of convergence of Muller method and Chebyshev method.
Title: Math 2.4 Numerical Analysis




19. Solutions to NonLinear System of ODE(Mathematics) 
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The objective of this unit is the study of Nonlinear Autonomous system of ordinary differential equations, critical points, path and their nature. The reader also studies the method to find the nature of critical points. stability and paths by Liapunov direct method.
Title: Math 1.5 Differential Equations




20. 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




21. Solutions to Linear system of ODE(Mathematics) 
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The main objective of this unit is the study of linear system of ordinary differential equations.
Title: Math 1.5 Differential Equations




22. 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




23. 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




24. Eigen function and Green's Function(Mathematics) 
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In this unit the reader studies about the Eigenfunctions. Eigenfunction expansion formula. Green's function.
Title: Math 1.5 Differential Equations




25. Differential Equations(Physics) 
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Euler method, Runge  Kutta II and IV order methods. Applications: Freely falling body in a resistive medium with resistance proportional to velocity, Projectile motion, LCR transient circuit, solution to Schrodinger wave equation for Harmonic potential (plotting wave function only)
Title: Concise Physics BSc VI Semester Volume 8 (603)






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