
AU Mathematics III Sem III Unit 2 : Introduction of Partial Differential Equations(Formation of partial differential equations, Solutions of PDEs, Equations solvable by direct
integration, Linear equations of first order, Homogeneous linear equations with constant
coefficients, Rules for finding the complimentary function, Rules of finding the particular
integral, Working procedure top solve homogeneous linear equations of any order, Nonhomogeneous linear equations) 



1. 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




2. 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




3. 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




4. Differential Equations(Advanced Mathematics I) 
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A large number of basic laws of nature in engineering mathematics, applied sciences etc., appear mathematically in the form of differential equations. The differential equations is the general goal of differential and integral calculus and the theory of differential equations has a very important role in mathematics for understanding physical sciences.
Title: Advance Mathematics I








5. 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




6. Differential Equations(Engineering Mathematics  I
) 
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A large number of basic laws of nature in engineering mathematics, applied sciences etc., appear mathematically in the form of differential equations. The problem of solving differential equations is a general goal of differential and integral calculus and the theory of differential equations is a very important part of mathematics for understanding physical sciences
Title: Engineering Mathematics  1





7. Differential Equations(Mathematics) 
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Ordinary differential equations of first order and of first degree, Separation of variables, Homogeneous differential equations, Reducible to homogeneous differential equations, Linear differential equations, Bernoulli's equations (reducible to linear differential equations), Exact differential equations, Reducible to exact differential equations, Orthogonal trajectories
Title: Introductory Mathematics II






8. Difference Equations and Generating Functions(Mathematics) 
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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




9. Partial Differential Equations(Mathematics) 
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If a physical quantity depends on more than one independent variable (for example, in one dimensional fluid flow problems, the velocity depends on the space variable x and time t) the governing differential equations are necessarily partial differential equations. Some of the fields where partial differential equations arise are fluid dynamics, electromagnetic theory, theory of heat conduction and
......
Title: Engineering Mathematics  III




10. Differential Equations  I(Mathematics) 
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In Chapter7 (Vol.I). In this chapter we study differential equations of second and higher orders. Differential equations of second order arise very often in physical problems, especially in connection with mechanical vibrations and electric circuits.
Title: Engineering Mathematics  II




11. Methods of Solving ODE 2(Mathematics) 
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In this unit the reader studies the zeros of solutions of ODE. Sturm's separation theorem. Sturm's comparison theorem , SturmLiouville problems. The reader also study the method of variation o f parameters. Eigenvalue problems.
Title: Math 1.5 Differential Equations




12. Differential EquationsI(Engineering Mathematics  II
) 
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A large number of basic laws of nature in science and technology appear mathematically in the form of differential equations. The solution of differential equations is one of the most important tools for engineers and scientists. It is presumed that the readers are already familiar in solving the differential equations of first order and first degree. In this chapter we shall discuss some standard
......
Title: Engineering Mathematics  II





14. Ordinary Differential Equations  II(Mathematics II) 
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This chapter is a continuation of Chapter 1. Here we first consider some standard methods of solving ordinary linear differential equations of second and higher orders with constant coefficients. Then we consider simultaneous linear differential equations of firstorder. Lastly, we illustrate some applications of secondorder linear differential equations.
Title: Engineering Mathematics Part  II





15. Elementary Combinatorics(Applied Mathematics) 
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Combinatorics is the branch of mathematics meant to solve counting problems without enumerating all possible cases. At an elementary level, Combinatorics is usually considered as a part of discrete mathematics in which the main problem is that of counting the number of ways of arranging or choosing objects from a finite set according to some simple specified rules. At an advanced level, combinator
......
Title: Discrete Structures and Graph Theory




16. 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




17. Ordinary Differential Equations  I(Mathematics II) 
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This chapter is a continuation of Chapter 6 of Part I_. Here, we consider ordinary differential equations of firstorder and higher degree. Some Applications of firstorder ordinary differential equations are illustrated at the end of the chapter.
Title: Engineering Mathematics Part  II




18. 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




19. 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




20. Differential Equations(Mathematics) 
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A large number of basic laws of nature in science and technology appear
mathematically in the form of differential equations. The problem of
solving differential equations is one of the most important tools for
engineers and scientists. The readers are already familiar in solving the
differential equations of first order and first degree. In this chapter we
discuss some standard methods of so
......
Title: Bridge Course II




21. Differential Equations(Mathematics) 
Total View (642) 

A large number of basic laws of nature in science and technology appear
mathematically in the form of differential equations. The problem of
solving differential equations is one of the most important tools for
engineers and scientists. The readers are already familiar in solving the
differential equations of first order and first degree. In this chapter we
discuss some standard methods of so
......
Title: Bridge Course II




22. Differential Equations(Mathematics) 
Total View (5) 

A large number of basic laws of nature in science and technology appear
mathematically in the form of differential equations. The problem of
solving differential equations is one of the most important tools for
engineers and scientists. The readers are already familiar in solving the
differential equations of first order and first degree. In this chapter we
discuss some standard methods of so
......
Title: Bridge Course II




23. Application of Partial Differential Equations(Mathematics) 
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We now study three linear homogeneous second order PDEs which are important in physical applications, the wave equation, the heat equation and Laplace's equation.
Title: Engineering Mathematics  III




24. Differential Equations  2(Mathematics I ) 
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This chapter is a continuation of Chapter 8. Here we consider some standard methods of solving ordinary linear differential equations of second and higher orders with constant coefficients, including the method of variation of parameters. Some simple applications are also illustrated.
Title: Engineering Mathematics Volume  I




25. Computational Algorithms for the Configuration Design (Aerodynamics Airworthiness)(Aeronautical Engineering) 
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Introduction, Theoretical Algorithms, Computational Algorithms, Optimization of Computational Grids , Parallel Computational Computing.
Title: Aerodynamics Airworthiness






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