Thursday, 15 August 2013

Bachelor of Computer Application (BCA) – Semester 3 BC0045 – Structured System Analysis & Design

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Tuesday, 13 August 2013

BC0045-Structured System Analysis and Design

BC0045-Structured System Analysis and Design

1.How do you and your organization define system? Mention the systems that require engineering.
The term “system” originates from the Greek term systema, which means to “place together.” Multiple business and engineering domains have definitions of a system. This text defines a system as:
• System: An integrated set of inter operable elements, each with explicitly specified and bounded capabilities, working synergistically to perform value-added processing to enable a User to satisfy mission oriented operational needs in a prescribed operating environment with a specified outcome and probability of success. To help us understand the rationale for this definition, let’s examine each part in detail.
Some systems require the analysis, design, and development of specialized structures,
complex interactions, and performance monitoring that may have an impact on the safety, health, and well-being of the public as well as the environment, engineering of systems may be required. As we investigate WHAT is required to analyze, design, and develop both types of systems, we will find that they both share a common set concepts, principles, and practices. Business systems, for example, may require application of
various analytically and mathematical principles to develop business models and
performance models to determine profitability and return on investment (ROI) and statistical theory for optimal waiting line or weather conditions, for example. In the case of highly complex systems, analytical, mathematical, and scientific principles may have to be applied. We refer to this as the engineering of systems, which may require a mixture of engineering disciplines such as system engineering, electrical engineering, mechanical
engineering, and software engineering.
2. Explain the guiding principles that govern system acceptability.
Principle System acceptability is determined user satisfaction; user satisfaction is determined by five User criteria:
1. Provide value – meaning operational utility.
2. Fit within the user’s system and mission applications – meaning
operational suitability.
3. Be available to conduct missions – meaning operational availability.
4. Accomplish performance objectives – meaning operational
effectiveness.
5. Be affordable – meaning cost effectiveness.

Principle Despite the most technically innovative and elegant SE design
solutions, Users’ perceptions of a system, product, or service constitute
reality.

3. Explain the types of behavior patterns emerge when systems interact with their .
When systems interact with their OPERATING ENVIRONMENT, two types
of behavior patterns emerge:
1. Systems interact with or respond to the dynamics in their OPERATING ENVIRONMENT. These interactions reflect peer-to-peer role-based behavioral patterns such as aggressor, predator, benign, and defender or combinations of these.
2. System Responses – behavior, products, by-products, or services – and
internal failures sometime result in adverse or catastrophic effects to the
system – creating instability, damage, degraded performance, for example – that may place the system’s mission or survival at risk.

When we analyze interactions of a SYSTEM OF INTEREST (SOI) with its OPERATING ENVIRONMENT, two fundamental types of behavior emerge :
1. Hierarchical interactions (i.e., vertical interactions under the command and control of higher order systems).
2. Peer level interactions.]

We characterize SOI interactions with its OPERATING ENVIRONMENT to include two types of entities:
1) HIGHER ORDER SYSTEMS and
2) a PHYSICAL ENVIRONMENT.

The identification of OPERATING ENVIRONMENT domains enables us to expand the System Architecture construct. Most engineering environments establish standards and conventions for interpretive reading. For example, graphics read from left to right and from top to bottom. The convention is that data processing and work flow progress from left to right. If we had placed the SOI on the left side and the OPERATING ENVIRONMENT on the right side, this would have created a false perception that the SOI drives its OPERATING ENVIRONMENT.

