Part 1 : Metrology and Quality Control

Part 2 : Industrial Engineering

Part 3 : Queuing Theory, Simplex Method, Transportation and Assignment Problems

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# Category: GATE

## GATE (Industrial Engineering Notes)

## GATE (Engineering Mathematics Notes)

## Numerical Solutions to Ordinary Differential Equations

## Taylor’s Series Method

## Euler’s Method and Modified Euler’s Method

## Runge Kutta 2nd Order Method

## Runge Kutta 4th Order Method

## Numerical Solutions to Linear Equations

## Gauss-Seidel Method

## Jacobi’s Iteration Method

## Numerical Integration

## Trapezoidal Rule

## Simpson’s 1/3rd Rule

## Simpson’s 3/8th Rule

## Numerical Solutions of Non-Linear Algebraic Equations

#### Many real world applications involve non-linear equations, such as . In most of the cases, such equations cannot be solved analytically. Numerical methods discussed below come to our rescue. These methods provide an approximate answer to the desired level of accuracy.

## Bisection Method

## Newton-Raphson Method

## Regula Falsi/ False Position/ Modified Secant Method

## Secant Method

## GATE 2017 Engineering Mathematics Solutions

# Chemical Engineering

Linear Algebra

Statistics

Numerical Methods

Calculus

Differential Equations

We will discuss the following methods:

We will discuss 2 methods :

Techniques of numerical integration have been developed because of the following reasons:

- Integration, in general, is a difficult operation.
- We may have experimental data, but we may not know the actual function generating those values.

In this article, we will discuss 3 commonly used numerical integration techniques, the trapezoidal rule, Simpson’s 1/3rd rule and Simpson’s 3/8th rule.

- Uses the single degree curve for integration

This rule is also known as Simpson’s rule.

- Uses a second degree curve for integration.

- It uses a third degree curve for integration