## Gauss Jordan Elimination Method

Here is a well explained solution to solve a set of equations using Gauss Jordan Elimination method –

## Gauss Elimination Method

Below is a well explained solution for a set of equations using Gauss Elimination method. Enjoy!

## Finding Roots of equation x3-3×2+x+1=0

We will be using Newton Raphson method to find the root of this equation. Enjoy!

## Parallel Lamp Connection

Below is the lab work for Parallel Lamp Connection –

## Dim and Bright Connection

Here is the detailed lab work for a Dim and Bright lamp connection –

## Master Electric Connection

We will see how to operate 3 lamps using a master switch and also simultaneously operating them.

## Fluorescent Tube connection

Below is a simple step by step description of a Fluorescent Tube connection. We will see the list of materials needed, the procedure to build it observation and result.

## Finding measure of skewness and kurtosis for Poisson distribution

Here we define what Poisson Distribution is how to measure its skewness and kurtosis.

## Proving Inversion Mapping

Here we venture to prove that Inversion Mapping maps the totality of circles lines in the Z plane on to the same that of W plane –

## Find 4th Root of 1 and Square root of -8i

Here is an interesting solution to find nth root of a complex number Z. Here we use a general equation to find the 4th root of 1 and square of -8i. Enjoy!

## Finding Linear Fractional Transformation

Ok, here is a beautiful mathematical solution to find the Linear Fractional Transformation which maps |Z| <= 1 on to |W| <=1 such that Z = i/4 is mapped onto W=0. Also we will graph out the images of the lines x=c and y=c.

## Transformation of W=eZ

Here we discuss transformation of W = eZ

## Forming a Bi-Linear Transformation which maps a set of points

Here is a mathematical solution for forming a Bi-Linear Transformation which maps the points (1, i,-1) onto the points  (i,0,-i) and hence finding the image of |Z| < 1 and also finding the Invarient points of this Transformation 🙂

## How to determine which mathematical functions are analytic

Here is the solution on how to determine if a mathematical function is analytic –

## Mathematical solution for checking a certain function satisfy Laplace Equation

Here is an attempt to check if a function satisfies Laplace Equation and determining corresponding analytical function –

## Locus of a point Z satisfying condition |Z-1| + |Z+1| = 4

Here is a fun solution for Mathematics students to find the locus of a point Z satisfying condition |Z-1| + |Z+1| = 4 –

## ARP (Address Resolution Protocol) in action

Suppose machine A wants to send its message packets to B which has the IP address 1B. A only knows B’s IP address and thus as a first step, sends an ARP request to B to get machine B’S hardware address. Now, before sending the ARP request, A checks up in its ARP cache whether…

## ARP – Address Resolution Protocol

ARP or Address Resolution Protocol is used to map Internet addresses to physical addresses. Address resolution is the process of mapping Internet IP addresses into physical addresses. Two machines in the internet cannot communicate with each other  without knowing each others actual physical address i.e address of its hardware interface, for e.g. the network interface…

Below are couple major weaknesses of IP addresses – A machine cannot be assigned a permanent IP address i.e. it should change when the machine is connected to different physical networks When class C networks grow beyond 255 hosts, they  should be changed to class B networks. Such changes in IP addresses requires high labor,…

## ‘This’ network and ‘this’ host address

An IP address with all 0’s in the host id, refers to this particular and the IP addresses with all 0’s in the network id refers to this particular network. This network addressing is useful in cases when a host wants to communicate with a network whose network address the host sends the ‘this’ type…

Network and Broadcast address are derived from the general IP addresses and are used for specific or reserved applications. Network address refers to the IP addresses with all the bits in the host address 0s. The network address refers to the network itself. For e.g, a class A address 96.0.0.0 refers to the same class…

Internet address refers to the unique identification or address assigned to each machine in the physical network. The basic need for assigning Internet address is to identify every machine in the network. Internet address is defined as the 32-bit (or 64 bit) address assigned to each machine on the internet so as to identify that…

## Internet Architecture

As shown above, the Internet consists of various physical networks (Net1 … Netn) connected together as a single large network. Each network may have host machines connected or other networks connected within it. G1 .. Gn represents the Gateways or routers that connects two networks. Gateways or routers routes data packets from a host in…

## Internetworking Concept and Architectural Model

Internetworking is the technology that makes it possible to interconnect many disparate physical networks with diverse underlying hardware technologies and make them function as a coordinated unit. The internetworking / Internet technology hides the details of network hardware and permits computers to communicate independent of their physical network connections. When we speak of interworking technology, we…