4. What do you understand from Organizational Aspects of system Life Cycles?
Each system product or service is an asset of a higher level organization that also has a system life cycle. Those same systems and products may include lower         level systems or products that also have system life cycles. Therefore we have multiple levels of system life cycles within higher level system life cycles.If we examine the system life cycle of Organizational Entity 2, we might find that the organization evolves through several lines of business (LOBs) LOB 1, LOB 2, and so on. Within each LOB, the organization has a core product line that consists of Product Model 1, which evolves into Product Model 2, and so forth. Observe the overlapping of Product 1 and Product 2 life cycles.
Application of System Life Cycles
We can apply the concept of system life cycles within system life cycles to an example such as small engine developer. The organization, which has a life cycle, may evolve through a number of organizational life cycles as small business, corporation, and so on. During Organizational Life Cycle 2  the organization may develop several LOBs two-cycle engines, four-cycle engines, and so on – to support marketplace opportunities such as lawn mowers, edger’s, and small tractors The organization's four cycle LOB may evolve through Product Model 1, Product Model 2, and so forth. Each product model builds on its predecessor
The preceding discussion focused on a system or product suppliers system life cycles. The same analogy applies to users of system, product, and services. Their organizations evolve through similar life cycles.

5. Create your own definitions of a system. Based on the “system” definitions.
a. Identify your viewpoint of shortcomings in the definitions.
b. Provide rationale as to why you believe that your definition overcomes those shortcomings.
c. From an historical perspective, identify three precedented systems that were replaced by unprecedented systems.

A system is a set of interacting or interdependent components forming an integrated whole[1] or a set of elements (often called 'components' ) and relationships which are different from relationships of the set or its elements to other elements or sets.[citation needed] Fields that study the general properties of systems include systems science, systems theory, systems engineering, cybernetics, dynamical systems, thermodynamics, and complex systems. They investigate the abstract properties of systems' matter and organization, looking for concepts and principles that are independent of domain, substance, type, or temporal scale.[citation needed] Some systems share common characteristics, including:[citation needed] A system has structure, it contains parts (or components) that are directly or indirectly related to each other; A system has behavior, it contains processes that transform inputs into outputs (material, energy or data); A system has inter connectivity  the parts and processes are connected by structural and/or behavioral relationships. A system's structure and behavior may be decomposed via subsystems and sub-processes to elementary parts and process steps. The term system may also refer to a set of rules that governs structure and/or behavior. Alternatively, and usually in the context of complex social systems, the term institution is used to describe the set of rules that govern structure and/or behavior.

6. State all the system decomposition and integration design guidelines.
System structures are viewed from two SE perspectives:
1. Analytically, as a top-down, hierarchical decomposition or expansion.
2. Physically, as bottom-up, vertically integrated sets of entities.
3. System composition entity relationships (ERs) enable us to analytically
decompose hierarchical systems into manageable design levels of
complexity. Figure 9.4 provides a framework for the rules stated in
Table

