## Recurrence relation

Prob. Find the generating function for the following numeric function

ar = 7.3r , r 0.

Prob. Find a*b where
ar = 3r , r ≥ 0.

br = 2r, r ≥ 0.

Prob. Determine the generating function of the numerical function ar, where Prob. Determine the generating function of the numerical function ar, where
Prob. Solve the recurrence relation ar – 6ar-1 + 8ar-2 = o given a0 = 3 and a1 = 2.

Prob. Solve the recurrence relation an – 6an-1 + 9an-2 ,
With initial condition a0 = 1 and a1 = 6.
Prob. Solve the recurrence relation ar – 7ar-1 + 10ar-2 = o given that a0 = 0 and a1 = 3.
Prob. Solve the difference equation ar – 4ar-1 + 4ar-2 = o and find the particular solution, given that a0 = 1 and a1 = 6.
Prob. Solve the difference equation ar – 6ar-1 + 9ar-2 = 3, given that a0 = 0 and a1 = 1.
Prob. Determine the particular solution and general solution that satisfies the given initial condition xn – 2xn-1 = 6n; x1 = 2.
Prob. Determine the particular solution for the difference equation – ar – 2ar-1 = f(r), where f(r) = 7r.
Prob. Obtain particular ar + 5ar-1 +  6ar-2 = 3r2 – 2r +1.
Prob. Solve the recurrence relation –
ar + 4ar-1 +  4ar-2 = (r+1)2 , r ≥ 2.

Discrete Structure

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Cloud Computing:

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1. Buyya, Selvi ,” Mastering Cloud Computing “,TMH Pub
2. Krutz , Vines, “Cloud Security “ , Wiley Pub
3. Velte, “Cloud Computing- A Practical Approach” ,TMH Pub
4. Sosinsky, “ Cloud Computing” , Wiley Pub
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Principles of Programming Languages ↓ 👆
Principles of Programming Languages
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#### Language Evaluation Criteria Influences on Language Design  Language Categories Programming Paradigms Compilation Virtual Machines  Programming Environments Issues in Language Translation Parse Tree  Pointer and Reference type Concept of Binding Type Checking Strong typing  Sequence control with Expression Subprograms Fundamentals of sub-programs Scope and lifetime of variable Static and dynamic scope Design issues of subprogram and operations Local referencing environments Parameter passing methods Overloaded sub-programs Generic sub-programs  Design issues for functions  Co routines  Abstract Data types Abstraction and encapsulation Static and Stack-Based Storage management Garbage Collection OOP in C++ OOP in Java  OOP in C#  OOP in PHP Concurrency Semaphores  Monitors Message passing Java threads  C# threads  Exception handling  Exceptions Exception Propagation  Exception handler in C++  Exception handler in Java Introduction and overview of Logic programming Basic elements of Prolog Application of Logic programming Functional programming languages Introduction to 4GL  Practicals: Memory Implementation of 2D Array.  Memory Implementation of 3D Array.  Implementation of pointers in C++.  Write a program in Java to implement exception handling. Write a program in C++ to implement call by value parameter passing Method. Write a program in C++ to implement call by reference parameter passing Method.  Write a program in Java to implement concurrent execution of a job using threads. Implement Inheritance in C#. Implement Encapsulation in C#. Implement static/compiletime Polymorphism in C#. Implement dynamic/runtime Polymorphism in C#. Previous years solved papers: PPL|RGPV|May 2018  PPL|RGPV|June 2017  A list of Video lectures Click here References: Sebesta,”Concept of programming Language”, Pearson Edu  Louden, “Programming Languages: Principles & Practices” , Cengage Learning  Tucker, “Programming Languages: Principles and paradigms “, Tata McGraw –Hill.  E Horowitz, "Programming Languages", 2nd Edition, Addison Wesley

Computer Organization and Architecture ↓ 👆

### Computer Organization and Architecture

#### References:

1. William stalling ,“Computer Architecture and Organization” PHI
2. Morris Mano , “Computer System Organization ”PHI

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Computer Network

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References:
1. Andrew S. Tanenbaum, David J. Wetherall, “Computer Networks” Pearson Education.
2. Douglas E Comer, “Internetworking with TCP/IP Principles, Protocols, And Architecture",Pearson Education
3. KavehPahlavan, Prashant Krishnamurthy, “Networking Fundamentals”, Wiley Publication.
4. Ying-Dar Lin, Ren-Hung Hwang, Fred Baker, “Computer Networks: An Open Source Approach”, McGraw Hill.
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### R Programming

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