## ARPANET Technology

ARPANET (Advanced research project agency network) is the oldest wide area packet switched network build by the DARPA (Defense advanced research project agency). Physically ARPANET consisted of about 50 BBN corp’s C30 and C300 minicomputers called the PSNs (packet switching nodes) that were scattered over US and Europe. Each PSN was a dedicated packet switching…

## ProNET variation – Start topology

ProNET variation as star topology is as shown below – The 3 hosts are connected logically by a ring connection and physically by a start connection via a wire center. The wire center consists of relays R1, R2, R3, R4 so that the relays connects the corresponding host to the wire center via the interface….

## ProNET 10 Token recovery

ProNET 10 token recovery is essential to handle situations of loss of token when the host want to transmit. Such token loses occur due to malfunction or electronic interference that damages the token. To recover the token, we implement two timers at each station – flag timers and token timers. The flag timer is reset…

## ProNET Token Ring Technology

ProNET Token ring technology is an alternative to ethernet technology and it also works fairly good speeds. It uses token ring technology- Token ring network as shown above consists of hosts connected as a ring via wires that comes out of each host and connected to the other host. Each host in the network engage…

## Ethernet Variations

Ethernet technology started with using the costly coaxial cables. Now it is possible to carry ethernet frames over cost-effective and cheaper twisted pair cables supporting greater speeds. Another variation of ethernet is to use cable like that of cable TV. This variation of Ethernet is called thin wire ethernet which is expensive but cover only…

## Ethernet Bridges

Ethernet bridge is a fast computer with two Ethernet interfaces and a fixed program that improve upon the functions of repeaters by replicating the packets, instead of amplifying them. Bridges, thus do not amplify the noise, errors or malformed frames like the repeaters, but only reproduces a completely valid frame. Ethernet bridges supports CSMA/CD mode…

## Ethernet addressing and frame format

Ethernet Addresses refers to the unique physical/hardware address assigned or hardcoded on to the Ethernet interface card in 48 bits machine readable form. Physical ethernet addresses are meant to be different for each interface card and moving the hardware to a new machine or replacing the existing card with a new one will change the…

## Collission detection and Recovery in Ethernet

Ethernet data transmission enabled by TCP/IP is a best-effort delivery method. i.e the sender is given no information about whether the data packets were received by the receiver or not. The hosts in the Ethernet participate in data communication over the common Ethernet bus by a process of carrier sense multiple access with collision detection…

## Ethernet Hardware and basic architecture

A cross section of a Ethernet cable is as shown below – Ethernet is typically a 10Mbps local area packet switched network technology. The cross section of an Ethernet cable is as shown above. The Ethernet coaxial cable is of 1/2 inch in diameter and is extendable upto 500-1500 meters. The outer insulating jacket and…

## LAN, WAN and MAN

WAN (Wide Area Network) connects machines over widely separated geographical locations. A WAN usually consists of various packet switches installed at various points on the network to carry the signals to long distances. LAN (Local Area Network) span shorter distances usually with an enterprise or within the enterprise department. Since LAN cover shorter distances, they…

## Differences between TCP/IP internet services and others

TCP/IP internet services and other internetworking services can be compared on the basis of following features of TCP/IP internet – Network Topology Independence While TCP/IP is based on conventional packet switching technology that defined datagram as the unit of data transmission, it is independent of any particular vendor’s hardware or other underlying network technologies.  …

## Internetworking

Internetworking is the technology that makes it possible to interconnect many disparate physical networks with diverse underlying hardware technologies and make them function as a coordinated unit. The internetworking/internet technology hides the details of network hardware and permits computers to communicate independent of their physical network connections. When we speak of internetworking technology, we speak of…

## ISDN – Integrated Services Digital Network

ISDN, though not popular in US, it is still one of the most popular data communication networks in UK, India and many other European countries. ISDN evolved from the IDN (Integrated Digital Network) in which both the transmission media and switches employs digital techniques. In this system, speech signals are converted to digital signal at…

## Basics setup of Mobile Communication services

One of the fastest growing telecommunication industry is obviously mobile radio communication. Below figure shows a basic architecture of such a mobile communication network – Radio telephones or cellphone, as they are generally called, provides a switched two way channel between two conversing parties like a conventional telephone. Telephones may be in vehicles which can…