Level or
Tier
Nomenclature
(Optional)
Scoping Definition
0
User’s
SYSTEM Level
A level of abstraction that represents the User’s business environment with your SYTEM OF INTEREST (SOI) as an embedded element. We refer to this as the Level 0 or Tier 0 system.
1
SYSTEM Level
A level of abstraction that describes on the top-level
representation of your SOI from the organization’s (observer’s) frame of reference. Architectural representations (i.e., an architectural block diagram,
ABD) of the SYSTEM level include the SOI boundaries, interfaces to external systems in the operating environment, and embedded SEGMENT level entities (if applicable) or PRODUCT level entities and their interfaces. This level of abstraction is referred to as a
Level 1 or Tier 1 system.
2
SEGMENT
Level
(optional)
Refers to system entities at the first level of decomposition below
the SYSTEM level. Each instance of a SEGMENT level entity is
referred to as a Level 2 or Tier 2 system.
An architectural representation of a SEGMENT level entity
includes:
1. Level 3 or Tier 3 PRODUCTS and lower level entities.
2. Their internal PRODUCT level relationships.
3. The SEGMENT’s relationships with external entities within the
SYSTEM
(i.e., with other SEGMENTS) and external systems beyond the
SYSTEM’s boundaries, as applicable. Consider the following
example:
EXAMPLE: A communications SYSTEM might consist of landbased,
sea-based, air-based, and space-based SEGMENTS.
3
PRODUCT
Level
(optional)
Refers to system entities at the first level of decomposition below
the SEGMENT level. Each instance of a PRODUCT Level entity is
referred to as a Level 3 or Tier 3 system.
An architectural representation of a PRODUCT level entity
includes:
1. Level 4 or Tier 4 SUBSYSTEMS and lower level entities.
2. Their internal SUBSYSTEM level entity relationships.
3. The PRODUCT’s relationships with external entities within the
SYSTEM
(i.e., with other PRODUCTS) and external systems beyond the
SYSTEM’s boundaries, as applicable.
4
SUBSYSTEM
Level
Refers to system entities at the first level of decomposition below
the PRODUCT Level. Each instance of a SUBSYSTEM level
entity is referred to as a Level 4 or Tier 4 system.
An architectural representation of a SUBSYSTEM level entity
includes:
1. Level 5 or Tier 5 ASSEMBLIES and lower level entities.
2. Their internal ASSEMBLY level entity relationships.
3. The SUBSYSTEM’s relationships with external entities within
the SYSTEM (i.e., with other SUBSYSTEMS) or external
systems beyond the SYSTEM’s boundaries, as applicable.
5
ASSEMBLY
Level
Refers to system entities at the first level of decomposition below
the SUBSYSTEM level. Each instance of an ASSEMBLY level
entity is referred to as a Level 5 or Tier 5 system.
An architectural representation of an ASSEMBLY level entity
includes:
Scoping Definition
1. Level 6 or Tier 6 COMPONENTS and lower level entities.
2. Their internal SUBASSEMBLY level entity relationships.
3. The ASSEMBLY’s relationships with external entities within the
SYSTEM (i.e., with other ASSEMBLIES) or external systems
beyond the SYSTEM’s boundaries, as applicable.
6
SUBASSEMBLY
Level
Refers to system entities at the first level of decomposition below
the ASSEMBLY level. Each instance of a SUBASSEMBLY level
entity is referred to as a Level 6 or Tier 6 system.
Architectural representation of a SUBASSEMBLY Level entity
includes:
1. Level 7 or Tier 7 PARTS.
2. Their internal PART level entity relationships.
3. The SUBASSEMBLY’s relationships with external entities within
the SYSTEM (i.e., with other SUBASSEMBLIES) or external
systems beyond the SYSTEM’s boundaries, as applicable.




                                               
7
PART Level
Refers to the lowest level decompositional element of a system.
An architectural representation of a PART includes form factor
envelope
drawings, schematics, and models.
Engineering drawings, which are produced at all
system levels of abstraction, consist of two basic types:
1. Dimensional drawings or schematics for internally developed or
externally procured and modified internally items.
2. Source control drawings that bound part parameters and
characteristics for externally procured parts.
For software systems, the PART level equates to a source line of
code (SLOC).


7. Identify three types of systems or system upgrades that may be ideal candidates for a Waterfall Development Model strategy.
1.rainfall
2.ground waterfall
 
3.drought 

The Waterfall Development Model represents one of the initial attempts to
characterize software development in terms of a model. Today, the Waterfall Model exemplifies how many organizations develop systems and products. The term “waterfall” has always been a misnomer and tends to confuse many people. The term reflects the graphical top-down, diagonal representation rather than the actual implementation. As we will see in a later Unit, the earlier stages do represent expansion of levels of design detail over time. Unlike the Waterfall Model, the V-Model is implemented with highly iterative and recursive feedback loops within and between levels of abstraction. In the Waterfall approach, “development activities are performed in sequential order, with possibly minor overlap, and minimal or no iteration between activities. User needs are determined, requirements are defined, and the full system is designed, built, and tested for ultimate delivery at one point in time. Some people refer to this as a stage-wise model.”

