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AU Mathematics III Sem III
Unit 3 : Applications of Partial Differential Equations(Method of separation of variables, Vibrations of a stretched string-wave equations, Onedimensional and two-dimensional heat flow equations, Solution of Laplace s equation, Laplace s equation in polar coordinates)
1. Situations giving rise to Partial Differential Equations(Mathematics) Total View (987)
 
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
Published on: 21/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 17
Price: Rs 12.75

2. 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 ......
Title: Math 3.4 Mathematical Modeling
Published on: 21/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 32
Price: Rs 24

3. 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 ......
Title: Math 3.4 Mathematical Modeling
Published on: 30/08/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 21
Price: Rs 15.75

4. Variational Principles Probability Generating Function and Model For Traffic Flow(Mathematics) Total View (966)
 
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
Published on: 21/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 19
Price: Rs 14.25

5. Introduction to PDE(Mathematics) Total View (758)
 
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
Published on: 09/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 8
Price: Rs 6

6. 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 ......
Title: Math 3.4 Mathematical Modeling
Published on: 30/08/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 16
Price: Rs 12

7. Cauchy Problem(Mathematics) Total View (760)
 
In this unit, the reader studies about the Cauchy problem, principle of superposition. They also study the method of characteristics to solve semi-linear, quasilinear and non-linear PDEs.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 14
Price: Rs 10.5

8. 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 ......
Title: Math 3.4 Mathematical Modeling
Published on: 30/08/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 17
Price: Rs 0

9. Complete Integrals of PDE(Mathematics) Total View (762)
 
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
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 12
Price: Rs 9

10. Limitations of Mathematical Modeling(Mathematics) Total View (907)
 
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
Published on: 30/08/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 3
Price: Rs 2.25

11. Existence of Solutions of ODE(Mathematics) Total View (767)
 
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
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 8
Price: Rs 0

12. 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.
Title: Math 2.4 Numerical Analysis
Published on: 01/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 13
Price: Rs 9.75

13. 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.
Title: Math 2.4 Numerical Analysis
Published on: 01/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 17
Price: Rs 12.75

14. Classification of Second Order PDE(Mathematics) Total View (764)
 
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
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 11
Price: Rs 8.25

15. Eigen function and Green's Function(Mathematics) Total View (758)
 
In this unit the reader studies about the Eigenfunctions. Eigenfunction expansion formula. Green's function.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 6
Price: Rs 4.5

16. Solutions to Non-Linear System of ODE(Mathematics) Total View (759)
 
The objective of this unit is the study of Non-linear 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
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 12
Price: Rs 9

17. Special Functions(Mathematics) Total View (756)
 
In this unit, the reader studies the power series solution by Frobenius method for Laguerre equation, Hermite differential equation, Chebyshev equation, hypergeometric equation.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 15
Price: Rs 11.25

18. Solutions to Linear system of ODE(Mathematics) Total View (759)
 
The main objective of this unit is the study of linear system of ordinary differential equations.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 8
Price: Rs 6

19. Methods of Solving ODE -2(Mathematics) Total View (757)
 
In this unit the reader studies the zeros of solutions of ODE. Sturm's separation theorem. Sturm's comparison theorem , Sturm-Liouville problems. The reader also study the method of variation o f parameters. Eigenvalue problems.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 16
Price: Rs 12

20. Methods of Solving ODE - 1(Mathematics) Total View (761)
 
In this unit, the reader first learn the definitions of linearly independent and linearly dependent set of functions. Then they study the fundamental set of solutions for ordinary differential equations, Wronskian, Adjoint differential equations and Green's formula.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 29
Price: Rs 21.75

21. Power Series Solution of ODE(Mathematics) Total View (755)
 
In this unit, the reader studies the power series solution o f linear equations of second order around ordinary and regular singular points.
Title: Math 1.5 Differential Equations
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 10
Price: Rs 7.5

22. The Laurent Series, Partial Fractions,Mittag-Leffler's Theorem(Mathematics) Total View (427)
 
In this unit, we discuss the infinite product and their relations with infinite series. Further, we study Weierstrass Factorization theorem which deals with representation of meromorphic function as an infinite product. We also study canonical product.
Title: Math 2.3 Complex Analysis - II
Published on: 03/10/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 14
Price: Rs 10.5

23. Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Rational Functions(Mathematics) Total View (735)
 
The objective of this unit to show that a function of a complex variable can have a derivative only if the real and imaginary parts satisfy a system of a partial differential equations called the Cauchy-Riemann equations. Further study of the Cauchy-Riemann equations shows a connect ion between complex analysis and harmonic functions.
Title: Math 1.3 Complex Analysis - I
Published on: 07/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 21
Price: Rs 15.75

24. Difference Equations and Generating Functions(Mathematics) Total View (738)
 
After going through this unit we can define and construct generating functions for sequences arising in various types of combination problems. Also we use generating functions to find the number of integer solution to linear equations. We solve recurrence relation using generating functions.
Title: Math 1.4 Discrete Mathematics
Published on: 08/01/14
Author: KSOU
Publisher: Karnataka State Open University
Pages: 16
Price: Rs 12

25. Bisection Method and Iterative Methods of Transcendental Equations (Mathematics) Total View (875)
 
This unit deals with the definition of transcendental function and explains the Bisection Method, Secant and Regula-Falsi 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
Published on: 29/08/13
Author: KSOU
Publisher: Karnataka State Open University
Pages: 15
Price: Rs 0



 
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