## Digitized Telephone services

In the past, we had manual exchanges which involved a great task in switching and routing of calls to various subscribers that increased network traffic and longer setup times. Also fault checking and identification was very difficult. Now, with the introduction of electronic exchanges which uses a stored program concept for switching of calls and…

## Evolution of Data Communication Systems

Almost all of the Data communication systems across the world evolved from Telegraph systems. Later with developments in the telephone systems, it was now possible to interconnect various computer terminals for data communication. With the advancements in the network computing and the digitization of telephone networks, it was now possible to setup an efficient data…

## Data Communication – Basic Definition and setup

Data communication is the function of transporting digital signal from one digital device to another. Data transmission and data communications means two different things. Data communications has a much wider meaning which embraces not just electrical transmission but many other factors involved in controlling, checking and handling the movement of information in a communication-based computer…

## Simple HTTP log analyzer

Here is a simple light weight HTTP analyzer written in PHP. I wrote this to brush up my skills writing schedulers for a typical LAMP stack. Nothing fancy, there are more things to implement on detecting malicious requests, but this will get you started – <?php /** //Simple http log parser and report generation script…

## Stack Vs Heap

Stack and Heap refers to 2 distinct memory areas utilized by an executing program based on the data type of data that it deals at a point during its execution. Stack is that part of memory that a program uses to keep track of its execution flow. For example it stores the currently executed method…

## What is the purpose of static modifier?

Static modifier is commonly used in all programming languages. There are two distinct reasons for using the static modifier whether its C, Java, C#, PHP or Ruby – To access the class members without instantiating the object. eg: public class CutGrass{ public static void CleanMower(){ } } var endTheJob = CutGrass.CleanMower(); 2. To restrict the representation…

## Arrays Vs Lists – Which one to use?

Both Arrays and Lists helps us to store list of elements. But which one to choose is an important design decision that is directly related to application performance. Arrays are strongly typed – meaning they can only store data of one type. Use Arrays where the size and type of elements is fixed and we…

## How to stop bulk spam emails to my mail account?

If you are not one of the people who have had the bad experience of having your email account being subjected to a bulk spam attack, you are lucky. But what to do if you are? Don’t panic. I recently faced this situation and I will explain how to solve this. Follow through the points…

## C# File, Directory Manipulation

C# provide two versions of File, Directory manipulation options – 1) Static methods based and 2) Instance methods based. Static method based operations are provided by the File and Directory classes both derived from System.IO class. Instance method based operations are provided by the FileInfo and DirectoryInfo classes again both derived from System.IO class. File…

## MVC Architecture

MVC architecture has been in place since past 4 decades or so when GUI (Graphical Use Interfaces) started to be used widely. The idea is simple – to implement separation of concerns.  Plainly put, to separate 1) presentation (UI) 2) user interactions and 3) underlying data and logic/behavior. It might be easy to build a web…

## C# Program to find Age

Below is a C# program to find Age from a Date of Birth. Enjoy! public class Person    {        public string Name { get; set; }        public Person(DateTime birthdate)        {            BirthDate = birthdate;        }        public DateTime BirthDate { get; private set; }        public int Age{                        get {                 var timeSpan = DateTime.Today – BirthDate;                var years = timeSpan.Days / 365;                return years;                                        }        }    }    public class Program    {        public static void Main(string[] argvs)        {            var person = new Person(new DateTime(1998,2,14));                        Console.WriteLine(person.Age);        }    }

## Usage of params modifier in C#

Lets see how to use params modifier in C#. The perfect example is Calculator implementation. ‘params’ access modifier when used on a method argument, allows it to accept multiple argument values. Lets see the simple Calculator implementation below. As you can see, method argument ‘numbers’ is defined as integer array and being called out by…

Constructors need to be overloaded depending on what extend of data/properties need to be initialized in order to set the object to a particular state. Below a good example using a Customer / Orders example. Note that Customer constructor is overloaded in 3 different ways based on what data need to be initialized. Here we…

## Using LINQ in C#

LINQ or Language Integrated Query gives the capability to query objects and C# allows two distinctive ways to achieve this – You can either use LINQ query operators model or LINQ extension methods model with Lamba expressions on Func<> delegate. We have –  LINQ to Objects – Objects in memory eg: Collections ·       LINQ to Entities…