8. List all the steps involved in mission analysis.
Organizational and system missions range from simple tasks such as writing
a letter to performing highly complex International Space Station (ISS)
operations, managing a government. Regardless of application, mission
analysis requires consideration of the steps specified below:
Step 1: Define the Primary Mission Objective(s)
Step 2: Develop a Mission Strategy
Step 3: Define Phase-Based Operations and Tasks

Step 4: Create a Mission Event Timeline (MET)
Step 5: Bound and Specify the Mission OPERATING ENVIRONMENT Interactions
Step 6: Identify Outcome-Based System Responses
Step 7: Identify Mission Resources and Sustainment Methods
Step 8: Perform a Mission Task Analysis
Step 9: Assess and Mitigate Mission and System Risk

9. Identify three types of systems or system upgrades that may be an ideal candidates for a Spiral Development Model strategy.
Some systems require the analysis, design, and development of specialized structures, complex interactions, and performance monitoring that may have an impact on the safety, health, and well-being of the public as well as the environment, engineering of systems may be required. As you investigate WHAT is required to analyze, design, and develop both types of systems, you will find that they both share a common set concepts, principles, and practices. Business systems, for example, may require application of various analytical and mathematical principles to develop business models and performance models to determine profitability and return on investment (ROI) and statistical theory for optimal waiting line or weather conditions, for example. In the case of highly complex systems, analytical, mathematical, and scientific principles may have to be applied. We refer to this as the engineering of systems, which may require a mixture of engineering disciplines such as system engineering, electrical engineering, mechanical
engineering, and software engineering. These disciplines may only be required at various stages during the analysis, design, and development of a system, product, or service. This text provides the concepts, principles, and practices that apply to the
analysis, design, and development of both types of systems. On the surface
these two categories imply a clear distinction between those that require
engineering and those that do not.


10. Explain in brief the four primary system development models.
1.    The Waterfall Development Model
The term “waterfall” has always been a misnomer and tends to
confuse many people. The term reflects the graphical top-down, diagonal
representation rather than the actual implementation. As we will see in a
later Unit, the earlier stages do represent expansion of levels of design
detail over time. Unlike the Waterfall Model, the V-Model is implemented
with highly iterative and recursive feedback loops within and between levels
of abstraction.
2.    The Evolutionary Development Model
In general, the Evolutionary Development Model is based on the premise
that “stages consist of expanding increments of an operational software
product, with the directions of evolution being determined by operational
experience.” (Source: Boehm, p. 63) This conception is based on an
evolutionary strategy of a system or product development through a series
of pre-planned product improvement (P3I) releases.
3.    The Spiral Development Model
Spiral development employs a series of highly iterative development
activities whereby the deliverable end product of each activity may not be
the deliverable system. Instead, the evolving set of knowledge and
subsequent system requirements that lead to development of a deliverable
system contribute to the maturing design solution.
4.    The Incremental Development Model
The incremental approach determines user needs and defines the
overall architecture, but then delivers the system in a series of increments –
i.e., software builds. The first build incorporates a part of the total planned
capabilities, the next build adds more capabilities, and so on, until the entire
system is complete.” (Source: Glossary: Defense Acquisition Acronyms and
Terms)




BC0043 Computer Oriented Numerical Methods

BC0043 Computer Oriented Numerical Methods


Question 1. Verify Rolle’s theorem for the function f(x) = |x| in (–1, 1).

f(x) = -x for  -1 < x < 0.
      
       = 0 for x = 0

       = x for 0 < x < 1

f(-1)= 1 f(1) -1 

f(-1)= f(1)
f1(x) = -1 for -1 < x < 0
f1 (x) = 1 for 0 < x < 1

Therefore f1  (x) does not exist at x =0 and hence f(x) is not differentiable in (-1,1) Rolle’s theorem is not applicable to the function f(x) = Ç€xÇ€ in (-1,1)



Question 2. Find the multiplicity root of the equation x3 – x2 – x + 1 = 0 near x0 = 0.9


F(x) = x3 – x2 –x + 1
F’(x) = 3x2 -2x -1 and f’’ (x) =6x – 2
Let x0 =0.9 (taken randomly) be the initial approximated value.
X0 – m f(x0)  =  x0 – (m -1) f’(x0)                   
           F’(x0)                        f’(x0)       

M=2, x0 = 0.9, f(x0) = f(x0)  = f(0.9) = 0.019, f’ (x0) = f’(0.9) = -0.37 and f’’ (x0) = f’’ (0.9) = 3.4

Therefore

X02 f (x0) = x0f’(x0)
        F’(x0)              f’’(x0)
We have x02f(x0)   =0.9 - 2×0.019 = 1.003, and    
                       F’(x0)              -0.37
X0f’(x0) = 0.9 – (-0.37) =  1.009
        F’’(x0)            3.4
The closeness of these values indicates that there is a double root near x =1.