## Using DateTime in C#

Below is very simple usage of DateTime – class DateTimePr     {         static void Main(string[] args)         {             var datetime = new DateTime();             var now = DateTime.Now;             var today = DateTime.Today;             Console.WriteLine(now);             Console.WriteLine(today);             Console.WriteLine(now.Hour);             Console.WriteLine(now.ToLongDateString());             Console.WriteLine(now.ToString());         }     }

## Reading a file in C#

Below is a simple program in C# that reads a file and outputs the longest word in it. Enjoy! using System; using System.IO; using System.Collections.Generic; namespace <yourNS> {     class FilesNDirs     {         public static void Main(string[] argvs)         {             var path = @”C:\Users\deepesh\Desktop\Test\test.txt”;             var textFile = File.ReadAllText(path);             var words = textFile.Split(‘ ‘);             var wordlenpt = new string[100];             var wordlenarr = new List<int>();             foreach (var i in words)             {                 if (i.Length > 0)                 {                     wordlenarr.Add(i.Length);                     wordlenpt[i.Length] = i;                     Console.WriteLine(i);                 }             }             wordlenarr.Sort();             foreach (var i in wordlenarr)             {                 Console.WriteLine(i);             }             Console.WriteLine(“\n\nLargest word in the file is >>” +  wordlenpt[wordlenarr[wordlenarr.Count – 1]]);         }     } }

## Finding Lowest number from a List in C#

Below is a simple program to find the lowest number from a list of numbers – using System; using System.Collections.Generic; namespace GroundCSApp {     class GetSmallest     {         public static void Main(string[] argvs)         {             var numlist = new List<int> { 1, 2, 3, 4, 5, 6 };             var finallst = GetSmallests(numlist, 3);             foreach (var i in finallst)             {                 Console.WriteLine(i);             }         }         public static List<int> GetSmallests(List<int> lst, int cnt)         {             if (cnt > lst.Count)             {                 throw new ArgumentOutOfRangeException(“cnt”, “Count of numbers is  greater than the list count”);             }             var buff = lst;             var smalllst = new List<int>();             while (buff.Count > cnt)             {                 var min = GetiSmallest(buff);                 smalllst.Add(min);                 buff.Remove(min);             }             return smalllst;         }         public static int GetiSmallest(List<int> lsti)         {             var min = lsti[0];             for (var j = 1; j < lsti.Count; j++)             {                 if (lsti[j] < min)                 {…

## Simple C# Programs

Here is some basic, simple, handy C# programs for you to enjoy and refresh your memory – using GroundCSApp; using System; using System.Collections.Generic; using System.Linq; namespace GroundCSApp {     public enum ShippingMethod     {         Regular = 1,         Priority = 2,         Snail = 3     }     class Program     {         static void Main(string[] args)         {             //——————————————————-             //non -primitive/reference type eg: number              //array creation and assignment                          var numbers = new int[3];             numbers[0] = 23;             var numbers2 = numbers;             numbers[0] = 24;             Console.WriteLine(“Value of variable numbers is changed  and it is >>” + numbers[0]);             //——————————————————–             //——————————————————–             //non-primitive, immutable, string array creation assignment             var names = new string[3] { “John”, “Luke”, “Mark” };             //String Join example             var joinedName = string.Join(“,”, names);             Console.WriteLine(“\n\n” + joinedName);             var strArray = new string[] { “Text”, “Book”, “Light” };             var strArray2 = strArray;             //example for reference type where             //original value is modified             strArray2[0] = “Candle”;…

## Code Reuse via Composition in C#

Composition is a common object oriented concept that enables us to implement loose coupling as well as code-reuse. Lot of times we recommend our developers to use more composition and less inheritance due this very fact. Inheritance supports code-reuse, but makes application tightly coupled and creates long inheritance hierarchies that creates inter-dependencies. Inheritance implements a…

## Constructor Inheritance in C#

Like any other Object Oriented Programming language, C# does not allow parent constructor to be automatically inherited. It need to explicitly defined in the derived class. Below is an example to explain this – Below is the parent class – namespace ConstructorInh {     public class Fruit     {         private readonly string _color;         public Fruit(string color)         {             _color = color;             Console.WriteLine(“I am a Fruit with Color {0}”, _color);         }     } } Below is the…

## Dynamic Typing in C#

Well, C# provides this option to prove that it is flexible. If you are too fond of dynamic typing, use scripting languages such as PHP! Below is an example of how to use it – you will see that program will compile without errors and will display two different values for a as intended –…