For the next approximation we choose x1 = 1.01
We get  x12f(x1) = 1.01 - 2×0.0002 = 1.0001
                     F’(x1)               0.0403
and x1f’(x1) = 1.01 – 0.0403  =  1.0001
              f’’(x1)                4.06
The show that there is a root at x =1.0001 which is quite near the actual root x =1.
Observation : for f(x) = x3-x2-x+1=(x-1)2 (x+1). Therefore x=1 is a double root with multiplicity m= 2.


Question 3. Use Bisection method to solve x3+3x-5 defined in the interval [1,2]

F(x)   = X3+ 3x-5
F(1)   = 1+3×1-5
         = 4 – 5 = -1
F(2)  = 23 + 3×2-5
        =  8+6-5
         = 9

F (1) is negative  &  f(2)  is  positive

 

X1  =  1+2  =  3   
            2        2
      =  1.5

F(x)  =  F(1.5)3 + 3×1.5 – 5

        =  3.375 + 4.5-5
        =  2.875   > 0
Hence the root ties between  1& 1.5.  Since f(1.5) > 0 & f(1) < 0


Question 4. Find AB and BA, when = A =  and  B =

Given A is a 2×3 matrix and B is a 3×2  matrix. So AB is a 2×2 matrix.

AB=  = 


Question 5. Find the solution of the following system of equations.
   
       
      x-  y- z =
        x+ y-  w =
        -  x+z -  w =
        -  y -   z+w =  

       
    
 using Gauss-Seidel method and perform the first five iterations.

The given system of equations can be rewritten as          ........(1)

Taking the initial approximation as y =z =0 on the right side of the equation (1) we get x(1) =0.5.
Taking  z=0 and w=0 and  the current value of x, we get
Y(1) =0.5 + (0.25)(0.5) + 0 = 0.625 from the second equation of (1).

Now taking w = 0 and the current value of x, we get
Z(3) = 0.25 + (0.25) (0.5) + 0 = 0.375 from the third equation of (1).
Lastly, using the current values of y and z, the fourth equation of (1) gives
W(1) = 0.25 + (0.25) (0.625) + (0.25)( 0.375) = 0.5 .
The Gauss-Seidal iterations for the given set of equations can be written as
     ........(1)


Now by Gauss – Seidel procedure ,  the second and the subsequent approximations can be obtained and the sequence of the first five approximations is tabulated below.

Iteration
Number (r)
                                         Variables
      x
            y
          z
         w
1
0.5
0.625
0.375
0.5
2
0.75
0.8125
0.5625
0.59375
3
0.84375
0.85938
0.60938
0.61719
4
0.86719
0.87110
0.62110
0.62305
5
0.87305
0.87402
0.62402
0.62451




Question 6. Fit parabola of second degree y = a + bx +  for the data


X
0
1
2
3
4
y
1
1.8
1.3
2.5
2.3

The normal equations for y=a +bx+c are
 
      =na + b + c
    Xy = a + b    +c
         y = a  + b+c

Here n = 5.
The relevant table is given below:
x
y
X2
X3
X4
xy
X2y
0
1
0
0
0
0
0
1
1.8
1
1
1
1.8
1.8
2
1.3
4
8
16
2.6
5.2
3
2.5
9
27
81
7.5
22.5
4
2.3
16
64
256
9.2
36.8
= 10
 8.9
 2 = 30
3 = 100
 354
 21.1
y = 66.3

The normal equations becomes
5a + 10 b + 30 c = 8.9
10 a +30 b +100 c =21.1
30 a +100 b +354 c = 66.3
Solving these simultaneous equations, we get
a = 1.078
b = 0.414
c = -0.021
Hence the required parabola is
Y = 1.078 + 0. 414 x – 0.021 x2